problem solving and creativity thinking are two main forms of

• Business Essentials
• Leadership & Management
• Credential of Leadership, Impact, and Management in Business (CLIMB)
• Entrepreneurship & Innovation
• Digital Transformation
• Finance & Accounting
• Business in Society
• For Organizations
• Support Portal
• Media Coverage
• Founding Donors
• Leadership Team

• Harvard Business School →
• HBS Online →
• Business Insights →

Business Insights

Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.

• Career Development
• Communication
• Decision-Making
• Earning Your MBA
• Negotiation
• News & Events
• Productivity
• Staff Spotlight
• Student Profiles
• Work-Life Balance
• AI Essentials for Business
• Alternative Investments
• Business Analytics
• Business Strategy
• Business and Climate Change
• Design Thinking and Innovation
• Digital Marketing Strategy
• Disruptive Strategy
• Economics for Managers
• Entrepreneurship Essentials
• Financial Accounting
• Global Business
• Launching Tech Ventures
• Leadership Principles
• Leadership, Ethics, and Corporate Accountability
• Leading with Finance
• Management Essentials
• Negotiation Mastery
• Organizational Leadership
• Power and Influence for Positive Impact
• Strategy Execution
• Sustainable Business Strategy
• Sustainable Investing
• Winning with Digital Platforms

What Is Creative Problem-Solving & Why Is It Important?

• 01 Feb 2022

One of the biggest hindrances to innovation is complacency—it can be more comfortable to do what you know than venture into the unknown. Business leaders can overcome this barrier by mobilizing creative team members and providing space to innovate.

There are several tools you can use to encourage creativity in the workplace. Creative problem-solving is one of them, which facilitates the development of innovative solutions to difficult problems.

Here’s an overview of creative problem-solving and why it’s important in business.

Access your free e-book today.

What Is Creative Problem-Solving?

Research is necessary when solving a problem. But there are situations where a problem’s specific cause is difficult to pinpoint. This can occur when there’s not enough time to narrow down the problem’s source or there are differing opinions about its root cause.

In such cases, you can use creative problem-solving , which allows you to explore potential solutions regardless of whether a problem has been defined.

Creative problem-solving is less structured than other innovation processes and encourages exploring open-ended solutions. It also focuses on developing new perspectives and fostering creativity in the workplace . Its benefits include:

• Finding creative solutions to complex problems : User research can insufficiently illustrate a situation’s complexity. While other innovation processes rely on this information, creative problem-solving can yield solutions without it.
• Adapting to change : Business is constantly changing, and business leaders need to adapt. Creative problem-solving helps overcome unforeseen challenges and find solutions to unconventional problems.
• Fueling innovation and growth : In addition to solutions, creative problem-solving can spark innovative ideas that drive company growth. These ideas can lead to new product lines, services, or a modified operations structure that improves efficiency.

Creative problem-solving is traditionally based on the following key principles :

1. Balance Divergent and Convergent Thinking

Creative problem-solving uses two primary tools to find solutions: divergence and convergence. Divergence generates ideas in response to a problem, while convergence narrows them down to a shortlist. It balances these two practices and turns ideas into concrete solutions.

2. Reframe Problems as Questions

By framing problems as questions, you shift from focusing on obstacles to solutions. This provides the freedom to brainstorm potential ideas.

3. Defer Judgment of Ideas

When brainstorming, it can be natural to reject or accept ideas right away. Yet, immediate judgments interfere with the idea generation process. Even ideas that seem implausible can turn into outstanding innovations upon further exploration and development.

4. Focus on "Yes, And" Instead of "No, But"

Using negative words like "no" discourages creative thinking. Instead, use positive language to build and maintain an environment that fosters the development of creative and innovative ideas.

Creative Problem-Solving and Design Thinking

Whereas creative problem-solving facilitates developing innovative ideas through a less structured workflow, design thinking takes a far more organized approach.

Design thinking is a human-centered, solutions-based process that fosters the ideation and development of solutions. In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar leverages a four-phase framework to explain design thinking.

The four stages are:

• Clarify: The clarification stage allows you to empathize with the user and identify problems. Observations and insights are informed by thorough research. Findings are then reframed as problem statements or questions.
• Ideate: Ideation is the process of coming up with innovative ideas. The divergence of ideas involved with creative problem-solving is a major focus.
• Develop: In the development stage, ideas evolve into experiments and tests. Ideas converge and are explored through prototyping and open critique.
• Implement: Implementation involves continuing to test and experiment to refine the solution and encourage its adoption.

Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.

Creative Problem-Solving Tools

While there are many useful tools in the creative problem-solving process, here are three you should know:

Creating a Problem Story

One way to innovate is by creating a story about a problem to understand how it affects users and what solutions best fit their needs. Here are the steps you need to take to use this tool properly.

1. Identify a UDP

Create a problem story to identify the undesired phenomena (UDP). For example, consider a company that produces printers that overheat. In this case, the UDP is "our printers overheat."

2. Move Forward in Time

To move forward in time, ask: “Why is this a problem?” For example, minor damage could be one result of the machines overheating. In more extreme cases, printers may catch fire. Don't be afraid to create multiple problem stories if you think of more than one UDP.

3. Move Backward in Time

To move backward in time, ask: “What caused this UDP?” If you can't identify the root problem, think about what typically causes the UDP to occur. For the overheating printers, overuse could be a cause.

Following the three-step framework above helps illustrate a clear problem story:

• The printer is overused.
• The printer overheats.
• The printer breaks down.

You can extend the problem story in either direction if you think of additional cause-and-effect relationships.

4. Break the Chains

By this point, you’ll have multiple UDP storylines. Take two that are similar and focus on breaking the chains connecting them. This can be accomplished through inversion or neutralization.

• Inversion: Inversion changes the relationship between two UDPs so the cause is the same but the effect is the opposite. For example, if the UDP is "the more X happens, the more likely Y is to happen," inversion changes the equation to "the more X happens, the less likely Y is to happen." Using the printer example, inversion would consider: "What if the more a printer is used, the less likely it’s going to overheat?" Innovation requires an open mind. Just because a solution initially seems unlikely doesn't mean it can't be pursued further or spark additional ideas.
• Neutralization: Neutralization completely eliminates the cause-and-effect relationship between X and Y. This changes the above equation to "the more or less X happens has no effect on Y." In the case of the printers, neutralization would rephrase the relationship to "the more or less a printer is used has no effect on whether it overheats."

Even if creating a problem story doesn't provide a solution, it can offer useful context to users’ problems and additional ideas to be explored. Given that divergence is one of the fundamental practices of creative problem-solving, it’s a good idea to incorporate it into each tool you use.

Brainstorming

Brainstorming is a tool that can be highly effective when guided by the iterative qualities of the design thinking process. It involves openly discussing and debating ideas and topics in a group setting. This facilitates idea generation and exploration as different team members consider the same concept from multiple perspectives.

Hosting brainstorming sessions can result in problems, such as groupthink or social loafing. To combat this, leverage a three-step brainstorming method involving divergence and convergence :

• Have each group member come up with as many ideas as possible and write them down to ensure the brainstorming session is productive.
• Continue the divergence of ideas by collectively sharing and exploring each idea as a group. The goal is to create a setting where new ideas are inspired by open discussion.
• Begin the convergence of ideas by narrowing them down to a few explorable options. There’s no "right number of ideas." Don't be afraid to consider exploring all of them, as long as you have the resources to do so.

Alternate Worlds

The alternate worlds tool is an empathetic approach to creative problem-solving. It encourages you to consider how someone in another world would approach your situation.

For example, if you’re concerned that the printers you produce overheat and catch fire, consider how a different industry would approach the problem. How would an automotive expert solve it? How would a firefighter?

Be creative as you consider and research alternate worlds. The purpose is not to nail down a solution right away but to continue the ideation process through diverging and exploring ideas.

Continue Developing Your Skills

Whether you’re an entrepreneur, marketer, or business leader, learning the ropes of design thinking can be an effective way to build your skills and foster creativity and innovation in any setting.

If you're ready to develop your design thinking and creative problem-solving skills, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses. If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

About the Author

Creative Problem Solving Explained

Creative problem solving is based on the belief that everyone is creative and can enhance their creative abilities with discipline.

Creative problem solving is a deliberate approach to solving complex problems. While creativity is an innate part of creative problem solving, the process uses a variety of steps and strategies designed to bring to the table solutions that are actionable and effective.

It’s a proven approach to use innovative ideas and views of a problem to develop viable options that can be brought to bear on the challenge. It can also redefine the problem, coming at it from a new perspective that results in an effective solution.

It also has powerful applications for addressing your greatest workflow challenges. Using creative problem solving lets you identify, refine, iterate, and select the best options to improve workflows using new technologies like automation.

Fundamentals of Creative Problem Solving

Many people hear “creative problem solving” and think it’s about brainstorming answers. However, creative problem solving is about much more. Creative answers to problems do not just appear magically but are the result of deliberate processes.

To work well, creative problem solving is rooted in two assumptions:

• Everyone is creative in some manner
• You can learn and enhance someone’s creative abilities

Those are powerful assumptions. They help to dispel the idea that there are “creative types” and “noncreative types.” All participants can be empowered to engage in the process by supporting and reinforcing the innate presence of creativity.

Alex Osborn helped define and formalize the idea of creative problem solving. He believed that two types of thinking are critical to creative problem solving.

Convergent Thinking focuses on the norms of problem solving and focuses on finding a singular solution that's well defined. Divergent Thinking is the opposite, with multiple options being considered after fostering creativity as part of the problem solving process.

Both play a role and have value in problem solving. Typically, both are used as part of the process.

For example, divergent thinking can create multiple ideas for possible solutions. Convergent thinking can whittle those down to a few or one idea to implement.

Principles of Creative Problem Solving

Here is a closer look at some key tenets of creative problem solving.

Reframe the Problem as a Question

Begin by restating the problem as a question or series of open-ended questions. The problem becomes more approachable with multiple possibilities available, and participants can be invited into the process.

By contrast, problems presented as declarative statements are often met by silence. These statements often lead to a limited response or no response at all.

There's a shift when asked as a question rather than a statement. The challenge is not an obstacle but rather an opportunity to solve. It opens the door to brainstorming and ideation.

Suspend Judgment

All too often, ideas that are generated in problem solving spaces are quickly dismissed. This instantaneous judgment has short- and long-term impacts.

First, it immediately dismisses the presented idea and the presenter. What’s more, the dismissal can have a chilling effect on others, stymieing the idea generation process.

There’s a time when judging presented ideas – when convergent thinking is at play. In the beginning, immediate judgment should be suspended.

Even the most implausible ideas presented at the beginning of the process may play a role later as long as they are still considered viable. If poisoned early in the process, they will unlikely be given any value later.

‘Yes, And’ Instead of ‘No, But’

The word “no” can have a similarly stifling effect on the creative problem solving work. "But," whether preceded by "yes” or "no," can close the conversation. It acts to negate everything that has come before.

You can create and maintain a more positive, encouraging tone using "yes, and" language instead of "no, but" language.

More positive language helps build on previously generated ideas. It creates an additive approach to the process instead of a dismissive one.

One Approach to Creative Problem Solving

Having a clearly defined approach to solving problems helps participants understand the scope and scale of the work. While multiple approaches can be used, here is one way to frame the engagement.

1. Clarify the Problem

The most critical step to creative problem solving is identifying and articulating the problem or goal. While it may appear to be easy to do so, often, what people think the problem is is not the true problem.

The critical step is to break down the problem, analyze it and understand the core issue.

One approach is to use the "five whys." Start by asking yourself, "Why is this a problem?" Once you have the answer, ask, "Why else?" four more times.

This iterative process can often refine and revise to unearth the true issue that needs to be addressed. You can ask other questions to further refine, such as:

• Why is this problem important to us?
• What is stopping us from solving this problem?
• Where will we be differently 6-12 months after solving the problem?

2. Define Evaluation Criteria

The creative problem solving process is likely to generate many potential ideas. It’s important to establish the process by which the ideas will be evaluated and, if selected, deployed.

These processes may have important factors, such as budget, staffing and time. The process needs to address what you seek to accomplish, avoid and act on. The process should be articulated to the participants in the problem solving and those affected by the outcomes.

3. Research the Problem

You want a clear understanding of the problem, which may require lots or a little research. Understand the common problem, how others may deal with it, and potential solutions.

4. Develop Creative Challenges

Once the problem is articulated and researched, it’s time to frame them. “Creative challenges” are simple and brief, question-based concepts. For example, "How can we …" or “What would it mean if …" These challenges will form the basis of your problem solving. They should be broadly focused and not include any evaluation criteria.

5. Create Ideas

Idea generation is what most people envision when they think of brainstorming or solving problems.

Start by taking just one of the creative challenges. Give yourself or the team some time to build at least 50 ideas. That may seem like a lot, but it can spark conversation and construction.

The ideas may or may not solve the presented challenge. By capturing them on paper or a computer (many programs support idea generation), you can have them readily available to organize, expand on, evaluate, and flesh out.

Be sure to use the following rules in this stage:

• Write down every idea
• Ensure no one critiques presented ideas
• Don’t stop until you’ve reached 50
• Present the full list of ideas and then ask if anyone has anything else to add
• If you have time, sleep on the ideas and return the next day. Try to add 25 more.

6. Sort and Assess Ideas

Take a break and reconvene to look at the ideas using the evaluation criteria. Combine ideas, then use the evaluation criteria to whittle down the list.

Some ideas may be implementable immediately. Others may need further analysis to prioritize.

7. Create a Plan

When you have your shortlist, create an action plan that outlines the steps necessary to implement the ideas. By breaking down the ideas into actionable steps, you’ll be better able to put them into play and see the results.

Problem Solving Your Workflows

When it comes to coming up with creative answers to your workflow problems, we have a variety of resources for you listed below. In addition, we're always interested in providing objective, experienced ideas through our Customer Success and Services teams.

• Reframe Your Business Processes
• Process Redesign Tips
• What is Business Process Re-Engineering?
• Process Improvement Examples
• https://online.hbs.edu/blog/post/what-is-creative-problem-solving
• https://www.mindtools.com/a2j08rt/creative-problem-solving
• https://www.creativeeducationfoundation.org/what-is-cps/
• https://innovationmanagement.se/2010/06/02/the-basics-of-creative-problem-solving-cps/
• https://asana.com/resources/convergent-vs-divergent

Tags creativity   problem solving   process improvement  

Categories Business Ideas   Workflow Ideas   Project Management  

Marketing the world's best workflow automation software and drinking way too much coffee. Connect with me on LinkedIn at  https://www.linkedin.com/in/michaelraia/

Subscribe to Receive the Latest Workflow Automation Tips

Subscribe →

Business Ideas

Customer corner, department focus, employee spotlight, flowchart friday, industry focus, productivity points, productivity tips, project management, using integrify, workflow ideas.

How it works

For Business

Join Mind Tools

Article • 5 min read

Understanding Creativity

Tools and techniques for creative thinking.

By the Mind Tools Content Team

It is important to start with a clear definition of what we mean by creativity, as there are two completely different types. The first is technical creativity , where people create new theories, technologies or ideas. This is the type of creativity we discuss here. The second is artistic creativity , which is more born of skill, technique and self-expression. Artistic creativity is beyond the scope of these articles.

Many of the techniques in this chapter have been used by great thinkers to drive their creativity. Albert Einstein, for example, used his own informal variant of Provocation to trigger ideas that led to the Theory of Relativity. But anyone can learn to be technically creative, and use these tools. They are designed to help you devise creative and imaginative solutions to problems, and help you to spot opportunities that you might otherwise miss.

Approaches to Creativity

There are two main strands to technical creativity: programmed thinking and lateral thinking. Programmed thinking relies on logical or structured ways of creating a new product or service. Examples of this approach are Morphological Analysis and the Reframing Matrix .

The other main strand uses "Lateral Thinking." Examples of this are Brainstorming , Random Input and Provocation. Lateral Thinking has been developed and popularized by Edward de Bono, whose books you can find in the appropriate articles.

Programmed Thinking and Lateral Thinking

Lateral thinking recognizes that our brains are pattern recognition systems, and that they do not function like computers. It takes years of training before we learn to do simple arithmetic – something that computers do very easily. On the other hand, we can instantly recognize patterns such as faces, language, and handwriting. The only computers that begin to be able to do these things do it by modeling the way that human brain cells work. Even then, computers will need to become more powerful before they approach our ability to handle patterns.

The benefit of good pattern recognition is that we can recognize objects and situations very quickly. Imagine how much time would be wasted if you had to do a full analysis every time you came across a cylindrical canister of effervescent fluid. Most people would just open their can of fizzy drink. Without pattern recognition, we would starve or be eaten. We could not cross the road safely.

Unfortunately, we get stuck in our patterns. We tend to think within them. Solutions we develop are based on previous solutions to similar problems. Normally it does not occur to us to use solutions belonging to other patterns.

We use lateral thinking techniques to break out of this patterned way of thinking.

Lateral thinking techniques help us to come up with startling, brilliant and original solutions to problems and opportunities.

It is important to point out that each type of approach has its strength. Logical, disciplined thinking is enormously effective in making products and services better. It can, however, only go so far before all practical improvements have been carried out. Lateral thinking can generate completely new concepts and ideas, and brilliant improvements to existing systems. In the wrong place, however, it can be sterile or unnecessarily disruptive.

Taking the Best of Each

A number of techniques fuse the strengths of the two different strands of creativity. Techniques such as the Concept Fan use a combination of programmed and lateral thinking. DO IT and Min Basadur's Simplex embed the two approaches within problem-solving processes. While these may be considered 'overkill' when dealing with minor problems, they provide excellent frameworks for solving difficult and serious ones.

The Creative Frame of Mind

Often the only difference between creative and uncreative people is self-perception. Creative people see themselves as creative and give themselves the freedom to create. Uncreative people do not think about creativity and do not give themselves the opportunity to create anything new.

Being creative may just be a matter of setting aside the time needed to take a step back and allow yourself to ask yourself if there is a better way of doing something. Edward de Bono calls this a "Creative Pause." He suggests that this should be a short break of maybe only 30 seconds, but that this should be a habitual part of thinking. This needs self-discipline, as it is easy to forget.

Another important attitude shift is to view problems as opportunities for improvement. While this is something of a cliché, it is true. Whenever you solve a problem, you have a better product or service to offer afterward.

Using Creativity

Creativity is sterile if action does not follow from it. Ideas must be evaluated, improved, polished and marketed before they have any value. Other sections of Mind Tools lay out the evaluation, analysis and planning tools needed to do this. They also explain the time and stress management techniques you will need when your creative ideas take off.

You've accessed 1 of your 2 free resources.

Get unlimited access

Discover more content

Starbursting.

Understanding New Ideas by Brainstorming Questions

Kano Model Analysis

Delivering Products That Will Delight

Add comment

Comments (0)

Be the first to comment!

Try Mind Tools for FREE

Get unlimited access to all our career-boosting content and member benefits with our 7-day free trial.

Sign-up to our newsletter

Subscribing to the Mind Tools newsletter will keep you up-to-date with our latest updates and newest resources.

Subscribe now

Business Skills

Personal Development

Leadership and Management

Member Extras

Most Popular

Newest Releases

Team Briefings

Onboarding With STEPS

Mind Tools Store

About Mind Tools Content

Discover something new today

New pain points podcast - perfectionism.

Why Am I Such a Perfectionist?

Pain Points Podcast - Building Trust

Developing and Strengthening Trust at Work

How Emotionally Intelligent Are You?

Boosting Your People Skills

Self-Assessment

What's Your Leadership Style?

Learn About the Strengths and Weaknesses of the Way You Like to Lead

Recommended for you

Influence maps.

Uncovering Where the Power Lies in Your Projects

Business Operations and Process Management

Strategy Tools

Customer Service

Business Ethics and Values

Handling Information and Data

Project Management

Knowledge Management

Self-Development and Goal Setting

Time Management

Presentation Skills

Learning Skills

Career Skills

Communication Skills

Negotiation, Persuasion and Influence

Working With Others

Difficult Conversations

Creativity Tools

Self-Management

Work-Life Balance

Stress Management and Wellbeing

Coaching and Mentoring

Change Management

Team Management

Managing Conflict

Delegation and Empowerment

Performance Management

Leadership Skills

Developing Your Team

Talent Management

Problem Solving

Decision Making

Member Podcast

Module 5: Thinking and Analysis

Solving problems creatively, learning objectives.

• Identify the value of creative thinking in education
• Describe the role of creative thinking skills in problem-solving

Creative Thinking Fiction and Facts

As you continue to develop your creative thinking skills, be alert to perceptions about creative thinking that could slow down progress. Remember that creative thinking and problem-solving are ways to transcend the limitations of a problem and see past barriers. It’s a way to think “outside of the box.”

Problem-Solving with Creative Thinking

Creative problem-solving is a type of problem-solving. It involves searching for new and novel solutions to problems. Unlike critical thinking, which scrutinizes assumptions and uses reasoning, creative thinking is about generating alternative ideas— practices and solutions that are unique and effective. It’s about facing sometimes muddy and unclear problems and seeing how “things” can be done differently—how new solutions can be imagined. [2]

Resources for Creative Thinking

• Creative Thinking Skills
• 45 Websites on Creative Thinking and Creative Skills
• Creativity Techniques A To Z

Contribute!

Improve this page Learn More

• Harris, Robert. "Introduction to Creative Thinking." Virtual Salt . 2 Apr 2012. Web. 16 Feb 2016. ↵
• "Critical and Creative Thinking, MA." University of Massachusetts Boston . 2016. Web. 16 Feb 2016. ↵
• College Success. Authored by : Linda Bruce. Provided by : Lumen Learning. License : CC BY: Attribution

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2023 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

Understanding the Psychology of Creativity

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Michael H / DigitalVision / Getty Images

What Is Creativity?

When does creativity happen, types of creativity, what does it take to be creative, creativity and the big five, how to increase creativity, frequently asked questions.

What is creativity? Creativity involves the ability to develop new ideas or utilize objects or information in novel ways. It can involve large-scale ideas that have the potential to change the world, such as inventing tools that impact how people live, or smaller acts of creation such as figuring out a new way to accomplish a task in your daily life.

This article explores what creativity is and when it is most likely to happen. It also covers some of the steps that you can take to improve your own creativity.

Studying creativity can be a tricky process. Not only is creativity a complex topic in and of itself, but there is also no clear consensus on how exactly to define creativity. Many of the most common definitions suggest that creativity is the tendency to solve problems or create new things in novel ways.

Two of the primary components of creativity include:

• Originality: The idea should be something new that is not simply an extension of something else that already exists.
• Functionality: The idea needs to actually work or possess some degree of usefulness.

In his book Creativity: Flow and the Psychology of Discovery and Invention , psychologist Mihaly Csikszentmihalyi suggested that creativity can often be seen in a few different situations.  

• People who seem stimulating, interesting, and have a variety of unusual thoughts.
• People who perceive the world with a fresh perspective, have insightful ideas and make important personal discoveries. These individuals make creative discoveries that are generally known only to them.
• People who make great creative achievements that become known to the entire world. Inventors and artists such as Thomas Edison and Pablo Picasso would fall into this category.

Experts also tend to distinguish between different types of creativity. The “four c” model of creativity suggests that there are four different types:

• “Mini-c” creativity involves personally meaningful ideas and insights that are known only to the self.
• “ Little-c” creativity involves mostly everyday thinking and problem-solving. This type of creativity helps people solve everyday problems they face and adapt to changing environments.
• “Pro-C” creativity takes place among professionals who are skilled and creative in their respective fields. These individuals are creative in their vocation or profession but do not achieve eminence for their works.
• “Big-C” creativity involves creating works and ideas that are considered great in a particular field. This type of creativity leads to eminence and acclaim and often leads to world-changing creations such as medical innovations, technological advances, and artistic achievements.

Csikszentmihalyi suggests that creative people tend to possess are ​a variety of traits that contribute to their innovative thinking. Some of these key traits include:

• Energy: Creative people tend to possess a great deal of both physical and mental energy. However, they also tend to spend a great deal of time quietly thinking and reflecting.
• Intelligence: Psychologists have long believed that intelligence plays a critical role in creativity. In Terman’s famous longitudinal study of gifted children, researchers found that while high IQ was necessary for great creativity, not all people with high IQs are creative. Csikszentmihalyi believes that creative people must be smart, but they must be capable of looking at things in fresh, even naïve, ways.
• Discipline: Creative people do not just sit around waiting for inspiration to strike. They ​are playful, yet they are also disciplined in the pursuit of their work and passions.

Certain personality traits are also connected to creativity. According to the big five theory of personality , human personality is made up of five broad dimensions:

• Conscientiousness
• Extroversion
• Agreeableness
• Neuroticism

Each dimension represents a continuum, so for each trait, people can be either high, low, or somewhere between the two. 

Openness to experience is a big five trait that is correlated with creativity. People who are high on this trait are more open to new experiences and ideas. They tend to seek novelty and enjoy trying new things, meeting new people, and considering different perspectives. 

However, other personality traits and characteristics can also play a role in creativity. For example, intrinsic motivation , curiosity, and persistence can all determine how much people tend to pursue new ideas and look for novel solutions.

While some people seem to come by creativity naturally, there are things that you can do to increase your own creativity .

Some strategies that can be helpful for improving creativity include: 

• Being open to new ideas : Openness to experience is the personality trait that is most closely correlated with creativity. Focus on being willing to try new things and explore new ideas.
• Be persistent : Creativity is not just about sitting around waiting for inspiration to strike. Creative people spend time working to produce new things. Their efforts don't always work out, but continued practice builds skills that contribute to creativity.
• Make time for creativity : In addition to being persistent, you also need to devote time specifically toward creative efforts. This might mean setting aside a little time each day or each week specifically to brainstorm, practice, learn, or create.

Csikszentmihalyi has noted that creativity requires both a fresh perspective combined with discipline. As Thomas Edison famously suggested, genius is 1% inspiration and 99% perspiration.

A Word From Verywell

Creativity is a complex subject and researchers are still working to understand exactly what factors contribute to the ability to think creatively. While some people seem to come by creativity naturally, there are also things you can do to build and strengthen this ability.

The late Maya Angelou also suggested that thinking creativity helps foster even greater creativity, "The important thing is to use it. You can’t use up creativity. The more you use it, the more you have," she suggested.

Creativity does not reside in one single area of the brain; many areas are actually involved. The frontal cortex of the brain is responsible for many of the functions that play a part in creativity.

However, other parts of the brain impact creativity as well, including the hippocampus (which is important to memory) and the basal ganglia (which is essential in the memory of how to perform tasks). The white matter of the brain, which keeps the various parts of the brain connected, is also essential for creative thinking.

Research suggests that people can train their brains to be more creative. Engaging in cognitively stimulating tasks, going on a walk, finding sources of inspiration, and meditating are a few strategies that may help boost creative thinking abilities. 

The "big five" are the broad categories of traits that make up personality. The five dimensions are openness, conscientiousness, extroversion, agreeableness, and neuroticism. Each trait involves a range between two extremes, and people can be either at each end or somewhere in the middle.

American Psychological Association. The science of creativity .

Csikszentmihalyi M. Creativity: Flow and the Psychology of Discovery and Invention .   New York: HarperCollins; 2013.

Kaufman J, Beghetto R. Beyond big and little: The four C model of creativity .  Review of General Psychology . 2009;13(1):1-12. doi:10.1037/a0013688

Kaufman SB, Quilty LC, Grazioplene RG, et al. Openness to experience and intellect differentially predict creative achievement in the arts and sciences .  J Pers . 2016;84(2):248-258. doi:10.1111/jopy.12156

Elliot J.  Conversations With Maya Angelou . Jackson, Miss.: University Press of Mississippi; 1998.

Cavdarbasha D, Kurczek J. Connecting the dots: your brain and creativity . Front Young Minds . 2017;5:19. doi:10.3389/frym.2017.00019

Sun J, Chen Q, Zhang Q, Li Y, Li H, Wei D, Yang W, Qiu J.  Training your brain to be more creative: brain functional and structural changes induced by divergent thinking training .  Hum Brain Mapp . 2016;37(10):3375-87. doi:10.1002/hbm.23246

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

• Concepts and inferences (7.1)
• Procedural knowledge (7.1)
• Metacognition (7.1)
• Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
• Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
• Fixation:  functional fixedness, mental set  (7.3)
• Algorithms, heuristics, and the role of confirmation bias (7.3)
• Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

• Identify which type of knowledge a piece of information is (7.1)
• Recognize examples of deductive and inductive reasoning (7.2)
• Recognize judgments that have probably been influenced by the availability heuristic (7.2)
• Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

• Use the principles of critical thinking to evaluate information (7.1)
• Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
• Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

• Take a few minutes to write down everything that you know about dogs.
• Do you believe that:
• Psychic ability exists?
• Hypnosis is an altered state of consciousness?
• Magnet therapy is effective for relieving pain?
• Aerobic exercise is an effective treatment for depression?
• UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

• Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
• Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
• Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

• Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

• What percentage of kidnappings are committed by strangers?
• Which area of the house is riskiest: kitchen, bathroom, or stairs?
• What is the most common cancer in the US?
• What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

• Statement #1: The forecaster on Channel 2 said it is going to rain today.
• Statement #2: The forecaster on Channel 5 said it is going to rain today.
• Statement #3: It is very cloudy and humid.
• Statement #4: You just heard thunder.
• Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

• A particular class will be interesting/useful/difficult
• You will be able to finish writing a paper by next week if you go out tonight
• Your laptop’s battery will last through the next trip to the library
• You will not miss anything important if you skip class tomorrow
• Your instructor will not notice if you skip class tomorrow
• You will be able to find a book that you will need for a paper
• There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

• What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

• Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

• Please take a few minutes to list a number of problems that you are facing right now.
• Now write about a problem that you recently solved.
• What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

• Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
• Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
• Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
• Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
• Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
• Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

7.5: What Are Intelligence and Creativity?

• Last updated
• Save as PDF
• Page ID 628

Learning Objectives

• Define intelligence
• Explain the triarchic theory of intelligence
• Identify the difference between intelligence theories
• Explain emotional intelligence

A four-and-a-half-year-old boy sits at the kitchen table with his father, who is reading a new story aloud to him. He turns the page to continue reading, but before he can begin, the boy says, “Wait, Daddy!” He points to the words on the new page and reads aloud, “Go, Pig! Go!” The father stops and looks at his son. “Can you read that?” he asks. “Yes, Daddy!” And he points to the words and reads again, “Go, Pig! Go!”

This father was not actively teaching his son to read, even though the child constantly asked questions about letters, words, and symbols that they saw everywhere: in the car, in the store, on the television. The dad wondered about what else his son might understand and decided to try an experiment. Grabbing a sheet of blank paper, he wrote several simple words in a list: mom, dad, dog, bird, bed, truck, car, tree. He put the list down in front of the boy and asked him to read the words. “Mom, dad, dog, bird, bed, truck, car, tree,” he read, slowing down to carefully pronounce bird and truck. Then, “Did I do it, Daddy?” “You sure did! That is very good.” The father gave his little boy a warm hug and continued reading the story about the pig, all the while wondering if his son’s abilities were an indication of exceptional intelligence or simply a normal pattern of linguistic development. Like the father in this example, psychologists have wondered what constitutes intelligence and how it can be measured.

Classifying Intelligence

What exactly is intelligence? The way that researchers have defined the concept of intelligence has been modified many times since the birth of psychology. British psychologist Charles Spearman believed intelligence consisted of one general factor, called \(g\) , which could be measured and compared among individuals. Spearman focused on the commonalities among various intellectual abilities and demphasized what made each unique. Long before modern psychology developed, however, ancient philosophers, such as Aristotle, held a similar view (Cianciolo & Sternberg, 2004).

Others psychologists believe that instead of a single factor, intelligence is a collection of distinct abilities. In the 1940s, Raymond Cattell proposed a theory of intelligence that divided general intelligence into two components: crystallized intelligence and fluid intelligence (Cattell, 1963). Crystallized intelligence is characterized as acquired knowledge and the ability to retrieve it. When you learn, remember, and recall information, you are using crystallized intelligence. You use crystallized intelligence all the time in your coursework by demonstrating that you have mastered the information covered in the course. Fluid intelligence encompasses the ability to see complex relationships and solve problems. Navigating your way home after being detoured onto an unfamiliar route because of road construction would draw upon your fluid intelligence. Fluid intelligence helps you tackle complex, abstract challenges in your daily life, whereas crystallized intelligence helps you overcome concrete, straightforward problems (Cattell, 1963).

Other theorists and psychologists believe that intelligence should be defined in more practical terms. For example, what types of behaviors help you get ahead in life? Which skills promote success? Think about this for a moment. Being able to recite all \(44\) presidents of the United States in order is an excellent party trick, but will knowing this make you a better person?

Robert Sternberg developed another theory of intelligence, which he titled the triarchic theory of intelligence because it sees intelligence as comprised of three parts (Sternberg, 1988): practical, creative, and analytical intelligence.

Practical intelligence , as proposed by Sternberg, is sometimes compared to “street smarts.” Being practical means you find solutions that work in your everyday life by applying knowledge based on your experiences. This type of intelligence appears to be separate from traditional understanding of IQ; individuals who score high in practical intelligence may or may not have comparable scores in creative and analytical intelligence (Sternberg, 1988).

This story about the 2007 Virginia Tech shootings illustrates both high and low practical intelligences. During the incident, one student left her class to go get a soda in an adjacent building. She planned to return to class, but when she returned to her building after getting her soda, she saw that the door she used to leave was now chained shut from the inside. Instead of thinking about why there was a chain around the door handles, she went to her class’s window and crawled back into the room. She thus potentially exposed herself to the gunman. Thankfully, she was not shot. On the other hand, a pair of students was walking on campus when they heard gunshots nearby. One friend said, “Let’s go check it out and see what is going on.” The other student said, “No way, we need to run away from the gunshots.” They did just that. As a result, both avoided harm. The student who crawled through the window demonstrated some creative intelligence but did not use common sense. She would have low practical intelligence. The student who encouraged his friend to run away from the sound of gunshots would have much higher practical intelligence.

Analytical intelligence is closely aligned with academic problem solving and computations. Sternberg says that analytical intelligence is demonstrated by an ability to analyze, evaluate, judge, compare, and contrast. When reading a classic novel for literature class, for example, it is usually necessary to compare the motives of the main characters of the book or analyze the historical context of the story. In a science course such as anatomy, you must study the processes by which the body uses various minerals in different human systems. In developing an understanding of this topic, you are using analytical intelligence. When solving a challenging math problem, you would apply analytical intelligence to analyze different aspects of the problem and then solve it section by section.

Creative intelligence is marked by inventing or imagining a solution to a problem or situation. Creativity in this realm can include finding a novel solution to an unexpected problem or producing a beautiful work of art or a well-developed short story. Imagine for a moment that you are camping in the woods with some friends and realize that you’ve forgotten your camp coffee pot. The person in your group who figures out a way to successfully brew coffee for everyone would be credited as having higher creative intelligence.

Multiple Intelligences Theory was developed by Howard Gardner, a Harvard psychologist and former student of Erik Erikson. Gardner’s theory, which has been refined for more than \(30\) years, is a more recent development among theories of intelligence. In Gardner’s theory, each person possesses at least eight intelligences. Among these eight intelligences, a person typically excels in some and falters in others (Gardner, 1983). The Table below describes each type of intelligence.

Gardner’s theory is relatively new and needs additional research to better establish empirical support. At the same time, his ideas challenge the traditional idea of intelligence to include a wider variety of abilities, although it has been suggested that Gardner simply relabeled what other theorists called “cognitive styles” as “intelligences” (Morgan, 1996). Furthermore, developing traditional measures of Gardner’s intelligences is extremely difficult (Furnham, 2009; Gardner & Moran, 2006; Klein, 1997).

Gardner’s inter- and intrapersonal intelligences are often combined into a single type: emotional intelligence. Emotional intelligence encompasses the ability to understand the emotions of yourself and others, show empathy, understand social relationships and cues, and regulate your own emotions and respond in culturally appropriate ways (Parker, Saklofske, & Stough, 2009). People with high emotional intelligence typically have well-developed social skills. Some researchers, including Daniel Goleman, the author of Emotional Intelligence: Why It Can Matter More than IQ , argue that emotional intelligence is a better predictor of success than traditional intelligence (Goleman, 1995). However, emotional intelligence has been widely debated, with researchers pointing out inconsistencies in how it is defined and described, as well as questioning results of studies on a subject that is difficulty to measure and study emperically (Locke, 2005; Mayer, Salovey, & Caruso, 2004)

Intelligence can also have different meanings and values in different cultures. If you live on a small island, where most people get their food by fishing from boats, it would be important to know how to fish and how to repair a boat. If you were an exceptional angler, your peers would probably consider you intelligent. If you were also skilled at repairing boats, your intelligence might be known across the whole island. Think about your own family’s culture. What values are important for Latino families? Italian families? In Irish families, hospitality and telling an entertaining story are marks of the culture. If you are a skilled storyteller, other members of Irish culture are likely to consider you intelligent.

Some cultures place a high value on working together as a collective. In these cultures, the importance of the group supersedes the importance of individual achievement. When you visit such a culture, how well you relate to the values of that culture exemplifies your cultural intelligence , sometimes referred to as cultural competence.

Creativity is the ability to generate, create, or discover new ideas, solutions, and possibilities. Very creative people often have intense knowledge about something, work on it for years, look at novel solutions, seek out the advice and help of other experts, and take risks. Although creativity is often associated with the arts, it is actually a vital form of intelligence that drives people in many disciplines to discover something new. Creativity can be found in every area of life, from the way you decorate your residence to a new way of understanding how a cell works.

Creativity is often assessed as a function of one’s ability to engage in divergent thinking . Divergent thinking can be described as thinking “outside the box;” it allows an individual to arrive at unique, multiple solutions to a given problem. In contrast, convergent thinking describes the ability to provide a correct or well-established answer or solution to a problem (Cropley, 2006; Gilford, 1967).

EVERYDAY CONNECTION: Creativity

Dr. Tom Steitz, the Sterling Professor of Biochemistry and Biophysics at Yale University, has spent his career looking at the structure and specific aspects of RNA molecules and how their interactions cold help produce antibiotics and ward off diseases. As a result of his lifetime of work, he won the Nobel Prize in Chemistry in 2009. He wrote, “Looking back over the development and progress of my career in science, I am reminded how vitally important good mentorship is in the early stages of one's career development and constant face-to-face conversations, debate and discussions with colleagues at all stages of research. Outstanding discoveries, insights and developments do not happen in a vacuum” (Steitz, 2010, para. 39). Based on Steitz’s comment, it becomes clear that someone’s creativity, although an individual strength, benefits from interactions with others. Think of a time when your creativity was sparked by a conversation with a friend or classmate. How did that person influence you and what problem did you solve using creativity?

Intelligence is a complex characteristic of cognition. Many theories have been developed to explain what intelligence is and how it works. Sternberg generated his triarchic theory of intelligence, whereas Gardner posits that intelligence is comprised of many factors. Still others focus on the importance of emotional intelligence. Finally, creativity seems to be a facet of intelligence, but it is extremely difficult to measure objectively.

Contributors and Attributions

Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact  [email protected] .Textbook content produced by OpenStax College is licensed under a  Creative Commons Attribution License 4.0  license. Download for free at http://cnx.org/contents/[email protected] .

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Ch 8: Thinking and Language

Thinking and language.

Why is it so difficult to break habits—like reaching for your ringing phone even when you shouldn’t, such as when you’re driving? Why is it hard to pay attention to a conversation when typing out a text message? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these.

As a part of this discussion, we will consider thinking, and briefly explore the development and use of language. We will also discuss problem solving and creativity. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Learning Objectives

• Understand why selective attention is important and how it can be studied.
• Learn about different models of when and how selection can occur.
• Understand how divided attention or multitasking is studied, and implications of multitasking in situations such as distracted driving.

Thinking and Problem-Solving

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

• Distinguish between concepts and prototypes
• Explain the difference between natural and artificial concepts
• Describe problem solving strategies, including algorithms and heuristics
• Explain some common roadblocks to effective problem solving

What is Cognition?

Categories and concepts, concepts and prototypes.

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nerve impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the brain also pulls information from emotions and memories (Figure 9). Emotion and memory are powerful influences on both our thoughts and behaviors.

In order to organize this staggering amount of information, the brain has developed a file cabinet of sorts in the mind. The different files stored in the file cabinet are called concepts. Concepts  are categories or groupings of linguistic information, images, ideas, or memories, such as life experiences. Concepts are, in many ways, big ideas that are generated by observing details, and categorizing and combining these details into cognitive structures. You use concepts to see the relationships among the different elements of your experiences and to keep the information in your mind organized and accessible.

Concepts are informed by our semantic memory (you will learn more about this concept when you study memory) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. In psychology, for example, Piaget’s stages of development are abstract concepts. Some concepts, like tolerance, are agreed upon by many people because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Concepts are at the core of intelligent behavior. We expect people to be able to know what to do in new situations and when confronting new objects. If you go into a new classroom and see chairs, a blackboard, a projector, and a screen, you know what these things are and how they will be used. You’ll sit on one of the chairs and expect the instructor to write on the blackboard or project something onto the screen. You do this even if you have never seen any of these particular objects before , because you have concepts of classrooms, chairs, projectors, and so forth, that tell you what they are and what you’re supposed to do with them. Furthermore, if someone tells you a new fact about the projector—for example, that it has a halogen bulb—you are likely to extend this fact to other projectors you encounter. In short, concepts allow you to extend what you have learned about a limited number of objects to a potentially infinite set of entities.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A prototype  is the best example or representation of a concept. For example, for the category of civil disobedience, your prototype could be Rosa Parks. Her peaceful resistance to segregation on a city bus in Montgomery, Alabama, is a recognizable example of civil disobedience. Or your prototype could be Mohandas Gandhi, sometimes called Mahatma Gandhi (“Mahatma” is an honorific title) (Figure 10).

Mohandas Gandhi served as a nonviolent force for independence for India while simultaneously demanding that Buddhist, Hindu, Muslim, and Christian leaders—both Indian and British—collaborate peacefully. Although he was not always successful in preventing violence around him, his life provides a steadfast example of the civil disobedience prototype (Constitutional Rights Foundation, 2013). Just as concepts can be abstract or concrete, we can make a distinction between concepts that are functions of our direct experience with the world and those that are more artificial in nature.

Link to Learning

Natural and artificial concepts.

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations or experiences of snow (Figure 11).

An artificial concept  on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A schema is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A role schema makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An event schema , also known as a cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator (Figure 12). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) (Figure 13).

Remember the elevator? It feels almost impossible to walk in and not face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that makes refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

Watch this CrashCourse video to see more examples of concepts and prototypes. You’ll also get a preview on other key topics in cognition, including problem-solving strategies like algorithms and heuristics.

You can view the transcript for “Cognition – How Your Mind Can Amaze and Betray You: Crash Course Psychology #15” here (opens in new window) .

Think It Over

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them. For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm  is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic  is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards  is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

What problem-solving method could you use to solve Einstein’s famous riddle?

You can view the transcript for “Can you solve “Einstein’s Riddle”? – Dan Van der Vieren” here (opens in new window) .

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Everyday Connections: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 14) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

Here is another popular type of puzzle that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Take a look at the “Puzzling Scales” logic puzzle below (Figure 16). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

Were you able to determine how many marbles are needed to balance the scales in the Puzzling Scales? You need nine. Were you able to solve the other problems above? Here are the answers:

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set  is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now. Functional fixedness   is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias  occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. This bias proves that first impressions do matter and that we tend to look for information to confirm our initial judgments of others.

Watch this video from the Big Think to learn more about the confirmation bias.

You can view the transcript for “Confirmation Bias: Your Brain is So Judgmental” here (opens in new window) .

Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias  describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . To use a common example, would you guess there are more murders or more suicides in America each year? When asked, most people would guess there are more murders. In truth, there are twice as many suicides as there are murders each year. However, murders seem more common because we hear a lot more about murders on an average day. Unless someone we know or someone famous takes their own life, it does not make the news. Murders, on the other hand, we see in the news every day. This leads to the erroneous assumption that the easier it is to think of instances of something, the more often that thing occurs.

Watch the following video for an example of the availability heuristic.

You can view the transcript for “Availability Heuristic: Are Planes More Dangerous Than Cars?” here (opens in new window) .

Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in Table 2 below.

Learn more about heuristics and common biases through the article, “ 8 Common Thinking Mistakes Our Brains Make Every Day and How to Prevent Them ” by Belle Beth Cooper.

You can also watch this clever music video explaining these and other cognitive biases.

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

• Understand how the use of language develops
• Explain the relationship between language and thinking

Language Development

Language is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language , be it spoken, signed, or written, has specific components: a lexicon and grammar. Lexicon refers to the words of a given language. Thus, lexicon is a language’s vocabulary. Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. Phonemes are combined to form morphemes , which are the smallest units of language that convey some type of meaning (e.g., “I” is both a phoneme and a morpheme).  Further, a morpheme is not the same as a word. The main difference is that a morpheme sometimes does not stand alone, but a word, by definition, always stands alone.

We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar. Semantics refers to the process by which we derive meaning from morphemes and words. Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011).

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. The flexibility that language provides to relay vastly different types of information is a property that makes language so distinct as a mode of communication among humans.

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F. Skinner (1957) proposed that language is learned through reinforcement. Noam Chomsky (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age (Table 1). In fact, it appears that this is occurring even before we are born. Newborns show preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

Dig Deeper: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thinking

Think about it:  the meaning of language.

Think about what you know of other languages; perhaps you even speak multiple languages. Imagine for a moment that your closest friend fluently speaks more than one language. Do you think that friend thinks differently, depending on which language is being spoken? You may know a few words that are not translatable from their original language into English. For example, the Portuguese word saudade originated during the 15th century, when Portuguese sailors left home to explore the seas and travel to Africa or Asia. Those left behind described the emptiness and fondness they felt as saudade (Figure 20) . The word came to express many meanings, including loss, nostalgia, yearning, warm memories, and hope. There is no single word in English that includes all of those emotions in a single description. Do words such as saudade indicate that different languages produce different patterns of thought in people? What do you think??

Language may indeed influence the way that we think, an idea known as linguistic determinism. One recent demonstration of this phenomenon involved differences in the way that English and Mandarin Chinese speakers talk and think about time. English speakers tend to talk about time using terms that describe changes along a horizontal dimension, for example, saying something like “I’m running behind schedule” or “Don’t get ahead of yourself.” While Mandarin Chinese speakers also describe time in horizontal terms, it is not uncommon to also use terms associated with a vertical arrangement. For example, the past might be described as being “up” and the future as being “down.” It turns out that these differences in language translate into differences in performance on cognitive tests designed to measure how quickly an individual can recognize temporal relationships. Specifically, when given a series of tasks with vertical priming, Mandarin Chinese speakers were faster at recognizing temporal relationships between months. Indeed, Boroditsky (2001) sees these results as suggesting that “habits in language encourage habits in thought” (p. 12).

Language does not completely determine our thoughts—our thoughts are far too flexible for that—but habitual uses of language can influence our habit of thought and action. For instance, some linguistic practice seems to be associated even with cultural values and social institution. Pronoun drop is the case in point. Pronouns such as “I” and “you” are used to represent the speaker and listener of a speech in English. In an English sentence, these pronouns cannot be dropped if they are used as the subject of a sentence. So, for instance, “I went to the movie last night” is fine, but “Went to the movie last night” is not in standard English. However, in other languages such as Japanese, pronouns can be, and in fact often are, dropped from sentences. It turned out that people living in those countries where pronoun drop languages are spoken tend to have more collectivistic values (e.g., employees having greater loyalty toward their employers) than those who use non–pronoun drop languages such as English (Kashima & Kashima, 1998). It was argued that the explicit reference to “you” and “I” may remind speakers the distinction between the self and other, and the differentiation between individuals. Such a linguistic practice may act as a constant reminder of the cultural value, which, in turn, may encourage people to perform the linguistic practice.

One group of researchers who wanted to investigate how language influences thought compared how English speakers and the Dani people of Papua New Guinea think and speak about color. The Dani have two words for color: one word for light and one word for dark . In contrast, the English language has 11 color words. Researchers hypothesized that the number of color terms could limit the ways that the Dani people conceptualized color. However, the Dani were able to distinguish colors with the same ability as English speakers, despite having fewer words at their disposal (Berlin & Kay, 1969). A recent review of research aimed at determining how language might affect something like color perception suggests that language can influence perceptual phenomena, especially in the left hemisphere of the brain. You may recall from earlier chapters that the left hemisphere is associated with language for most people. However, the right (less linguistic hemisphere) of the brain is less affected by linguistic influences on perception (Regier & Kay, 2009)

Learn more about language, language acquisition, and especially the connection between language and thought in the following CrashCourse video:

You can view the transcript for “Language: Crash Course Psychology #16” here (opens in new window) .

In this chapter, you learned to

• describe attention
• describe cognition and problem-solving strategies
• describe language acquisition and the role language plays in communication and thought

You learned about non-memory cognitive processes in this chapter. Because each of you reading this is using language in some shape or form, we will end with a quick summary and a video on this topic. Language is a communication system that has both a lexicon and a system of grammar. Language acquisition occurs naturally and effortlessly during the early stages of life, and this acquisition occurs in a predictable sequence for individuals around the world. Language has a strong influence on thought, and the concept of how language may influence cognition remains an area of study and debate in psychology.

In this TED talk, Lera Boroditsky summarizes unique ways that language and culture intersect with some basic cognitive processes. How was your language shaped your thinking?

Abler, W. (2013). Sapir, Harris, and Chomsky in the twentieth century. Cognitive Critique, 7, 29–48.

Aronson, E. (Ed.). (1995). Social cognition. In The social animal (p. 151). New York: W.H. Freeman and Company.

Bartlett, F. C. (1932). Remembering: A study in experimental and social psychology. Cambridge, England: Cambridge University Press.

Bayer, J. B., & Campbell, S. W. (2012). Texting while driving on automatic: Considering the frequency-independent side of habit. Computers in Human Behavior, 28, 2083–2090.

Beilock, S. L., & Carr, T. H. (2001). On the fragility of skilled performance: What governs choking under pressure?  Journal of Experimental Psychology: General, 130 , 701–725.

Berlin, B., & Kay, P. (1969). Basic color terms: Their universality and evolution. Berkley: University of California Press.

Blossom, M., & Morgan, J. L. (2006). Does the face say what the mouth says? A study of infants’ sensitivity to visual prosody. In the 30th annual Boston University Conference on Language Development, Somerville, MA.

Boroditsky, L. (2001). Does language shape thought? Mandarin and English speakers’ conceptions of time. Cognitive Psychology, 43, 1–22.

Boroditsky, L. (2011, February). How language shapes thought. Scientific American, 63–65.Chomsky, N. (1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press

Broadbent, D. A. (1958).  Perception and communication . London, England: Pergamon Press.

Cairns Regional Council. (n.d.). Cultural greetings. Retrieved from http://www.cairns.qld.gov.au/__data/assets/pdf_file/0007/8953/CulturalGreetingExercise.pdf

Callero, P. L. (1994). From role-playing to role-using: Understanding role as resource. Social Psychology Quarterly, 57, 228–243.

Cherry, E. C. (1953). Experiments on the recognition of speech with one and two ears.  Journal of the Acoustical Society of America, 25 , 975–979.

Chomsky, N.(1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press

Corballis, M. C., & Suddendorf, T. (2007). Memory, time, and language. In C. Pasternak (Ed.), What makes us human (pp. 17–36). Oxford, UK: Oneworld Publications.

Curtiss, S. (1981). Dissociations between language and cognition: Cases and implications. Journal of Autism and Developmental Disorders, 11(1), 15–30.

Cyclopedia of Puzzles. (n.d.) Retrieved from http://www.mathpuzzle.com/loyd/

Deutsch, J. A., & Deutsch, D. (1963). Attention: some theoretical considerations.  Psychological Review, 70 , 80–90.

Fernández, E. M., & Cairns, H. S. (2011). Fundamentals of psycholinguistics. West Sussex, UK: Wiley-Blackwell.

Fromkin, V., Krashen, S., Curtiss, S., Rigler, D., & Rigler, M. (1974). The development of language in Genie: A case of language acquisition beyond the critical period. Brain and Language, 1, 81–107.

German, T. P., & Barrett, H. C. (2005). Functional fixedness in a technologically sparse culture. Psychological Science, 16, 1–5.

Goldstone, R. L., & Kersten, A. (2003). Concepts and categorization. In A. F. Healy, R. W. Proctor, & I.B. Weiner (Eds.), Handbook of psychology (Volume IV, pp. 599–622). Hoboken, New Jersey: John Wiley & Sons, Inc.

Hirst, W. C., Neisser, U., & Spelke, E. S. (1978). Divided attention.  Human Nature, 1 , 54–61.

James, W. (1983).  The principles of psychology . Cambridge, MA: Harvard University Press. (Original work published 1890)

Jensen, J. (2011). Phoneme acquisition: Infants and second language learners. The Language Teacher, 35(6), 24–28.

Johnson, J. S., & Newport, E. L. (1989). Critical period effects in second language learning: The influence of maturational state on the acquisition of English as a second language. Cognitive Psychology, 21, 60–99.

Johnston, W. A., & Heinz, S. P. (1978). Flexibility and capacity demands of attention.  Journal of Experimental Psychology: General, 107 , 420–435.

Kahneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus, and Giroux.

Lenneberg, E. (1967). Biological foundations of language. New York: Wiley.

Monsell, S. (2003). Task switching.  Trends in Cognitive Science, 7 (3), 134–140.

Moray, N. (1959). Attention in dichotic listening: Affective cues and the influence of instructions.  Quarterly Journal of Experimental Psychology, 11 , 56–60.

Moskowitz, B. A. (1978). The acquisition of language. Scientific American, 239, 92–108. Petitto, L. A., Holowka, S., Sergio, L. E., Levy, B., & Ostry, D. J. (2004). Baby hands that move to the rhythm of language: Hearing babies acquiring sign languages babble silently on the hands. Cognition, 93, 43–73.

Neyfakh, L. (2013, October 7). “Why you can’t stop checking your phone.” Retrieved from http://www.bostonglobe.com/ideas/2013/10/06/why-you-can-stop-checking-your-phone/rrBJzyBGDAr1YlEH5JQDcM/story.html

Petitto, L. A., Holowka, S., Sergio, L. E., Levy, B., & Ostry, D. J. (2004). Baby hands that move to the rhythm of language: Hearing babies acquiring sign languages babble silently on the hands. Cognition, 93, 43–73.

Pickens, J. (1994). Full-term and preterm infants’ perception of face-voice synchrony. Infant Behavior and Development, 17, 447–455.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Regier, T., & Kay, P. (2009). Language, thought, and color: Whorf was half right. Trends in Cognitive Sciences, 13(10), 439–446.

Rymer, R. (1993). Genie: A Scientific Tragedy. New York: Harper Collins.

Sapir, E. (1964). Culture, language, and personality. Berkley: University of California Press. (Original work published 1941)

Simons, D. J., & Chabris, C. F. (1999). Gorillas in our midst: Sustained inattentional blindness for dynamic events.  Perception, 28 , 1059–1074.

Skinner, B. F. (1957). Verbal behavior. Acton, MA: Copley Publishing Group.

Spelke, E. S., & Cortelyou, A. (1981). Perceptual aspects of social knowing: Looking and listening in infancy. In M.E. Lamb & L.R. Sherrod (Eds.), Infant social cognition: Empirical and theoretical considerations (pp. 61–83). Hillsdale, NJ: Erlbaum.

Spelke, E. S., Hirst, W. C., & Neisser, U. (1976). Skills of divided attention.  Cognition, 4 , 215–250.

Strayer, D. L., & Drews, F. A. (2007). Cell-phone induced inattention blindness.  Current Directions in Psychological Science, 16 , 128–131.

Strayer, D. L., & Johnston, W. A. (2001). Driven to distraction: Dual-task studies of simulated driving and conversing on a cellular telephone.  Psychological Science, 12 , 462–466.

Strayer, D. L., Watson, J. M., & Drews, F. A. (2011) Cognitive distraction while multitasking in the automobile. In Brian Ross (Ed.),  The Psychology of Learning and Motivation  (Vol. 54, pp. 29–58). Burlington, VT: Academic Press.

Tomasello, M., & Rakoczy, H. (2003). What makes human cognition unique? From individual to shared to collective intentionality. Mind & Language, 18(2), 121–147.

Treisman, A. (1960). Contextual cues in selective listening.  Quarterly Journal of Experimental Psychology, 12 , 242–248.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131.

van Troyer, G. (1994). Linguistic determinism and mutability: The Sapir-Whorf “hypothesis” and intercultural communication. JALT Journal, 2, 163–178.

Watson, J. M., & Strayer, D. L. (2010). Supertaskers: Profiles in extraordinary multitasking ability.  Psychonomic Bulletin & Review, 17 , 479–485.

Werker, J. F., & Lalonde, C. E. (1988). Cross-language speech perception: Initial capabilities and developmental change. Developmental Psychology, 24, 672–683.

Werker, J. F., & Tees, R. C. (1984). Cross-language speech perception: Evidence for perceptual reorganization during the first year of life. Infant Behavior and Development, 7, 49–63.

Whorf, B. L. (1956). Language, thought and relativity. Cambridge, MA: MIT Press.

CC original content.

Attention, Thinking and Language.  Authored by:  Karenna Malavanti Provided by: PressBooks. License: CC BY-SA: Attribution-ShareAlike

CC licensed content, Shared previously

• Why It Matters: Thinking and Intelligence.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/introduction-10/
• Attention. Authored by: Frances Friedrich. Located at NOBA Psychology. License: CC-BY-NC-SA. Retrieved from: Retrieved from  http://noba.to/uv9x8df5
• Introduction to Thinking and Intelligence. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-introduction .
• What Is Cognition?. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-1-what-is-cognition .
• A Thinking Man Image. Authored by : Wesley Nitsckie. License : CC BY-SA: Attribution-ShareAlike   Located at : https://www.flickr.com/photos/nitsckie/5507777269 .
• What Is Cognition?.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/what-is-cognition/
• Categories and Concepts. Authored by : Gregory Murphy. Provided by : New York University. Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike   Located at : http://nobaproject.com/textbooks/wendy-king-introduction-to-psychology-the-full-noba-collection/modules/categories-and-concepts .
• Solving Problems.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at : https://pressbooks.online.ucf.edu/lumenpsychology/chapter/problem-solving/
• Problem-Solving. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction . Located at : https://openstax.org/books/psychology-2e/pages/7-3-problem-solving .
• Pitfalls to Problem Solving.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/reading-pitfalls-to-problem/
• Introduction to Language.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/outcome-language/
• Language. Authored by : OpenStax College.  License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction   Located at : https://openstax.org/books/psychology-2e/pages/7-2-language .
• Language. Authored by : geralt. Provided by : Pixabay. License : CC0: No Rights Reserved   Located at : https://pixabay.com/en/school-board-languages-blackboard-1063556/ .
• Language and Language Use.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/language-and-language-use/
• Language and Language Use. Authored by : Yoshihisa Kashima. Project : The Noba Project. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike   Located at : http://nobaproject.com/textbooks/introduction-to-psychology-the-full-noba-collection/modules/language-and-language-use .
• Language Development.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/language/
• Morpheme. Provided by : Wikipedia. License : CC BY-SA: Attribution-ShareAlike   Located at : https://en.wikipedia.org/wiki/Morpheme .
• Language and Thinking.  Authored by : Lumen Learning License :  CC BY: Attribution   Located at :  https://pressbooks.online.ucf.edu/lumenpsychology/chapter/reading-language-and-thought/
• Summary. Authored by : OpenStax College. License : CC BY: Attribution . License Terms : Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction . Located at : https://openstax.org/books/psychology-2e/pages/7-summary .

All rights reserved content

• Cognition: How Your Mind Can Amaze and Betray You – Crash Course Psychology #15. Provided by : CrashCourse. License : All Rights Reserved . License Terms : Standard YouTube License   Located at : https://www.youtube.com/watch?v=R-sVnmmw6WY&feature=youtu.be&list=PL8dPuuaLjXtOPRKzVLY0jJY-uHOH9KVU6 .
• Can you solve Einsteinu2019s Riddle? . Authored by : Dan Van der Vieren. Provided by : Ted-Ed. License : Other . License Terms : Standard YouTube License .  Located at : https://www.youtube.com/watch?v=1rDVz_Fb6HQ&index=3&list=PLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a .
• Language: Crash Course Psychology #16. Authored by : CrashCourse. License : Other . License Terms : Standard YouTube License .  Located at : https://www.youtube.com/watch?v=s9shPouRWCs&feature=youtu.be&list=PL8dPuuaLjXtOPRKzVLY0jJY-uHOH9KVU6 .
• How language shapes the way we think Authored by: Lera Boroditsky.  Provided by :  TED.  License : Other . License Terms : Standard YouTube License .  Located at :  https://youtu.be/RKK7wGAYP6k

thinking, including perception, learning, problem solving, judgment, and memory

field of psychology dedicated to studying every aspect of how people think

a set of objects that can be treated as equivalent in some way

category or grouping of linguistic information, objects, ideas, or life experiences

best representation of a concept

mental groupings that are created “naturally” through your experiences

concept that is defined by a very specific set of characteristics

(plural = schemata) mental construct consisting of a cluster or collection of related concepts

set of expectations that define the behaviors of a person occupying a particular role

set of behaviors that are performed the same way each time; also referred to as a cognitive script

set of behaviors that are performed the same way each time; also referred to as an event schema

method for solving problems

problem-solving strategy in which multiple solutions are attempted until the correct one is found

problem-solving strategy characterized by a specific set of instructions

mental shortcut that saves time when solving a problem

heuristic in which you begin to solve a problem by focusing on the end result

continually using an old solution to a problem without results

inability to see an object as useful for any other use other than the one for which it was intended

faulty heuristic in which you fixate on a single aspect of a problem to find a solution

belief that the event just experienced was predictable, even though it really wasn’t

subset of the population that accurately represents the general population

faulty heuristic in which you make a decision based on information readily available to you

communication system that involves using words to transmit information from one individual to another

Words and expressions.

set of rules that are used to convey meaning through the use of a lexicon

basic sound unit of a given language

smallest unit of language that conveys some type of meaning

process by which we derive meaning from morphemes and words

manner by which words are organized into sentences

extension of a rule that exists in a given language to an exception to the rule

Psychological Science: Understanding Human Behavior Copyright © by Karenna Malavanti is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

7.4 What Are Intelligence and Creativity?

Learning objectives.

By the end of this section, you will be able to:

• Define intelligence
• Explain the triarchic theory of intelligence
• Identify the difference between intelligence theories
• Explain emotional intelligence
• Define creativity

A four-and-a-half-year-old boy sits at the kitchen table with his father, who is reading a new story aloud to him. He turns the page to continue reading, but before he can begin, the boy says, “Wait, Daddy!” He points to the words on the new page and reads aloud, “Go, Pig! Go!” The father stops and looks at his son. “Can you read that?” he asks. “Yes, Daddy!” And he points to the words and reads again, “Go, Pig! Go!”

This father was not actively teaching his son to read, even though the child constantly asked questions about letters, words, and symbols that they saw everywhere: in the car, in the store, on the television. The dad wondered about what else his son might understand and decided to try an experiment. Grabbing a sheet of blank paper, he wrote several simple words in a list: mom, dad, dog, bird, bed, truck, car, tree. He put the list down in front of the boy and asked him to read the words. “Dad, dog, bird, bed, truck, car, tree,” he read, slowing down to carefully pronounce bird and truck. Then, “Did I do it, Daddy?” “You sure did! That is very good.” The father gave his little boy a warm hug and continued reading the story about the pig, all the while wondering if his son’s abilities were an indication of exceptional intelligence or simply a normal pattern of linguistic development. Like the father in this example, psychologists have wondered what constitutes intelligence and how it can be measured.

Classifying Intelligence

What exactly is intelligence? The way that researchers have defined the concept of intelligence has been modified many times since the birth of psychology. British psychologist Charles Spearman believed intelligence consisted of one general factor, called g , which could be measured and compared among individuals. Spearman focused on the commonalities among various intellectual abilities and de-emphasized what made each unique. Long before modern psychology developed, however, ancient philosophers, such as Aristotle, held a similar view (Cianciolo & Sternberg, 2004).

Other psychologists believe that instead of a single factor, intelligence is a collection of distinct abilities. In the 1940s, Raymond Cattell proposed a theory of intelligence that divided general intelligence into two components: crystallized intelligence and fluid intelligence (Cattell, 1963). Crystallized intelligence is characterized as acquired knowledge and the ability to retrieve it. When you learn, remember, and recall information, you are using crystallized intelligence. You use crystallized intelligence all the time in your coursework by demonstrating that you have mastered the information covered in the course. Fluid intelligence encompasses the ability to see complex relationships and solve problems. Navigating your way home after being detoured onto an unfamiliar route because of road construction would draw upon your fluid intelligence. Fluid intelligence helps you tackle complex, abstract challenges in your daily life, whereas crystallized intelligence helps you overcome concrete, straightforward problems (Cattell, 1963).

Other theorists and psychologists believe that intelligence should be defined in more practical terms. For example, what types of behaviors help you get ahead in life? Which skills promote success? Think about this for a moment. Being able to recite all of the presidents of the United States in order is an excellent party trick, but will knowing this make you a better person?

Robert Sternberg developed another theory of intelligence, which he titled the triarchic theory of intelligence because it sees intelligence as comprised of three parts (Sternberg, 1988): practical, creative, and analytical intelligence ( Figure 7.12 ).

Practical intelligence , as proposed by Sternberg, is sometimes compared to “street smarts.” Being practical means you find solutions that work in your everyday life by applying knowledge based on your experiences. This type of intelligence appears to be separate from traditional understanding of IQ; individuals who score high in practical intelligence may or may not have comparable scores in creative and analytical intelligence (Sternberg, 1988).

Analytical intelligence is closely aligned with academic problem solving and computations. Sternberg says that analytical intelligence is demonstrated by an ability to analyze, evaluate, judge, compare, and contrast. When reading a classic novel for literature class, for example, it is usually necessary to compare the motives of the main characters of the book or analyze the historical context of the story. In a science course such as anatomy, you must study the processes by which the body uses various minerals in different human systems. In developing an understanding of this topic, you are using analytical intelligence. When solving a challenging math problem, you would apply analytical intelligence to analyze different aspects of the problem and then solve it section by section.

Creative intelligence is marked by inventing or imagining a solution to a problem or situation. Creativity in this realm can include finding a novel solution to an unexpected problem or producing a beautiful work of art or a well-developed short story. Imagine for a moment that you are camping in the woods with some friends and realize that you’ve forgotten your camp coffee pot. The person in your group who figures out a way to successfully brew coffee for everyone would be credited as having higher creative intelligence.

Multiple Intelligences Theory was developed by Howard Gardner, a Harvard psychologist and former student of Erik Erikson. In Gardner’s theory, each person possesses at least eight intelligences. The eight intelligences are linguistic intelligence, logical-mathematical intelligence, musical intelligence, bodily kinesthetic intelligence, spatial intelligence, interpersonal intelligence, intrapersonal intelligence, and naturalistic intelligence. Among cognitive psychologists, Gardner’s theory has been heavily criticized for lacking empirical evidence. However, educators continue to study and use Gardner’s theory, with some colleges even discussing how they integrate Gardner’s theory into their classrooms. Gottfredson describes one possible reason for the continued use of Gardner’s theory: “ . . . that there are multiple independent intelligences, suggesting that everyone can be smart in some way. This is, understandably, a very attractive idea in democratic societies” (2004).

Gardner’s inter- and intrapersonal intelligences are often combined into a single type: emotional intelligence. Emotional intelligence encompasses the ability to understand the emotions of yourself and others, show empathy, understand social relationships and cues, and regulate your own emotions and respond in culturally appropriate ways (Parker, Saklofske, & Stough, 2009). People with high emotional intelligence typically have well-developed social skills. Some researchers, including Daniel Goleman, the author of Emotional Intelligence: Why It Can Matter More than IQ , argue that emotional intelligence is a better predictor of success than traditional intelligence (Goleman, 1995). However, emotional intelligence has been widely debated, with researchers pointing out inconsistencies in how it is defined and described, as well as questioning results of studies on a subject that is difficult to measure and study empirically (Locke, 2005; Mayer, Salovey, & Caruso, 2004).

The most comprehensive theory of intelligence to date is the Cattell-Horn-Carroll (CHC) theory of cognitive abilities (Schneider & McGrew, 2018). In this theory, abilities are related and arranged in a hierarchy with general abilities at the top, broad abilities in the middle, and narrow (specific) abilities at the bottom. The narrow abilities are the only ones that can be directly measured; however, they are integrated within the other abilities. At the general level is general intelligence. Next, the broad level consists of general abilities such as fluid reasoning, short-term memory, and processing speed. Finally, as the hierarchy continues, the narrow level includes specific forms of cognitive abilities. For example, short-term memory would further break down into memory span and working memory capacity.

Intelligence can also have different meanings and values in different cultures. If you live on a small island, where most people get their food by fishing from boats, it would be important to know how to fish and how to repair a boat. If you were an exceptional angler, your peers would probably consider you intelligent. If you were also skilled at repairing boats, your intelligence might be known across the whole island. Think about your own family’s culture. What values are important for Latinx families? Italian families? In Irish families, hospitality and telling an entertaining story are marks of the culture. If you are a skilled storyteller, other members of Irish culture are likely to consider you intelligent.

Some cultures place a high value on working together as a collective. In these cultures, the importance of the group supersedes the importance of individual achievement. When you visit such a culture, how well you relate to the values of that culture exemplifies your cultural intelligence , sometimes referred to as cultural competence.

Link to Learning

Watch this video that compares different theories of intelligence to learn more.

Creativity is the ability to generate, create, or discover new ideas, solutions, and possibilities. Very creative people often have intense knowledge about something, work on it for years, look at novel solutions, seek out the advice and help of other experts, and take risks. Although creativity is often associated with the arts, it is actually a vital form of intelligence that drives people in many disciplines to discover something new. Creativity can be found in every area of life, from the way you decorate your residence to a new way of understanding how a cell works.

Creativity is often connected to a person’s ability to engage in divergent thinking . Divergent thinking can be described as thinking “outside the box;” it allows an individual to arrive at unique, multiple solutions to a given problem. In contrast, convergent thinking describes the ability to provide a correct or well-established answer or solution to a problem (Cropley, 2006; Gilford, 1967)

Everyday Connection

Dr. Tom Steitz, former Sterling Professor of Biochemistry and Biophysics at Yale University, spent his career looking at the structure and specific aspects of RNA molecules and how their interactions could help produce antibiotics and ward off diseases. As a result of his lifetime of work, he won the Nobel Prize in Chemistry in 2009. He wrote, “Looking back over the development and progress of my career in science, I am reminded how vitally important good mentorship is in the early stages of one's career development and constant face-to-face conversations, debate and discussions with colleagues at all stages of research. Outstanding discoveries, insights and developments do not happen in a vacuum” (Steitz, 2010, para. 39). Based on Steitz’s comment, it becomes clear that someone’s creativity, although an individual strength, benefits from interactions with others. Think of a time when your creativity was sparked by a conversation with a friend or classmate. How did that person influence you and what problem did you solve using creativity?

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction

• Authors: Rose M. Spielman, William J. Jenkins, Marilyn D. Lovett
• Publisher/website: OpenStax
• Book title: Psychology 2e
• Publication date: Apr 22, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/psychology-2e/pages/1-introduction
• Section URL: https://openstax.org/books/psychology-2e/pages/7-4-what-are-intelligence-and-creativity

© Jan 6, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Creativity in problem solving: integrating two different views of insight

• Original Paper
• Open access
• Published: 02 September 2021
• Volume 54 , pages 83–96, ( 2022 )

Cite this article

You have full access to this open access article

• Per Øystein Haavold   ORCID: orcid.org/0000-0002-6786-9400 1 &
• Bharath Sriraman 2  

9664 Accesses

6 Citations

2 Altmetric

Explore all metrics

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking and a sequence of conscious and stepwise steps. The second view suggests that insight is the result of unconscious processes that come about only after an impasse has occurred. Extant models of problem solving within mathematics education tend to highlight the first view of insight, while Gestalt inspired creativity research tends to emphasize the second view of insight. In this study, we explore how the two views of insight—and the corresponding set of models—can describe and explain different aspects of the problem solving process. Our aim is to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important, aspects of the problem solving process. We pursue this aim by studying how expert and novice mathematics students worked on two ill-defined mathematical problems. We apply both a problem solving model and a creativity model in analyzing students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. The results of this study indicate that sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by problem solving models and analytic views of insight. We therefore propose that extant problem solving models should adopt aspects of the Gestalt inspired views of insight.

Similar content being viewed by others

Linking Mathematical Creativity to Problem Solving: Views from the Field

Creativity and Challenge: Task Complexity as a Function of Insight and Multiplicity of Solutions

Creativity and Problem-Based Learning (PBL): A Neglected Relation

Avoid common mistakes on your manuscript.

1 Introduction

Most mathematics educators would probably agree that the development of students’ problem solving abilities is an important objective of instruction. Thus there has been a considerable amount of research on problem solving in the last several decades (Lester, 2013 ). In general, researchers into problem solving have usually defined the term problem as tasks or questions that an individual or group of individuals do not immediately know how to answer (Lester, 2013 ). However, this definition says very little about how to teach individuals to become better problem solvers (Lester, 2013 ). Several models of problem solving have therefore been developed to describe and explain factors and processes involved in problem solving—most of which have drawn heavily on Pólya’s ( 1949 ) famous four-stage model of problem solving. Nevertheless, problem solving instruction is still considered ineffective. There are many reasons for this perception, but one key issue is the lack of concern for the complexity and the many factors involved in problem solving processes (Lester, 2013 ).

The focus of this paper is one of the more subtle yet essential factors involved in problem solving. Ever since the Gestaltists first began studying problem solving nearly 100 years ago, insight in problem solving has been of interest to psychologists (Hadamard, 1945 ; Ohlsson, 2011 ; Poincaré, 1948 ; Weisberg, 2015 ). Here, it is important to note that insight ( Einsicht ) within the Gestalt approach, and much of the literature on insight and problem solving, have a broader meaning than the standard definition in English. According to the Gestaltists, an individual’s comprehension of a problem cannot be reduced to a collection of individual perceptual features. Instead, the individual perceives a particular Gestalt of the problem, which can be interpreted as the totality of the relations between its parts. Insight, to the Gestaltists, was therefore considered a mental restructuring of the problem into a more productive Gestalt (Ohlsson, 2011 ; Wertheimer, 1959 ). In this study, we draw on the Gestalt view and consider insight as a perceptual and conceptual restructuring of a problem in a more productive manner. This view of insight has also been described as mentally crossing a ‘logical gap’, and it has often been referred to as a sudden and unexpected feeling of comprehension during an attempt at solving a problem (Ohlsson, 2011 ; Sternberg & Davidson, 1995 ).

Currently there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking in which the problem is matched with information in memory. The solution typically unfolds in a sequence of conscious steps, and the individual has a feeling of steady incremental progress. Insight is gained gradually and consciously. The Gestaltists called this reproductive thinking (Weisberg, 2015 ). The second view, termed productive thinking by the Gestaltists, suggests that insight is the result of a particular set of processes distinct from conscious analytical thinking. Here, insight is the result of unconscious processes that come about only after an impasse has occurred. Furthermore, insight is gained quickly, often spontaneously, and as a result of mental restructuring of the problem (Weisberg, 2015 ). Extant models of problem solving within mathematics education tend to highlight the first view of insight. Lester and Kehle ( 2003 ), for example, characterizes successful problem solving as “coordinating previous experiences, knowledge, familiar representations and patterns of inference, and intuition…” (p. 510). Although unconscious processes such as intuition are sometimes mentioned, they are usually not explained or elaborated in problem solving models, and the emphasis is on analytic and conscious cognitive processes. On the other hand, within the field of creativity research and theoretical models of creativity—in particular Gestaltist inspired research—analytic thinking is considered unable to produce novelty. Highly inspired by the Gestaltists, the focus has therefore often been on more spontaneous processes that can result in a new interpretation of the problem (Weisberg, 2015 ).

In this study, we investigated how the two views of insight—a and corresponding set of models—can describe and explain different aspects of the problem solving process. The aim of our study was to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important aspects of the problem solving process. We pursued this aim by studying how expert and novice mathematics students at a large research university in Norway approached and worked on two ambiguous and ill-defined mathematical problems. We then applied both a problem solving model and a creativity model in our analysis of students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. More specifically, we set out to answer the following research question:

How do expert and novice students approach and attempt to gain insight into ill-defined mathematical problems?

To work towards our aim, we made use of a novice-expert comparison, which has proven to be useful within cognitive research (National Research Council, 2000 ). Expertise has commonly been described as 10 years of intense preparation in some field (Ericsson & Lehmann, 1996 ), or “proficiency taken to its highest level” (Glaser, 1987 ). However, expertise has also been defined in terms of cognitive development and knowledge structures (Hoffman, 1998 ), and described as a continuum or multiple stages rather than a dichotomy between experts and novices (e.g. Dreyfus & Dreyfus, 2005 ). In this study, we therefore differentiated between expert and novice students according to educational background and mathematical attainment. The main rationale for this choice was to contrast mathematical performance with two different theoretical perspectives of insight during problem solving.

We also made use of ill-defined problems , which are those problems for which there are conflicting assumptions, evidence, and opinions that may lead to different solution (e.g., Kitchener, 1983 ; Krutetskii, 1976 ). They force the problem solver to deal with uncertainty, and facilitate multiple possible approaches by looking at the problem in new and productive ways. Ill-defined problems are therefore particularly useful for facilitating perceptual restructuring and insight during the problem solving process (Webb et al., 2016 ).

1.1 Problem solving models

Problem solving has long been of interest to mathematics education researchers. At the root of this research, and most problem-solving frameworks, lies the work of the eminent mathematician George Polya (Schoenfeld, 1985a ). In his work How to Solve It , Pólya ( 1949 ) presented a four-step model of problem solving which consisted of the four steps understanding , planning , implementing , and looking back . The model outlines problem solving as a systematic and gradual process that facilitates insight primarily by building on prior knowledge and conscious evaluation. Because of the structured and pedagogical approach to problem solving and the explicit focus on prior knowledge, Polya’s four step model has become the most popular approach to teaching and learning problem solving (Liljedahl et al., 2016 ).

One of the shortcomings of Polya’s model is that research generated under its umbrella focused almost entirely on heuristics, or rules of thumb for making progress on difficult problems, while ignoring “managerial skills necessary to regulate one’s activity (metacognitive skills)” (Lester, 1985 , p. 62). Lester ( 1985 ) and Schoenfeld ( 1985a ) suggested that metacognitive activity (knowledge of one’s thought processes or self-regulation) underlies the application of heuristics and algorithms. As a result, Polya’s model was modified (Lester, 1985 ; Schoenfeld, 1985a ) to include a cognitive component and a metacognitive component. In the cognitive component, the four phases of understanding, planning, implementing, and looking back are labeled as orientation , organization , execution , and verification respectively. The metacognitive component consists of three classes of variables attributed to Flavell and Wellman ( 1977 ). This model purports to describe the four cognitive categories in terms of ‘points’ where metacognitive actions occur during problem-solving (see Fig.  1 ).

The cognitive-metacognitive model (Lester, 1985 )

The cognitive component Orientation refers to strategic behavior to assess and understand a problem. It includes comprehension strategies, analysis of information, initial and subsequent representation, and assessment of familiarity and chance of success. Organization refers to identification of goals, global planning, and local planning. The category of execution refers to regulation of behavior to conform to plans. It includes performance of local actions, monitoring progress and consistency of local plans, and trade-off decisions (speed vs. accuracy). Finally, verification consists of evaluating decisions made and evaluating the outcomes of the executed plans. It includes evaluation of actions carried out in the orientation, organization, and execution categories. The metacognitive component of the model is comprised of three classes of variables, namely person variables, task variables, and strategy variables. Person variables refer to an individual’s belief system and affective characteristics that may influence performance. Task variables refer to features of a task, such as the content, context, structure, syntax and process. An individual’s awareness of features of a task influences performance. Finally, strategy variables are those that refer to an individual’s awareness of strategies that help in comprehension, organizing, executing plans, and checking and evaluation.

The main purpose of this model is to show that metacognitive actions can influence cognitive behavior at all phases of problem solving (Lester, 1985 ; Schoenfeld, 1985a ). The introduction of metacognitive actions is an important modification of Polya’s model (Liljedahl et al., 2016 ). In contrast to Polya’s non-specific heuristics, the introduction of metacognitive components is an acknowledgment that problem solving is an emergent process that depends on the individual’s prior knowledge and internal dialogue. Unlike Pólya ( 1949 ), who prescribed heuristics applicable to all problems and problem solvers, Schoenfeld ( 1985a ) and Lester ( 1985 ) portray problem solving heuristics as personal objects that are limited to the individual’s existing knowledge and understanding of the problem (Liljedahl et al., 2016 ).

Nevertheless, both the original model by Pólya ( 1949 ) and the revised model (Lester, 1985 ; Schoenfeld, 1985a ) lay out problem solving as a conscious and incremental process in which the problem solver gains insight primarily through past experience and conscious evaluation. Generally, the first step in the process, after gaining an initial understanding of the problem, would entail attempts at matching the problem with prior knowledge and evaluating whether a solution method could be transferred to the new problem. If this attempt is unsuccessful, the problem solver would then move on to applying heuristic methods. Through the use of heuristics, the problem solver attempts to modify the present state of the problem so that he/she can advance towards the final goal (Weisberg, 2015 ). Of course, the process is not nearly this simple or linear, but it provides a general overview of the analytic approach to problem solving. Insight, or restructuring of the problem in a new and more productive manner, is gradually gained through a stepwise and conscious process.

However, within most of creativity research, which leans heavily on the Gestalt view of insight, this view of gradually gaining insight is rejected (Weisberg, 2015 ). Problem solving models, and similar reproductive approaches to insight in problem solving, do not explain how existing knowledge and analytic thinking can produce novel ideas, which are usually necessary for solving problems that require some form of insight. The argument is essentially that a logical system can only produce information that is already present, at least implicitly, in the premises, and that is therefore not novel (Weisberg, 2015 ). Therefore, insight has to be the result of some kind of special cognitive process different from the conscious and evaluative approach that characterizes analytic thinking (Ohlsson, 2011 ).

1.2 Creativity models

From the perspective of creativity research then, when one tries to solve a problem the individual will first try solutions based on similarities with other problems and consciously evaluate the progress. However, those attempts will often fail as problems that require some form of novelty will not be solved by transferring methods from similar problems. The problem solver will eventually reach an impasse. It is at this point that the person may suddenly and unconsciously gain insight through a mental restructuring of the problem and come up with a solution. This notion of insight as a result of sudden and unconscious illumination is usually attributed to the Gestalt psychologists, and it is currently the dominant view of creative thinking (Ohlsson, 2011 ).

According to the Gestaltists, creative thinking and insight follow a sequence of four stages, namely, preparation - incubation - illumination , and verification (Wallas, 1926 ; Hadamard, 1945 ; Poincaré, 1948 ). The first stage consists of working hard to understand the problem at hand. Poincaré calls this the preliminary period of conscious work. The second stage occurs when the problem is put aside for a period of time and the mind is occupied with other things. The third stage is where the solution suddenly appears while the individual is perhaps engaged in other unrelated activities. "This appearance of sudden illumination is a manifest sign of long, unconscious prior work." (Poincaré, 1948 , p. 16). However, the creative process does not end here. There is a fourth and final stage, namely verification, which includes expressing the results by language or writing. At this stage one verifies the result, makes it precise, and looks for possible extensions through utilization of the result.

More recently, Ohlsson ( 2011 ) reformulated the four step Gestalt model of creativity as the insight sequence in an effort to draw a clear distinction between problem solving through analytic thinking and problem solving through sudden insight. Furthermore, while the Gestaltists were concerned with insight and creative thought on timescales of months and years, proponents of more recent Gestalt inspired research that uses the insight sequence, consider aspects of insight and creativity also on much shorter timescales (Beghetto & Karwowski, 2019 ; Ohlsson, 2011 ). The insight sequence describes successful problem solving as a chain consisting of the following events: attempted solution \(\to\) consistent failure \(\to\) impasse \(\to\) restructuring \(\to\) insight \(\to\) Solution. Unlike problem solving models that describe insight as something gained gradually through analytic and conscious thinking, the insight sequence emphasizes impasse and sudden (and unconscious) cognitive restructuring as the basis for insight (Weisberg, 2015 ). Presently, this restructuring is thought to occur by an impasse that causes an altered balance in a lower layer of cognitive processing systems, which leads to a new, and possibly more productive, representation in a higher and more conscious layer (Ohlsson, 2011 ).

An important idea in the setting of perceptual restructuring is cognitive flexibility . Cognitive flexibility refers to our ability to switch between different mental sets, tasks and strategies in light of uncertainty and impasse (Ionescu, 2012 ). According to Nijstad et al. ( 2010 ), cognitive flexibility is a key element for achieving creative insights, problem solutions, or ideas through the use of flexible switching among categories, approaches, and sets, and through the use of remote (rather than close) associations. Cognitive fixation , on the other hand, is the counterpart to flexibility. The notion of people struggling to come up with creative solutions because they fixate, or fail to abandon non-productive strategies, has its roots a long way back in psychological literature and features particularly in the writings of the Gestalt school (Haylock, 1987 ).

Although cognitive flexibility seems to relate to the intuitive concept, we still lack a clear definition and comprehension of the phenomenon (Ionescu, 2012 ). For example, in a review of the literature, Ionescu ( 2012 ) identified several behaviors that are considered flexible, as follows: switching between tasks or multitasking; changing behavior in light of a new rule; finding a new solution to a problem; and creating new knowledge or tools. In this paper, we consider flexibility as the ability to break away from inappropriate approaches, i.e., particular methods and strategies, within a single problem (Haylock, 1987 ). Regarding cognitive fixation, Haylock ( 1987 ) concluded that there are two particularly important types of fixation in mathematical problem solving: algorithmic fixation and content universe fixation . Algorithmic fixation is closely related to the Einstellung effect , and it refers to individuals continuing to use an initially successful algorithm or method learnt beforehand or developed through the sequence of tasks themselves. The other type of fixation, content universe fixation, refers to situations where students’ thinking about mathematical problems is restricted unnecessarily to an insufficient range of elements that may be used or related to the problem (Haylock, 1987 ). The overcoming of these kinds of fixations, and thus allowing the mind to range over a wider set of possibilities than might first come to one’s conscious awareness, is an important aspect of successful problem solving.

1.3 Expert and novice problem solvers

Besides the use of metacognition to describe phases of problem-solving performance, another widespread approach within the problem solving research paradigm has been to describe in detail solutions used by ‘expert’ problem solvers and compare this to solutions of ‘novices’ (Simon & Simon, 1978 ). The rationale behind this genre of research was to identify strategies used by experts, and develop prescriptive models to teach students how to problem solve like experts. The main findings of studies in the ‘expert-novice’ genre were that experts and novices differed in their problem solving strategies because of the following:

Knowledge for understanding and representing problems (Orientation).

Strategic knowledge (Organization).

Repertoires of known procedures and familiar patterns (Execution and Verification).

Experts are adept at creating a representation of the problem, and understanding it in terms of fundamental principles. While experts tend to focus on structural properties of problems, novices place a greater emphasis on surface properties. Furthermore, novices are often not able to construct problem representations that are helpful in achieving solutions. This description fits into the orientation category of Lester’s ( 1985 ) cognitive-metacognitive model. Experts also solve problems by using a process of successful refinements. Global planning and qualitative analysis characterize their strategies, before generating specific equations to solve the problems. Novices, on the other hand, tend to go directly from the problem text in search of equations that could be used. This behavior fits into the organization category of Lester’s model. Finally, experts have developed a repertoire of problem types and solution methods besides having an extensive knowledge of basic principles. Novices are lacking much of this knowledge and experience. This observation fits into the execution and verification categories of Lester’s model.

Expert and novice differences have also been studied within creativity research. In general, it is believed that the more knowledge we have in a domain, the more flexible problem solvers we are in that domain (Ionescu, 2012 ). The most common explanation for this aspect is that experts have acquired, over many years of practice, a vast knowledge base of techniques, methods, strategies, etc., when solving problems. This large knowledge base enables the expert often to solve novel problems by small modifications to what they already know, which in turn requires relatively minor cognitive effort (Ohlsson, 2011 ). However, it has also been argued that expertise could lead to less flexibility and more cognitive fixations. Expertise is generally considered to be domain specific, as skills tend to go from higher levels of generality to greater specificity as a result of practice (Ohlsson, 2011 ). As a result, it is conceivable that expertise can lead to less flexibility and a greater fixation on a narrow pattern of previous experiences. Others have found non-linear relationships between expertise and flexibility. In a series of clever studies on the relationship between expertise and flexibility among chess experts, Bilalic et al. ( 2008 ) found a clear difference between ordinary (3 SDs above average performance) and super experts (5 SDs above average performance). While ordinary chess experts demonstrated cognitive fixation, possibly caused by knowledge specificity, the super experts demonstrated cognitive flexibility and not fixations induced by previous mental sets. Somewhat similarly, Elgrably and Leikin ( 2021 ) recently investigated the relationship between different types of mathematical expertise and creativity. Two groups of students—expert problem solvers in mathematics and mathematics majors in university—were given a problem-posing-through investigation-task. The results showed that the expert problem solvers posed three times as many problems, with more flexible and original properties, than the mathematics majors. These findings are in line with much of the literature that indicates a clear, yet somewhat nuanced relationship between mathematical knowledge and flexibility (e.g., Haavold et al., 2020 ).

2.1 Data collection and materials

To answer our research question and work towards the aim of the study, we investigated how expert and novice mathematics students approached and attempted to gain insight into two ill-defined mathematical problems. We report here on data from task-based interviews with small (3–4) groups of students. Each session lasted for about 60 min, in which the students worked on two ill-defined mathematical problems. During the interview, the interviewer answered clarification questions, but deflected more task specific and content related questions back to the students. We opted to make use of group based protocols as they are particularly appropriate for observing decision-making and students’ real social cognitive behavior (Schoenfeld, 1985b ).

The participants in the study consisted of two different groups of students aged 22–24 years, both of which are in their fifth and final year of their study programmes. All participants volunteered and were recruited by the first author of this paper via postings on the university’s learning management system (Canvas). The first group (novice group) consisted of 12 students, divided into four groups of three, enrolled in a 5 year pre-service teacher education programme specifically aimed at teaching in primary school and lower secondary school. The students in the novice group were not mathematics specialists, and had studied only 1 year of mathematics after upper secondary school. The mathematical content in their previous mathematics studies was focused on elementary mathematical topics such as geometry, algebra, and numeracy—with a particular didactical emphasis. The expert group consisted of four master’s students who excelled at graduate level mathematics. We classified this group as experts as they all were, at the time, working on their master’s degree in mathematics and had demonstrated proficiency (i.e., high grades—85th percentile) in advanced mathematics courses in calculus, number theory, algebra, and statistics.

Two ill-defined problems were given to the students. Each of them provided different types of misdirection and extensions of the problem space for the problem solvers.

Problem 1: the Roman inheritance problem The first problem comes from The Moscow Puzzles and is usually referred to as the Roman problem:

A dying Roman knowing his wife was pregnant, left a will saying that if she had a son, he would inherit two-thirds of the estate and the widow one-third, but if she had a daughter, the daughter would get one-third and the widow two-thirds. Soon after his death, his widow had twins- a boy and a girl, a possibility the will had not foreseen. What division of the estate keeps as closely as possible to the terms of the will?

There isn’t a single right answer to this problem as the constraints are not fully exhaustive. This presents the students with a problem that can be repeatedly restructured and facilitate many approaches, and insight is predicated on recognizing this ambiguity. The Roman jurist, Salvian Julian, proposed for instance that the father’s intent is that the daughter should receive half as much as her mother, and the son twice as much. The inheritance should be divided into seven parts, and the mother should get two parts, the son four parts, and the daughter one part. However, an opposing view is that the father wished the mother to inherit at least 1/3 of the estate, but Salvian Julian would give her only 2/7. Therefore, give instead the mother 1/3 and divide the rest between son and daughter according to the intended ratio of four to one. The solution of the problem depends on which of the constraints the line of reasoning is based on.

Problem 2: wrong arithmetic, but correct result The second problem was based on the idea of mathematical pathologies, which refer to examples that are specifically designed to violate properties that are perceived as valid (Sriraman & Dickman, 2017 ):

Sometimes the wrong method gives us the right answer. When does this method work?

This example is ‘cooked up’ knowingly to violate common properties of fraction multiplication. To gain insight into this problem, the students need to accept the counterintuitive properties as a premise and break away from established mental sets related to arithmetic. So when does this method work? One possible approach is to use algebra to identify the constraints of each digit:

which boils down to

and finally

As ten is on the left side, there are now four cases that can be investigated further: \(b-a=5, b-a=-5, c=5, and d=5.\) For each of these cases, new constraints can be imposed and the situation further investigated.

2.2 Data analysis

Ill-defined problems contain conflicting or incomplete constraints, and they necessitate restructuring of the problem in a new and more productive manner—which is how we define insight in this paper. To identify how the students attempted to gain insight into the two ill-defined problems, we carried out a three-step analysis (e.g., Simon, 2019 ) in which the interviews and students’ written work were analyzed retrospectively using approaches from qualitative content analysis (Mayring, 2015 ).

In the first step, we investigated the students’ work on each problem through an inductive analysis. The goal was to isolate and identify each individual solution that the students attempted. We refer to this step as approaches as it includes students’ solution attempts at solving the particular task, the type of strategies and reasoning employed by the students, and explicit assumptions made by the students. As we mentioned earlier, insight is predicated on some form of mental restructuring that allows the problem solver to view the problem a new and more productive manner. Although we cannot observe the cognitive processes directly, we can observe and identify the individuals’ approaches, in the form of actions and utterances, which indicate how they conceive the problem’s starting and goal state, constraints and operators. In other words, each approach indicates a particular mental structuring or restructuring of the problem (Weisberg, 2015 ).

In the second step, we made use of a mixed content analysis (Mayring, 2015 ) and looked more closely at the students’ approaches from both creativity and problem solving perspectives. More specifically, from a problem solving perspective, we first imposed the four stages of orientation, organization, execution, and verification (Lester, 1985 ) on to the previously identified approaches, and examined how the students moved between approaches. This step was accomplished by further categorizing all the observed behavior, i.e., utterances and actions, for each of the identified approaches. All behavior related to assessing or understanding the problem was coded as orientation. We then coded all behavior related to organizing and execution as a common category, as it can be very difficult to distinguish planning and execution of plans (Schoenfeld, 1985a ). The last category, verification, referred to all behavior related to evaluation of decisions made and the outcome of the executed plans. After the deductive coding, we made use of inductive coding with two goals in mind, as follows: (1) identify common characteristics of each phase across both problems for both groups of students respectively, and (2) identify how the groups of students moved between problem solving phases during the problem solving process.

To investigate the students’ work from a creativity perspective, we made use of a creativity model based on the Gestalt view of insight in the second step of our analysis. As mentioned earlier, the Gestaltists viewed insight as dependent on sudden and cognitive restructuring (Weisberg, 2015 ). Although cognitive flexibility can refer to various categories and sets, in this study we considered the identified approaches as a particular mental structuring, or restructuring, of the problem. Cognitive flexibility then, in this context, becomes the ability to switch between different approaches to the ill-defined problems. Furthermore, and as Nijstad et al. ( 2010 ) point out, the use of remote associations is a particular characteristic of cognitive flexibility. Thus, we looked more closely at (1) how many different approaches the students’ in each group made use of, (2) to what extent and in what way each approach differed from previous approaches in terms of strategies used and assumptions made, and 3) to what extent and in what way impasses during the problem solving process occurred—indicating the occurrence of fixations. Here, it is important to point out that we did not consider the success of each approach. It is often necessary to produce several attempts at solving an ill-defined problem in the absence of a priori knowledge of a valid solution, before finally solving it. Failed attempts are therefore often crucial to the creative process, as creative products are generated in the course of a dynamic process of exploration and assessment across both failed and successful attempts (Corazza, 2016 ).

In the third and final step, we attempted to develop explanatory inferences and work towards the aim of the paper. Here we compare and contrast how the two models—and corresponding views of insight—can describe and explain different aspects of the problem solving process. More specifically, we attempted to identify how and to what extent each of the two different models can describe and explain how the two groups of students gained, or failed to gain, insight into the ill-defined problems.

3.1 Problem 1: the Roman inheritance problem

Expert students The expert group approached the problem in two ways. At the start of the first approach, the students read the problem several times, first individually and then aloud, and discussed what they were “supposed to actually find out” as one student said. Simultaneously, they wrote down some of the constraints that they had identified in the problem: the wife should get more than the daughter, but less than the son. They then quickly reasoned what the wife’s proportion of the will would be if the total sum were halved. As one student said, “the wife should get exactly half of one third plus two third”. They concluded the wife should get half, and the rest be split between the daughter and the son. However, they quickly concluded that this was incorrect as this would either leave the son with less than the wife, or an inheritance exceeding the upper limit.

After rejecting the first approach, the expert students made a second attempt at solving the problem. They went back to talking about the information and conditions of the problem. They then decided to set up an equation, as this would “impose the all the necessary conditions on to the problem and we can solve it” as one student said. The right side of the equation had to be 1, as this represented the entire inheritance. The mother’s share was set as x, the son as y and the daughter z. They then substituted the variables and solved the equation (see Fig.  2 ).

Experts’ equation solution to the Roman problem

The students concluded that this was the right result. One of the students said: “The wife gets \(\frac{2}{7}\) , the daughter gets \(\frac{1}{7}\) , and the son gets \(\frac{4}{7}\) . This is the right result I guess”. However, this solution takes into account only the ratio between the wife, son and daughter, and not the share of the inheritance each person was promised. The students in the expert group mentioned this inconsistency a few times, but as one of the students said: “this is a bit weird, but I guess this is how you solve the problem”.

Novice students We identified three approaches for the novice groups.

As did the experts, all four novice groups first read the problem several times. However, unlike the experts, none of the novice groups discussed the information or constraints in the problem. Instead, they immediately started proposing possible solution strategies. The first approach all four novice groups attempted was some form of fraction expansion, followed by an empirically test to see if a more fine grained partition could make the inheritance division correct. The students would first set up a preliminary model, for instance imposing the constraints that the son would get more than the wife, and the wife would get more than the daughter. Then, they would adjust the model according to the results using bar charts, matrices or other heuristic approaches, and compare them to the conditions of the task. All four groups of students came up with at least three different partitions, before concluding that they were not able to build a model that satisfied all conditions of the task (see Fig. 3 ).

Example of novices’ model solution for the Roman problem

After concluding that the first approach did not satisfy all the conditions of the problem, all four novice groups immediately moved on to what we identified as a second approach. In the second approach, the novice students would use one of the son, the wife or daughter as a starting point based on the information in the task, and then quantify what share of the inheritance the others would get. For instance, if the son would receive \(\frac{2}{3}\) of the inheritance, then the wife would get \(\frac{2}{9}\) and the daughter would get \(\frac{1}{9}\) . The students would then use the daughter or the wife as the starting point, respectively, and quantify how much the others would get. However, after trying different starting points, all four novice groups concluded that this approach would not provide a correct solution.

The third approach we observed for all four novice groups was similar to the expert group’s second approach. The students wrote down and identified the ratios between the wife, the son and the daughter as the key constraints of the task. This approach was observed immediately after the novice students concluded their second approach was inappropriate, and it was also clear that this approach was inspired by the second approach. As one student said: “We have to take into account all constraints. At the same time. Not one by one. The son should get twice as much as the wife, and the wife should get twice as much as the daughter.” However, unlike the expert students, the novice students did not explicitly formulate equations that represented the conditions of the problem. Instead, they reasoned more informally. As one student said: “the wife should get twice as much as the daughter, and the son should get twice as much as the wife. The daughter then gets one part, the wife two parts, and the son four parts. That gives us seven parts in total”. All three novice groups concluded that this was the solution closest to the intentions of the will, but still not a satisfactory solution. After the third approach, three of the novice groups discussed the overall intentions of the will and which of their approaches was most in line with the wishes of the dying Roman. All three novice groups concluded that it was impossible to find a solution that was in full accordance with the will. However, all three groups also concluded that the main intention of the will was that the son should get more than the wife, and the wife should get more than the daughter.

3.2 Problem 2: wrong arithmetic, but correct result

Expert students The expert students approached the problem in two ways. First, the expert students read the problem, first individually and then out aloud. The experts then spent a few minutes talking about how “weird the expression was”, while verifying that both sides of the equation were equal, and the proposed method was correct. The students quickly agreed on both the meaning and goal of the problem. As one student said: “oh, they’ve just placed the digits together, and we need to find out when fraction multiplication gives this kind of product.” After verifying that the expression was indeed correct, the students proposed a hypothesis for which type of numbers this method was correct based on the example given. The students quickly mentioned that the sums of the digits in both the numerators and denominators were nine, and that nine was also a common factor of both 18 and 45. However, this hypothesis was not pursued further. Instead, the students quickly rejected the first approach and decided to represent the problem algebraically, which we have identified as their second approach.

After setting up the algebraic expression seen in Fig.  4 , the students repeatedly stated that this expression wasn’t appropriate. As one student said: “you can’t use correct algebra on something that is incorrect. The left side is ok, but the right side is completely wrong”. One of the students mentioned that they could have further identified constraints on each of the four “unknowns”, but he quickly decided that such a pursuit was pointless as it was “not correct mathematics”. The students then concluded that they couldn’t find any other solutions, as it couldn’t be solved algebraically and it was difficult to generalize any sort of pattern from just one case.

Experts’ algebraic solution for the Wrong arithmetic, but right result problem

Novice students Each of the four novice groups approached the problem in two ways. As with the Roman inheritance problem, all four novice groups first read the problem both individually and out loud. However, unlike the experts, the novice students did not explicitly discuss and agree on the meaning and goal of the problem. Instead, they seemed to spend a few minutes on their own trying to understand the problem. This period of apparent uncertainty was then interrupted by one of the students in the group proposing a particular solution strategy. For all four novice groups this involved a proposed hypothesis regarding the relationship between the numbers, which they refined empirically without considering the mathematical structure of the problem. For instance, the students explored commutativity and tried \(\frac{8}{5}\times \frac{1}{4}=\frac{81}{54}\) , they added the same numbers to denominators and numerators, and attempted to work with more or less randomly chosen fractions that, according to one student, were “in the same ballpark” as the fractions in the task. Common to all these hypotheses were that they were inferred from the specific numerical example in the problem text, and they were not based on any systematic investigation of the structural properties of the expression. One student, for example, evaluated the hypothesis according to “how close they came to giving an equal left and right side”. The students switched back and forth between several different hypotheses, but did not explicitly consider how the right side of the expression was constructed mathematically. Eventually, all four novice groups concluded that this approach was not “fruitful”, as one student said.

Eventually, all four novice groups rejected the first approach. Although there were some variations between the four groups, it seemed the second approach was an informal line of reasoning similar in structure to the novice students’ third approach on the Roman inheritance problem. Furthermore, the second approach seemed to evolve out of the seemingly superficial hypotheses proposed in the first approach. As one student said, “We need to make things easier… we’re just looking for connections between the numbers here, but there can so many of them.” In the second approach, the novice students seemed to look for specific examples that would satisfy the conditions of the problem and thus identify possible structural relationships. For instance, three of the novice groups realized eventually that they could just “turn the fractions upside down and maintain the same ratio between them” as one student said. Two of the groups also listed several trivial solutions that satisfied the criterion 1 × 1 = 1. The main difference between the novices’ first and second approaches, was that the first approach seemed to focus on identifying properties in the numbers given in the task, while the second approach seemed to focus on finding other examples that also satisfied the proposed method (see Fig. 5 ).

Example of novices’ empirical model solution to the Wrong arithmetic, but right result problem

3.3 Problem solving model

During the orientation phase of both tasks, both the experts and novices first read the task instructions individually and aloud. Both groups of students seemed to prefer to read the problem first and gain an initial understanding of it before talking about it to the other students. However, after reading the problem carefully, either quietly or aloud, the rest of the orientation phase was different for the experts and novices. While the experts wrote down and discussed the goals and conditions of the problems, seemingly to make sure everyone had the same understanding of the problem and its goal, the novices immediately began working on a solution strategy proposed by one of the students. Furthermore, after rejecting their first more informal approach, the experts went back to the orientation phase to make sure they all understood the problem correctly and had identified all the relevant conditions of the problem. There were also similarities and differences between the experts and novices in the organization and execution phases. For both problems, the experts first quickly proposed and rejected a hypothesis that seemed to be based on surface properties and incomplete constraints of the problems. For example, regarding problem two, there seemed to be no deeper analysis of the problem behind the first approach other than trying to identify common properties of the numbers on both sides of the equation sign. Similarly, the novices also first proposed hypotheses that seemed to be based on surface properties and incomplete constraints of the two problems. However, after rejecting the first approach, the experts then quickly sought a generalized and formalized solution, by representing and applying algebraic expressions and equations. The novices, on the other hand, continued to formulate hypotheses that they tested empirically, or they looked for numerical examples that satisfied given constraints of the problems. Finally, during the verification phase, there were also some noticeable differences between the two groups of students. The expert students quickly concluded, without any form of justification, that their first approach, for both problems, was incorrect. The students then similarly concluded quickly that their second approach was either correct or that the problem couldn’t be solved, for problem 1 and problem 2 respectively. Unlike the expert students, who evaluated each approach quickly and conclusively after the organization and execution phase, the novices seemed to evaluate the approach continuously and gradually come to a conclusion regarding its correctness.

These observations are in line with much of the existing literature on expert vs. novice problem solvers (Lester & Kehle, 2003 ; Schoenfeld, 1985a ). The experts placed a greater focus on understanding the problem, global planning, and creating representations that captured the structural properties of the problems. The novices, on the other hand, tended to go directly from the problem text in search of solution strategies that could be productive. Furthermore, the novices tended to create representations of the problems that were either incomplete or focused on surface properties. We also noticed that the experts quickly determined whether or not a particular approach was correct, while the novices seemed to explore each approach to a much greater extent before assessing its validity. This could be a result of a more extensive knowledge base. How the two groups of students moved between the different problem solving phases is also similar to results in the literature regarding expert and novice problem solving. Schoenfeld ( 1985a ) found, for example, that novices tend to spend much time on what he called the explore phase, which can be said to be an unstructured exploration of the problem analogous to orientation and organization. Experts, on the other hand, tend to display greater control and monitoring as they cycle more purposefully between the different problem solving phases. In this study, the experts’ problem solving behavior seemed to consist of repeating cycles of orientation → organizing/execution → verification. The novices, on the other hand, seemed to stick to cycling back and forth between the organizing/execution phase and the verification phase, after a single and initial orientation phase.

3.4 Creativity model

For the experts, we identified two approaches for each of the two problems. For the novices, we identified three approaches for the first problem and two approaches for the second problem. Immediately, a purely quantitative analysis would seem to indicate that the novices displayed greater cognitive flexibility during the problem solving process. However, a more detailed analysis reveals a more nuanced picture. For both problems, the experts’ first approach seemed to be unstructured exploration based on either surface or an incomplete set of properties of the problem. The second approach, on the other hand, for both problems, was a more general and structured approach, where all the relational properties of the problem were represented using algebraic equations. For example, the experts’ first approach to the Roman inheritance problem seemed to conclude that the wife’s part of the inheritance would simply be the midpoint of the two different situations described in the will. The second approach, on the other hand, was an equation that seemingly covered all the relational properties described in the problem. The experts’ work on both problems indicates a prominent mental shift between the first and the second approaches. It seems they were able to quickly break away from an inappropriate approach and instead pursue a more appropriate approach. Furthermore, the second approach is vastly different from the first approach in terms of both assumptions and strategies. As Nijstad et al. ( 2010 ) pointed out, sudden switching between remote mental sets—such as assumptions and strategies within a particular approach—is a key feature of cognitive flexibility. The novices, on the other hand, seemed to switch between approaches that were related to each other. For example, the novices’ two approaches on the Wrong arithmetic, but correct result problem were both based on unstructured exploration around arithmetic properties. This pattern indicates that although the novices were able to break away from unproductive approaches, the closely related approaches indicate less cognitive flexibility than that shown by the experts. This interpretation is in line with much of the relevant literature which concludes that extensive knowledge is positively associated with flexible problem solving (Ionescu, 2012 ).

Turning to the issue of cognitive fixation, we observed several incidents of ostensible impasses from which the experts and novices were unable to break. For both problems, the novices stuck to empirical investigations of hypotheses and informal reasoning. Although the novices shifted fluidly between different assumptions and strategies for both problems, the fact that they stuck to a particular set of approaches, indicates to some extent the presence of algorithmic fixation (Haylock, 1987 ). Although algorithmic fixation primarily refers to the inappropriate continued use of a particular algorithm, this kind of fixation also includes a more general predisposition to solve a problem in a specific manner even though better or more appropriate methods of solving the problem exist. Creating, for example, algebraic representations for both problems, in particular the second problem, would have helped the novices determine the relevant structural properties. The experts also experienced incidents of prolonged impasse that could indicate cognitive fixations. However, unlike the novices who displayed tendencies of algorithmic fixation, the experts seemed to primarily display tendencies of content universe fixation (Haylock, 1987 ). Working on the first problem, the experts concluded quickly that their second approach was “the correct solution”, as one student said, even though the constraints of the problem were not fully exhaustive and the ill-defined nature of the problem allowed multiple interpretations. For the second problem, the experts repeatedly stated that the algebraic expression (see Fig.  4 ) they had created was not appropriate, as they believe you could not apply “correct algebra on something that is incorrect”, as one student said. However, within the context of the problem, creating an equation that captures all the relevant structural properties is perfectly appropriate. In fact, analyzing the algebraic expression would have help the students’ identify the constraints of each digit. Overall though, the findings in the context of creativity is also in line with much of the literature. Both the experts and the novices displayed both flexibility and fixation during the problem solving process—although somewhat differently.

3.5 How students gained insight

Immediately, it would appear that the findings in this study are in line with much of the literature on expert and novice problem solving. Furthermore, both the experts’ and the novices’ work seemed to progress largely in a stepwise manner, as described and explained both by the problem solving model utilized in this study (Lester, 1985 ) and the analytic view of insight (Weisberg, 2015 ). One instance of this aspect can be seen in the novices’ work on the first problem. While their second approach was premised only on a single constraint of the problem, their third approach took into account all the relational properties between the wife, the daughter and the son simultaneously. In this instance, the novice students’ clearly modified their approach in a gradual and stepwise manner and further insight was gained as a result. A second important instance can be found in the experts’ work. For both problems, the experts returned to the orientation phase after their first approach, and then produced a new and more effective approach. This chain of events indicates that the experts’ first ineffective approach and return to the orientation phase somehow led to a productive mental restructuring of the problem—or greater insight in other words—which in turn resulted in a more effective approach.

However, a more finely-grained scrutiny of the students’ work reveals several limitations of the problem solving model. One such discrepancy is the emphasis on past experiences during problem solving (Liljedahl et al., 2016 ). Problem solving models (Lester, 1985 ; Pólya, 1949 ; Schoenfeld, 1985a ), and the analytic view of insight (Weisberg, 2015 ), highlight the importance of past experiences during problem solving and argue that insight is a consequence of matching the problem with information in memory. In this study, we did not observe a single incident in which either group explicitly referenced past experiences or compared the problem to other problems. It could be argued that the ill-defined structure of the problems themselves was unfamiliar, but it is still noticeable that neither group of students performed any sort overt assessment of familiarity with the task (Lester, 1985 ).

Another ostensible discrepancy can be found in the novices’ many approaches to the problems. Although the novices did not move between the different problem solving phases to the same extent as the experts, they did not stick to one particular approach “come hell or high water”—as Schoenfeld ( 1985a ) observed to be common among novice problem solvers. Instead, the novices moved seemingly effortlessly between different approaches, constantly adapting to the ambiguity of the ill-defined problems. This behavior is a clear indication of cognitive flexibility (Ionescu, 2012 ). Furthermore, each of these apparent mental restructurings of the problems seemed to follow small impasses in the problem solving process—as predicted by the Gestaltists (Weisberg, 2015 ).

Insight as a consequence of impasses and sudden mental restructuring, as opposed to a stepwise and conscious process, was even more prominent in the experts’ work. The experts’ work on both problems indicates a significant mental shift between the first and the second approach. After trying and concluding that their first and more informal approach was inappropriate, the experts quickly decided to pursue a completely different and more structured approach. Although this behavior can be projected on to the four phases of the problem solving model (Lester, 1985 ), as seen earlier, the model itself cannot qualitatively explain the drastic shift in terms of assumptions and strategies. The experts’ second approach was in no way a further refinement of their first approach, and they did not explicitly reference past experiences. Instead, it seemed the second approach appeared suddenly, unconsciously and as a response to the failure of the first approach. This chain of events is similar to what Ohlsson ( 2011 ) refers to as the insight sequence , which describes insight as something gained after an attempted solution fails and a sudden and meaningful mental restructuring is required. After an impasse has occurred, insight is gained after dealing with the problem from a completely novel perspective.

Finally, our analyses also indicate occurrences in which both groups of students failed to gain insight. For example, while the novices applied mostly empirical and informal reasoning, the experts sought generalized and formalized solutions. Although much of the literature explains this as a consequence of the experts’ more extensive knowledge base (Lester & Kehle, 2003 ; Schoenfeld, 1985a ), neither problem used in this study required advanced mathematics. The algebraic representations that the experts made use of were fairly simple and seemingly within the grasp of individuals who have taken at least upper secondary algebra. An alternative explanation can therefore be cognitive fixation (Haylock, 1987 ), in which individuals fail to abandon ineffective approaches and move beyond impasses. This was perhaps seen most clearly in the experts’ work on the second problem. After creating an algebraic representation of the structural properties of the problem, the experts quickly rejected, in unison, the approach as inappropriate. We propose that this is a clear example of an unnecessary restriction to an insufficient range of elements (Haylock, 1987 ). In other words, the experts imposed an unnecessary set of restrictions on to the problem solving process based on their conceptions of the situation, rather than the properties of the problem itself. Now, it can be argued that this fixation can be linked to the experts’ past experiences. However, the problem solving model, and the analytic view of insight, do not explain or describe how the problem solver can break away from established mental sets. In fact, the problem solving model, and the analytic view of insight, emphasize the use of prior knowledge and reliance on past experiences when first attacking a problem (Liljedahl, 2016). When facing a new problem, in particular an ill-defined problem such as those made use of in this study, the focus on past experiences could actually be a hindrance to making progress (Weisberg, 2015 ).

4 Final thoughts

In this study, we aimed to integrate two different views on insight during problem solving, and explore how they each highlight different aspects of the problem solving process. Looking back, applying both problem solving and creativity models on to the experts’ and novices’ work reveals and explains different aspects of the students’ problem solving processes. While the problem solving model helps us analyze and understand parts of the problem solving process, there are crucial aspects of the students’ work that it does not explain. In this study, we observed what we claim to be the occurrence of cognitive flexibility, cognitive fixation, and more importantly, sudden, and seemingly unconscious, insight during the problem solving process—for both experts and novices. The results of this study therefore dovetail with what the Gestaltists said all along: Sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by standardized problem solving models and an analytic view of insight. Current researchers inspired by the Gestaltists have dubbed this understanding of insight as the special process view of insight (Ohlsson, 2011 ; Weisberg, 2015 ), as it asserts that the thought processes underlying insight are distinctly different from those thought processes underlying analytic thinking.

We suggest, based on the results of this study and the review of the relevant literature, that research into problem solving within mathematics education would benefit from adopting aspects of Gestalt inspired views of insight. Although we do not go as far as some who claim that adherence to any sort of heuristics can be a hindrance to the problem solving process, we do agree that there are no prescriptive heuristics for some of the more unconscious, yet highly important, cognitive aspects of problem solving (Liljedahl et al., 2016 ). So, what happens during the moment of insight or subconscious work? What is the source of creative thought? Although we do not fully understand mental restructuring and creative thought, Ohlsson ( 2011 ) has proposed redistribution theory as a Gestalt-inspired response. Here, the problem solver first creates an initial inappropriate representation of the problem. This particular interpretation activates one or more incorrect solutions, which the problem solver then works through. At some point, after working through the incorrect solutions, the problem solver reaches an impasse. It is at this point that the initial, and inappropriate, representation of the problem could be inhibited. This inhibition of the original representation of the problem might then result in a new representation of the problem, which causes the problem solver to realize that the problem can be thought of in a different way—in other words, a mental restructuring has occurred. Somewhat ironically, the Gestalt inspired method of problem solving can therefore also be said to rely heavily on past experience. What is entailed is not to match the problem with past experiences to find an appropriate solution, but rather to relax unnecessary constraints and inhibit knowledge that is not necessary. We propose that this line of reasoning can add to extant problem solving models in at least two ways, as follows: 1) Most problem solving models highlight the importance of assessing the familiarity of the problem (Lester, 1985 ; Liljedahl et al., 2016 ; Pólya, 1949 ; Schoenfeld, 1985a ). However, the heuristic emphasis seems to be on identifying similarities between the problem at hand and past experiences. We suggest that identifying divergences between the problem at hand and past experiences is also important, as it may help the problem solver recognize unnecessary constraints. 2) Working through numerous incorrect approaches and solutions can be helpful to the overall problem solving process, as it may lead to an impasse and a subsequent more appropriate restructuring of the problem. We suggest that problem solving models should also emphasize the value of working hard on problems for an extended period of time, and even failed attempts.

Beghetto, R. A., & Karwowski, M. (2019). Unfreezing creativity: A dynamic micro-longitudinal approach. In R. A. Beghetto & G. E. Corazza (Eds.), Dynamic perspectives on creativity (pp. 7–25). Springer.

Chapter   Google Scholar  

Bilalic, M., McLeod, P., & Gobet, F. (2008). Inflexibility of experts—Reality or myth? Quantifying the Einstellung effect in chess masters. Cognitive Psychology, 56 , 73–102.

Article   Google Scholar  

Corazza, G. E. (2016). Potential originality and effectiveness: The dynamic definition of creativity. Creativity Research Journal, 28 , 258–267.

Dreyfus, H. L., & Dreyfus, S. E. (2005). Peripheral vision: Expertise in real world contexts. Organization Studies, 26 (5), 779–792.

Elgrably, H. & Leikin, R. (2021). Creativity as a function of problem-solving expertise: posing new problems through investigations. ZDM Mathematics Education , 53 , 891–904.

Ericsson, K. A., & Lehmann, A. C. (1996). Expert and exceptional performance: Evidence of maximal adaptation to task constraints. Annual Review of Psychology, 47 (1), 273–305.

Flavell, J. H., & Wellman, H. (1977). Metamemory. In R. Kail & J. Hagen (Eds.), Perspectives on the development of memory and cognition. Lawrence Erlbaum Associates.

Google Scholar  

Glaser, R. (1987). Thoughts on expertise. In C. Schooler & W. Schaie (Eds.), Cognitive functioning and social structure over the lifecourse (pp. 81–94). Ablex.

Haavold, P., Sriraman, B., & Lee, K. H. (2020). Creativity in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 145–154). Springer.

Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field . Princeton University Press.

Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18 (1), 59–74.

Hoffman, R. R. (1998). How can expertise be defined? Implications of research from cognitive psychology. In R. Williams, W. Faulker, & J. Fleck (Eds.), Exploring expertise (pp. 81–100). Macmillan.

Ionescu, T. (2012). Exploring the nature of cognitive flexibility. New Ideas in Psychology, 30 (2), 190–200.

Kitchener, K. S. (1983). Cognition, metacognition, and epistemic cognition: A three-level model of cognitive processing. Human Development, 4 , 222–232.

Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren . University of Chicago Press.

Lester, F. K. (1985). Methodological considerations in research on mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving. Multiple research perspectives (pp. 41–70). Hillsdale: Lawrence Erlbaum Associates.

Lester, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10 (1), 245–278.

Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 501–518). Lawrence Erlbaum Associates.

Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education . Springer International Publishing.

Book   Google Scholar  

Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. Examples of methodology and methods (pp. 365–380). Springer.

National Research Council. (2000). How people learn: Brain, mind, experience, and school . National Academy Press.

Nijstad, B. A., De Dreu, C. K., Rietzschel, E. F., & Baas, M. (2010). The dual pathway to creativity model: Creative ideation as a function of flexibility and persistence. European Review of Social Psychology, 21 (1), 34–77.

Ohlsson, S. (2011). Deep learning: How the mind overrides experience . Cambridge University Press.

Poincaré, H. (1948). Science and method . Dover.

Pólya, G. (1949). How to solve it . Princeton University Press.

Schoenfeld, A. H. (1985a). Mathematical problem solving . Academic Press.

Schoenfeld, A. H. (1985b). Making sense of “out loud” problem-solving protocols. The Journal of Mathematical Behavior, 4 (2), 171–191.

Simon, M. A. (2019). Analyzing qualitative data in mathematics education. In K. R. Leatham (Ed.), Designing, conducting, and publishing quality research in mathematics education (pp. 111–123). Springer.

Simon, D. P., & Simon, H. A. (1978). Individual differences in solving physics problems. In R. Siegler (Ed.), Children’s thinking: What develops? (pp. 325–348). Lawrence Erlbaum Associates.

Sriraman, B. & Dickman, B. (2017). Mathematical pathologies as pathways into creativity. ZDM Mathematics Education , 49 (1), 137–145.

Sternberg, R. J., & Davidson, J. E. (1995). The nature of insight . MIT Press.

Wallas, G. (1926). The art of thought . New York, NY: Harcort Brace and World.

Webb, M. E., Little, D. R., & Cropper, S. J. (2016). Insight is not in the problem: Investigating insight in problem solving across task types. Frontiers in Psychology, 7 , 1–13.

Weisberg, R. W. (2015). Toward an integrated theory of insight in problem solving. Thinking & Reasoning, 21 (1), 5–39.

Wertheimer, M. (1959). Productive thinking (Enlarged Edition) . Harper and Brothers.

Download references

Open access funding provided by UiT The Arctic University of Norway (incl University Hospital of North Norway).

Author information

Authors and affiliations.

UiT The Arctic University of Norway, Tromsø, Norway

Per Øystein Haavold

University of Montana, Missoula, USA

Bharath Sriraman

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Per Øystein Haavold .

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Haavold, P.Ø., Sriraman, B. Creativity in problem solving: integrating two different views of insight. ZDM Mathematics Education 54 , 83–96 (2022). https://doi.org/10.1007/s11858-021-01304-8

Download citation

Accepted : 24 August 2021

Published : 02 September 2021

Issue Date : April 2022

DOI : https://doi.org/10.1007/s11858-021-01304-8

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Problem solving
• Find a journal
• Publish with us
• Track your research

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Front Psychol

Intelligence and Creativity in Problem Solving: The Importance of Test Features in Cognition Research

Associated data.

This paper discusses the importance of three features of psychometric tests for cognition research: construct definition, problem space, and knowledge domain. Definition of constructs, e.g., intelligence or creativity, forms the theoretical basis for test construction. Problem space, being well or ill-defined, is determined by the cognitive abilities considered to belong to the constructs, e.g., convergent thinking to intelligence, divergent thinking to creativity. Knowledge domain and the possibilities it offers cognition are reflected in test results. We argue that (a) comparing results of tests with different problem spaces is more informative when cognition operates in both tests on an identical knowledge domain, and (b) intertwining of abilities related to both constructs can only be expected in tests developed to instigate such a process. Test features should guarantee that abilities can contribute to self-generated and goal-directed processes bringing forth solutions that are both new and applicable. We propose and discuss a test example that was developed to address these issues.

The definition of the construct a test is to measure is most important in test construction and application, because cognitive processes reflect the possibilities a task offers. For instance, a test constructed to assess intelligence will operationalize the definition of this construct, being, in short, finding the correct answer. Also, the definition of a construct becomes important when selecting tests for the confirmation of a specific hypothesis. One can only find confirmation for a hypothesis if the chosen task instigates the necessary cognitive operations. For instance, in trying to confirm the assumed intertwining of certain cognitive abilities (e.g., convergent thinking and divergent thinking), tasks should be applied that have shown to yield the necessary cognitive process.

The second test feature, problem space , determines the degrees of freedom cognition has to its disposal in solving a problem. For instance, cognition will go through a wider search path when problem constraints are less well defined and, consequently, data will differ accordingly.

The third test feature, knowledge domain , is important when comparing results from two different tests. When tests differ in problem space, it is not advisable they should differ in knowledge domain. For instance, when studying the differences in cognitive abilities between tests constructed to asses convergent thinking (mostly defined problem space) and divergent thinking (mostly ill-defined problem space), in general test practice, both tests also differ in knowledge domain. Hence, data will reflect cognition operating not only in different problem spaces, but also operating on different knowledge domains, which makes the interpretation of results ambiguous.

The proposed approach for test development and test application holds the promise of, firstly, studying cognitive abilities in different problem spaces while operating on an identical knowledge domain. Although cognitions’ operations have been studied extensively and superbly in both contexts separately, they have rarely been studied in test situations where one or the other test feature is controlled for. The proposed approach also presents a unique method for studying thinking processes in which cognitive abilities intertwine. On the basis of defined abilities, tasks can be developed that have a higher probability of yielding the hypothesized results.

The construct of intelligence is defined as the ability to produce the single best (or correct) answer to a clearly defined question, such as a proof to a theorem ( Simon, 1973 ). It may also be seen as a domain-general ability ( g -factor; Spearman, 1904 ; Cattell, 1967 ) that has much in common with meta cognitive functions, such as metacognitive knowledge, metacognitive monitoring, and metacognitive control ( Saraç et al., 2014 ).

The construct of creativity, in contrast, is defined as the ability to innovate and move beyond what is already known ( Wertheimer , 1945/1968 ; Ghiselin , 1952/1985 ; Vernon, 1970 ). In other words, it emphasizes the aspect of innovation. This involves the ability to consider things from an uncommon perspective, transcend the old order ( Ghiselin , 1952/1985 ; Chi, 1997 ; Ward, 2007 ), and explore loosely associated ideas ( Guilford, 1950 ; Mednick, 1962 ; Koestler, 1964 ; Gentner, 1983 ; Boden, 1990 ; Christensen, 2007 ). Creativity could also be defined as the ability to generate a solution to problems with ill-defined problem spaces ( Wertheimer , 1945/1968 ; Getzels and Csikszentmihalyi, 1976 ). In this sense it involves the ability to identify problematic aspects of a given situation ( Ghiselin , 1952/1985 ) and, in a wider sense, the ability to define completely new problems ( Getzels, 1975 , 1987 ).

Guilford (1956) introduced the constructs of convergent thinking and divergent thinking abilities. Both thinking abilities are important because they allow us insights in human problem solving. On the basis of their definitions convergent and divergent thinking help us to structurally study human cognitive operations in different situations and over different developmental stages. Convergent thinking is defined as the ability to apply conventional and logical search, recognition, and decision-making strategies to stored information in order to produce an already known answer ( Cropley, 2006 ). Divergent thinking, by contrast, is defined as the ability to produce new approaches and original ideas by forming unexpected combinations from available information and by applying such abilities as semantic flexibility, and fluency of association, ideation, and transformation ( Guilford, 1959 , as cited in Cropley, 2006 , p. 1). Divergent thinking brings forth answers that may never have existed before and are often novel, unusual, or surprising ( Cropley, 2006 ).

Guilford (1967) introduced convergent and divergent thinking as part of a set of five operations that apply in his Structure of Intellect model (SOI model) on six products and four kinds of content, to produce 120 different factors of cognitive abilities. With the SOI model Guilford wanted to give the construct of intelligence a comprehensive model. He wanted the model to include all aspects of intelligence, many of which had been seriously neglected in traditional intelligence testing because of a persistent adherence to the belief in Spearman’s g ( Guilford, 1967 , p. vii). Hence, Guilford envisaged cognition to embrace, among other abilities, both convergent and divergent thinking abilities. After these new constructs were introduced and defined, tests for convergent and divergent thinking emerged. Despite the fact that Guilford reported significant loadings of tests for divergent production on tests constructed to measure convergent production ( Guilford, 1967 , p. 155), over the years, both modes of thinking were considered as separate identities where convergent thinking tests associated with intelligence and divergent thinking tests with creativity ( Cropley, 2006 ; Shye and Yuhas, 2004 ). Even intelligence tests that assess aspects of intelligence that supposedly reflect creative abilities do not actually measure creativity ( Kaufman, 2015 ).

The idea that both convergent and divergent thinking are important for solving problems, and that intelligence helps in the creative process, is not really new. In literature we find models of the creative process that define certain stages to convergent and divergent thinking; the stages of purposeful preparation at the start and those of critical verification at the end of the process, respectively ( Wallas, 1926 ; Webb Young , 1939/2003 ). In this view, divergent thinking enables the generation of new ideas whereas the exploratory activities of convergent thinking enable the conversion of ideas into something new and appropriate ( Cropley and Cropley, 2008 ).

We argue that studying the abilities of divergent and convergent thinking in isolation does not suffice to give us complete insight of all possible aspects of human problem solving, its constituent abilities and the structure of its processes. Processes that in a sequence of thoughts and actions lead to novel and adaptive productions ( Lubart, 2001 ) are more demanding of cognition for understanding the situation at hand and planning a path to a possible solution, than abilities involved in less complex situations ( Jaušovec, 1999 ). Processes that yield self-generated and goal-directed thought are the most complex cognitive processes that can be studied ( Beaty et al., 2016 ). Creative cognition literature is moving toward the view that especially in those processes that yield original and appropriate solutions within a specific context, convergent and divergent abilities intertwine ( Cropley, 2006 ; Ward, 2007 ; Gabora, 2010 ).

The approach of intertwining cognitive abilities is also developed within cognitive neuroscience by focusing on the intertwining of brain networks ( Beaty et al., 2016 ). In this approach divergent thinking relates to the default brain network. This network operates in defocused or associative mode of thought yielding spontaneous and self-generated cognition ( Beaty et al., 2015 ). Convergent thinking relates to the executive control network operating in focused or analytic modes of thought, yielding updating, shifting, and inhibition ( Benedek et al., 2014 ). Defocused attention theory ( Mendelssohn, 1976 ) states that less creative individuals operate with a more focused attention than do creative individuals. This theory argues that e.g., attending to two things at the same time, might result in one analogy, while attending to four things might yield six analogies ( Martindale, 1999 ).

In the process of shifting back and forth along the spectrum between associative and analytic modes of thinking, the fruits of associative thought become ingredients for analytic thought processes, and vice versa ( Gabora, 2010 ). In this process, mental imagery is involved as one sensory aspect of the human ability to gather and process information ( Jung and Haier, 2013 ). Mental imagery is fed by scenes in the environment that provide crucial visual clues for creative problem solving and actuates the need for sketching ( Verstijnen et al., 2001 ).

Creative problem solving processes often involve an interactive relationship between imagining, sketching, and evaluating the result of the sketch ( van Leeuwen et al., 1999 ). This interactive process evolves within a type of imagery called “visual reasoning” where forms and shapes are manipulated in order to specify the configurations and properties of the design entities ( Goldschmidt, 2013 ). The originality of inventions is predicted by the application of visualization, whereas their practicality is predicted by the vividness of imagery ( Palmiero et al., 2015 ). Imaginative thought processes emerge from our conceptual knowledge of the world that is represented in our semantic memory system. In constrained divergent thinking, the neural correlates of this semantic memory system partially overlap with those of the creative cognition system ( Abraham and Bubic, 2015 ).

Studies of convergent and divergent thinking abilities have yielded innumerable valuable insights on the cognitive and neurological aspects involved, e.g., reaction times, strategies, brain areas involved, mental representations, and short and long time memory components. Studies on the relationship between both constructs suggest that it is unlikely that individuals employ similar cognitive strategies when solving more convergent than more divergent thinking tasks ( Jaušovec, 2000 ). However, to arrive at a quality formulation the creative process cannot do without the application of both, convergent and divergent thinking abilities (e.g., Kaufmann, 2003 ; Runco, 2003 ; Sternberg, 2005 ; Dietrich, 2007 ; Cropley and Cropley, 2008 ; Silvia et al., 2013 ; Jung, 2014 ).

When it is our aim to study the networks addressed by the intertwining of convergent and divergent thinking processes that are considered to operate when new, original, and yet appropriate solutions are generated, then traditional thinking tests like intelligence tests and creativity tests are not appropriate; they yield processes related to the definition of one or the other type of construct.

Creative Reasoning Task

According to the new insights gained in cognition research, we need tasks that are developed with the aim to instigate precisely the kind of thinking processes we are looking for. Tasks should also provide a method of scoring independently the contribution of convergent and divergent thinking. As one possible solution for such tasks we present the Creative Reasoning Task (CRT; Jaarsveld, 2007 ; Jaarsveld et al., 2010 , 2012 , 2013 ).

The CRT presents participants with an empty 3 × 3 matrix and asks them to fill it out, as original and complex as possible, by creating components and the relationships that connect them. The created matrix can, in principle, be solved by another person. The creation of components is entirely free, as is the generation of the relationships that connects them into a completed pattern. Created matrices are scored with two sub scores; Relations , which scores the logical complexity of a matrix and is, therefore, considered a measure for convergent thinking, and Components and Specifications , which scores the originality, fluency, and flexibility and, therefore, is considered an indication for divergent thinking (for a more detailed description of the score method, see Appendix 1 in Supplementary Material).

Psychometric studies with the CRT showed, firstly, that convergent and divergent thinking abilities apply within this task and can be assessed independently. The CRT sub score Relations correlated with the Standard Progressive Matrices test (SPM) and the CRT sub score Components and Specifications correlated with a standard creativity test (TCT–DP, Test of Creative Thinking–Drawing Production; Urban and Jellen, 1995 ; Jaarsveld et al., 2010 , 2012 , 2013 ). Studies further showed that, although a correlation was observed for the intelligence and creativity test scores, no correlation was observed between the CRT sub scores relating to intelligent and creative performances ( Jaarsveld et al., 2012 , 2013 ; for further details about the CRT’s objectivity, validity, and reliability, see Appendix 2 in Supplementary Material).

Reasoning in creative thinking can be defined as the involvement of executive/convergent abilities in the inhibition of ideas and the updating of information ( Benedek et al., 2014 ). Jung (2014) describes a dichotomy for cognitive abilities with at one end the dedicated system that relies on explicit and conscious knowledge and at the other end the improvisational system that relies more upon implicit or unconscious knowledge systems. The link between explicit and implicit systems can actually be traced back to Kris’ psychoanalytic approach to creativity dating from the 1950s. The implicit system refers to Kris’ primary process of adaptive regression, where unmodulated thoughts intrude into consciousness; the explicit system refers to the secondary process, where the reworking and transformation of primary process material takes place through reality-oriented and ego-controlled thinking ( Sternberg and Lubart, 1999 ). The interaction between explicit and implicit systems can be seen to form the basis of creative reasoning, i.e., the cognitive ability to solve problems in an effective and adaptive way. This interaction evolved as a cognitive mechanism when human survival depended on finding effective solutions to both common and novel problem situations ( Gabora and Kaufman, 2010 ). Creative reasoning solves that minority of problems that are unforeseen and yet of high adaptability ( Jung, 2014 ).

Hence, common tests are insufficient when it comes to solving problems that are unforeseen and yet of high adaptability, because they present problems that are either unforeseen and measure certain abilities contained in the construct of creativity or they address adaptability and measure certain abilities contained in the construct of intelligence. The CRT presents participants with a problem that they could not have foreseen; the form is blank and offers no stimuli. All tests, even creativity tests, present participants with some kind of stimuli. The CRT addresses adaptability; to invent from scratch a coherent structure that can be solved by another person, like creating a crossword puzzle. Problems, that are unforeseen and of high adaptability, are solved by the application of abilities from both constructs.

Neuroscience of Creative Cognition

Studies in neuroscience showed that cognition operating in ill-defined problem space not only applies divergent thinking but also benefits from additional convergent operations ( Gabora, 2010 ; Jung, 2014 ). Understanding creative cognition may be advanced when we study the flow of information among brain areas ( Jung et al., 2010 ).

In a cognitive neuroscience study with the CRT we focused on the cognitive process evolving within this task. Participants performed the CRT while EEG alpha activity was registered. EEG alpha synchronization in frontal areas is understood as an indication of top-down control ( Cooper et al., 2003 ). When observed in frontal areas, for divergent and convergent thinking tasks, it may not reflect a brain state that is specific for creative cognition but could be attributed to the high processing demands typically involved in creative thinking ( Benedek et al., 2011 ). Top-down control, relates to volitionally focusing attention to task demands ( Buschman and Miller, 2007 ). That this control plays a role in tasks with an ill-defined problem space showed when electroencephalography (EEG) alpha synchronization was stronger for individuals engaged in creative ideation tasks compared to an intelligence related tasks ( Fink et al., 2007 , 2009 ; Fink and Benedek, 2014 ). This activation was also found for the CRT; task related alpha synchronization showed that convergent thinking was integrated in the divergent thinking processes. Analyzes of the stages in the CRT process showed that this alpha synchronization was especially visible at the start of the creative process at prefrontal and frontal sites when information processing was most demanding, i.e., due to multiplicity of ideas, and it was visible at the end of the process, due to narrowing down of alternatives ( Jaarsveld et al., 2015 ).

A functional magnetic resonance imaging (fMRI) study ( Beaty et al., 2015 ) with a creativity task in which cognition had to meet specific constraints, showed the networks involved. The default mode network which drives toward abstraction and metaphorical thinking and the executive control network driving toward certainty ( Jung, 2014 ). Control involves not only maintenance of patterns of activity that represent goals and the means to achieve those ( Miller and Cohen, 2001 ), but also their voluntary suppression when no longer needed, as well as the flexible shift between different goals and mental sets ( Abraham and Windmann, 2007 ). Attention can be focused volitionally by top-down signals derived from task demands and automatically by bottom-up signals from salient stimuli ( Buschman and Miller, 2007 ). Intertwining between top-down and bottom-up attention processes in creative cognition ensures a broadening of attention in free associative thinking ( Abraham and Windmann, 2007 ).

These studies support and enhance the findings of creative cognition research in showing that the generation of original and applicable ideas involves an intertwining between different abilities, networks, and attention processes.

Problem Space

A problem space is an abstract representation, in the mind of the problem solver, of the encountered problem and of the asked for solution ( Simon and Newell, 1971 ; Simon, 1973 ; Hayes and Flowers, 1986 ; Kulkarni and Simon, 1988 ; Runco, 2007 ). The space that comes with a certain problem can, according to the constraints that are formulated for the solution, be labeled well-defined or ill-defined ( Simon and Newell, 1971 ). Consequently, the original problems are labeled closed and open problems, respectively ( Jaušovec, 2000 ).

A problem space contains all possible states that are accessible to the problem solver from the initial state , through iterative application of transformation rules , to the goal state ( Newell and Simon, 1972 ; Anderson, 1983 ). The initial state presents the problem solver with a task description that defines which requirements a solution has to answer. The goal state represents the solution. The proposed solution is a product of the application of transformation rules (algorithms and heuristics) on a series of successive intermediate solutions. The proposed solution is also a product of the iterative evaluations of preceding solutions and decisions based upon these evaluations ( Boden, 1990 ; Gabora, 2002 ; Jaarsveld and van Leeuwen, 2005 ; Goldschmidt, 2014 ). Whether all possible states need to be passed through depends on the problem space being well or ill-defined and this, in turn, depends on the character of the task descriptions.

When task descriptions clearly state which requirements a solution has to answer then the inferences made will show little idiosyncratic aspects and will adhere to the task constraints. As a result, fewer options for alternative paths are open to the problem solver and search for a solution evolves in a well-defined space. Vice versa, when task or problem descriptions are fuzzy and under specified, the problem solver’s inferences are more idiosyncratic; the resulting process will evolve within an ill-defined space and will contain more generative-evaluative cycles in which new goals are set, and the cycle is repeated ( Dennett, 1978 , as cited in Gabora, 2002 , p. 126).

Tasks that evolve in defined problem space are, e.g., traditional intelligence tests (e.g., Wechsler Adult Intelligence Scale, WAIS; and SPM, Raven , 1938/1998 ). The above tests consist of different types of questions, each testing a different component of intelligence. They are used in test practice to assess reasoning abilities in diverse domains, such as, abstract, logical, spatial, verbal, numerical, and mathematical domains. These tests have clearly stated task descriptions and each item has one and only one correct solution that has to be generated from memory or chosen from a set of alternatives, like in multiple choice formats. Tests can be constructed to assess crystallized or fluid intelligence. Crystallized intelligence represents abilities acquired through learning, practice, and exposure to education, while fluid intelligence represents a more basic capacity that is valuable to reasoning and problem solving in contexts not necessarily related to school education ( Carroll, 1982 ).

Tasks that evolve in ill-defined problem space are, e.g., standard creativity tests. These types of test ask for a multitude of ideas to be generated in association with a given item or situation (e.g., “think of as many titles for this story”). Therefore, they are also labeled as divergent thinking test. Although they assess originality, fluency, flexibility of responses, and elaboration, they are not constructed, however, to score appropriateness or applicability. Divergent thinking tests assess one limited aspect of what makes an individual creative. Creativity depends also on variables like affect and intuition; therefore, divergent thinking can only be considered an indication of an individual’s creative potential ( Runco, 2008 ). More precisely, divergent thinking explains just under half of the variance in adult creative potential, which is more than three times that of the contribution of intelligence ( Plucker, 1999 , p. 103). Creative achievement , by contrast, is commonly assessed by means of self-reports such as biographical questionnaires in which participants indicate their achievement across various domains (e.g., literature, music, or theater).

Studies with the CRT showed that problem space differently affects processing of and comprehension of relationships between components. Problem space did not affect the ability to process complex information. This ability showed equal performance in well and ill-defined problem spaces ( Jaarsveld et al., 2012 , 2013 ). However, problem space did affect the comprehension of relationships, which showed in the different frequencies of relationships solved and created ( Jaarsveld et al., 2010 , 2012 ). Problem space also affected the neurological activity as displayed when individuals solve open or closed problems ( Jaušovec, 2000 ).

Problem space further affected trends over grade levels of primary school children for relationships solved in well-defined and applied in ill-defined problem space. Only one of the 12 relationships defined in the CRT, namely Combination, showed an increase with grade for both types of problem spaces ( Jaarsveld et al., 2013 ). In the same study, cognitive development in the CRT showed in the shifts of preference for a certain relationship. These shifts seem to correspond to Piaget’s developmental stages ( Piaget et al., 1977 ; Siegler, 1998 ) which are in evidence in the CRT, but not in the SPM ( Jaarsveld et al., 2013 ).

Design Problems

A sub category of problems with an ill-defined problem space are represented by design problems. In contrast to divergent thinking tasks that ask for the generation of a multitude of ideas, in design tasks interim ideas are nurtured and incrementally developed until they are appropriate for the task. Ideas are rarely discarded and replaced with new ideas ( Goel and Pirolli, 1992 ). The CRT could be considered a design problem because it yields (a) one possible solution and (b) an iterative thinking process that involves the realization of a vague initial idea. In the CRT a created matrix, which is a closed problem, is created within an ill-defined problem space. Design problems can be found, e.g., in engineering, industrial design, advertising, software design, and architecture ( Sakar and Chakrabarti, 2013 ), however, they can also be found in the arts, e.g., poetry, sculpting, and dance geography.

These complex problems are partly determined by unalterable needs, requirements and intentions but the major part of the design problem is undetermined ( Dorst, 2004 ). This author points out that besides containing an original and a functional value, these types of problems contain an aesthetic value. He further states that the interpretation of the design problem and the creation and selection of possible suitable solutions can only be decided during the design process on the basis of proposals made by the designer.

In design problems the generation stage may be considered a divergent thinking process. However, not in the sense that it moves in multiple directions or generates multiple possibilities as in a divergent thinking tests, but in the sense that it unrolls by considering an initially vague idea from different perspectives until it comes into focus and requires further processing to become viable. These processes can be characterized by a set of invariant features ( Goel and Pirolli, 1992 ), e.g., structuring. iteration , and coherence .

Structuring of the initial situation is required in design processes before solving can commence. The problem contains little structured and clear information about its initial state and about the requirements of its solution. Therefore, design problems allow or even require re-interpretation of transformation rules; for instance, rearranging the location of furniture in a room according to a set of desirable outcomes. Here one uncovers implicit requirements that introduce a set of new transformations and/or eliminate existing ones ( Barsalou, 1992 ; Goel and Pirolli, 1992 ) or, when conflicting requirements arise, one creates alternatives and/or introduces new trade-offs between the conflicting constraints ( Yamamoto et al., 2000 ; Dorst, 2011 ).

A second aspect of design processes is their iterative character. After structuring and planning a vague idea emerges, which is the result of the merging of memory items. A vague idea is a cognitive structure that, halfway the creative process is still ill defined and, therefore, can be said to exist in a state of potentiality ( Gabora and Saab, 2011 ). Design processes unroll in an iterative way by the inspection and adjustment of the generated ideas ( Goldschmidt, 2014 ). New meanings are created and realized while the creative mind imposes its own order and meaning on the sensory data and through creative production furthers its own understanding of the world ( Arnheim , 1962/1974 , as cited in Grube and Davis, 1988 , pp. 263–264).

A third aspect of design processes is coherence. Coherence theories characterize coherence in, for instance, philosophical problems and psychological processes, in terms of maximal satisfaction of multiple constraints and compute coherence by using, a.o., connectionist algorithms ( Thagard and Verbeurgt, 1998 ). Another measure of coherence is characterized as continuity in design processes. This measure was developed for a design task ( Jaarsveld and van Leeuwen, 2005 ) and calculated by the occurrence of a given pair of objects in a sketch, expressed as a percentage of all the sketches of a series. In a series of sketches participants designed a logo for a new soft drink. Design series strong in coherence also received a high score for their final design, as assessed by professionals in various domains. Indicating that participants with a high score for the creative quality of their final sketch seemed better in assessing their design activity in relation to the continuity in the process and, thereby, seemed better in navigating the ill-defined space of a design problem ( Jaarsveld and van Leeuwen, 2005 ). In design problems the quality of cognitive production depends, in part, on the abilities to reflect on one’s own creative behavior ( Boden, 1996 ) and to monitor how far along in the process one is in solving it ( Gabora, 2002 ). Hence, design problems are especially suited to study more complex problem solving processes.

Knowledge Domain

Knowledge domain represents disciplines or fields of study organized by general principles, e.g., domains of various arts and sciences. It contains accumulated knowledge that can be divided in diverse content domains, and the relevant algorithms and heuristics. We also speak of knowledge domains when referring to, e.g., visuo-spatial and verbal domains. This latter differentiation may refer to the method by which performance in a certain knowledge domain is assessed, e.g., a visuo-spatial physics task that assesses the content domain of the workings of mass and weights of objects.

In comparing tests results, we should keep in mind that apart from reflecting cognitive processes evolving in different problem spaces, the results also arise from cognition operating on different knowledge domains. We argue that, the still contradictory and inconclusive discussion about the relationship between intelligence and creativity ( Silvia, 2008 ), should involve the issue of knowledge domain.

Intelligence tests contain items that pertain to, e.g., verbal, abstract, mechanical and spatial reasoning abilities, while their content mostly operates on knowledge domains that are related to contents contained in school curricula. Items of creativity tests, by contrast, pertain to more idiosyncratic knowledge domains, their contents relating to associations between stored personal experiences ( Karmiloff-Smith, 1992 ). The influence of knowledge domain on the relationships between different test scores was already mentioned by Guilford (1956 , p. 169). This author expected a higher correlation between scores from a typical intelligence test and a divergent thinking test than between scores from two divergent thinking tests because the former pair operated on identical information and the latter pair on different information.

Studies with the CRT showed that when knowledge domain is controlled for, the development of intelligence operating in ill-defined problem space does not compare to that of traditional intelligence but develops more similarly to the development of creativity ( Welter et al., in press ).

Relationship Intelligence and Creativity

The Threshold theory ( Guilford, 1967 ) predicts a relationship between intelligence and creativity up to approximately an intelligence quotient (IQ) level of 120 but not beyond ( Lubart, 2003 ; Runco, 2007 ). Threshold theory was corroborated when creative potential was found to be related to intelligence up to certain IQ levels; however, the theory was refuted, when focusing on achievement in creative domains; it showed that creative achievement benefited from higher intelligence even at fairly high levels of intellectual ability ( Jauk et al., 2013 ).

Distinguishing between subtypes of general intelligence known as fluent and crystallized intelligence ( Cattell, 1967 ), Sligh et al. (2005) observed an inverse threshold effect with fluid IQ: a correlation with creativity test scores in the high IQ group but not in the average IQ group. Also creative achievement showed to be affected by fluid intelligence ( Beaty et al., 2014 ). Intelligence, defined as fluid IQ, verbal fluency, and strategic abilities, showed a higher correlation with creativity scores ( Silvia, 2008 ) than when defined as crystallized intelligence. Creativity tests, which involved convergent thinking (e.g., Remote Association Test; Mednick, 1962 ) showed higher correlations with intelligence than ones that involved only divergent thinking (e.g., the Alternate Uses Test; Guilford et al., 1978 ).

That the Remote Association test also involves convergent thinking follows from the instructions; one is asked, when presented with a stimulus word (e.g., table) to produce the first word one thinks of (e.g., chair). The word pair table–chair is a common association, more remote is the pair table–plate, and quite remote is table–shark. According to Mednick’s theory (a) all cognitive work is done essentially by combining or associating ideas and (b) individuals with more commonplace associations have an advantage in well-defined problem spaces, because the class of relevant associations is already implicit in the statement of the problem ( Eysenck, 2003 ).

To circumvent the problem of tests differing in knowledge domain, one can develop out of one task a more divergent and a more convergent thinking task by asking, on the one hand, for the generation of original responses, and by asking, on the other hand, for more common responses ( Jauk et al., 2012 ). By changing the instruction of a task, from convergent to divergent, one changes the constraints the solution has to answer and, thereby, one changes for cognition its freedom of operation ( Razumnikova et al., 2009 ; Limb, 2010 ; Jauk et al., 2012 ). However, asking for more common responses is still a divergent thinking task because it instigates a generative and ideational process.

Indeed, studying the relationship between intelligence and creativity with knowledge domain controlled for yielded different results as defined in the Threshold theory. A study in which knowledge domain was controlled for showed, firstly, that intelligence is no predictor for the development of creativity ( Welter et al., 2016 ). Secondly, that the relationship between scores of intelligence and creativity tests as defined under the Threshold theory was only observed in a small subset of primary school children, namely, female children in Grade 4 ( Welter et al., 2016 ). We state that relating results of operations yielded by cognitive abilities performing in defined and in ill-defined problem spaces can only be informative when it is ensured that cognitive processes also operate on an identical knowledge domain.

Intertwining of Cognitive Abilities

Eysenck (2003) observed that there is little justification for considering the constructs of divergent and convergent thinking in categorical terms in which one construct excludes the other. In processes that yield original and appropriate solutions convergent and divergent thinking both operate on the same large knowledge base and the underlying cognitive processes are not entirely dissimilar ( Eysenck, 2003 , p. 110–111).

Divergent thinking is especially effective when it is coupled with convergent thinking ( Runco, 2003 ; Gabora and Ranjan, 2013 ). A design problem study ( Jaarsveld and van Leeuwen, 2005 ) showed that divergent production was active throughout the design, as new meanings are continuously added to the evolving structure ( Akin, 1986 ), and that convergent production was increasingly important toward the end of the process, as earlier productions are wrapped up and integrated in the final design. These findings are in line with the assumptions of Wertheimer (1945/1968) who stated that thinking within ill-defined problem space is characterized by two points of focus; one is to work on the parts, the other to make the central idea clearer.

Parallel to the discussion about the intertwining of convergent and divergent thinking abilities in processes that evolve in ill-defined problem space we find the discussion about how intelligence may facilitate creative thought. This showed when top-down cognitive control advanced divergent processing in the generation of original ideas and a certain measure of cognitive inhibition advanced the fluency of idea generation ( Nusbaum and Silvia, 2011 ). Fluid intelligence and broad retrieval considered as intelligence factors in a structural equation study contributed both to the production of creative ideas in a metaphor generation task ( Beaty and Silvia, 2013 ). The notion that creative thought involves top-down, executive processes showed in a latent variable analysis where inhibition primarily promoted the fluency of ideas, and intelligence promoted their originality ( Benedek et al., 2012 ).

Definitions of the Constructs Intelligence and Creativity

The various definitions of the constructs of intelligence and creativity show a problematic overlap. This overlap stems from the enormous endeavor to unanimously agree on valid descriptions for each construct. Spearman (1927) , after having attended many symposia that aimed at defining intelligence, stated that “in truth, ‘intelligence’ has become a mere vocal sound, a word with so many meanings that finally it has none” (p. 14).

Intelligence is expressed in terms of adaptive, goal-directed behavior; and the subset of such behavior that is labeled “intelligent” seems to be determined in large part by cultural or societal norms ( Sternberg and Salter, 1982 ). The development of the IQ measure is discussed by Carroll (1982) : “Binet (around 1905) realized that intelligent behavior or mental ability can be ranged along a scale. Not much later, Stern (around 1912) noticed that, as chronological age increased, variation in mental age changes proportionally. He developed the IQ ratio, whose standard deviation would be approximately constant over chronological age if mental age was divided by chronological age. With the development of multiple-factor-analyses (Thurstone, around 1935) it could be shown that intelligence is not a simple unitary trait because at least seven somewhat independent factors of mental ability were identified.”

Creativity is defined as a combined manifestation of novelty and usefulness ( Jung et al., 2010 ). Although it is identified with divergent thinking, and performance on divergent thinking tasks predicts, e.g., quantity of creative achievements ( Torrance, 1988 , as cited in Beaty et al., 2014 ) and quality of creative performance ( Beaty et al., 2013 ), it cannot be identified uniquely with divergent thinking.

Divergent thinking often leads to highly original ideas that are honed to appropriate ideas by evaluative processes of critical thinking, and valuative and appreciative considerations ( Runco, 2008 ). Divergent thinking tests should be more considered as estimates of creative problem solving potential rather than of actual creativity ( Runco, 1991 ). Divergent thinking is not specific enough to help us understand what, exactly, are the mental processes—or the cognitive abilities—that yield creative thoughts ( Dietrich, 2007 ).

Although current definitions of intelligence and creativity try to determine for each separate construct a unique set of cognitive abilities, analyses show that definitions vary in the degree to which each includes abilities that are generally considered to belong to the other construct ( Runco, 2003 ; Jaarsveld et al., 2012 ). Abilities considered belonging to the construct of intelligence such as hypothesis testing, inhibition of alternative responses, and creating mental images of new actions or plans are also considered to be involved in creative thinking ( Fuster, 1997 , as cited in Colom et al., 2009 , p. 215). The ability, for instance, to evaluate , which is considered to belong to the construct of intelligence and assesses the match between a proposed solution and task constraints, has long been considered to play a role in creative processes that goes beyond the mere generation of a series of ideas as in creativity tasks ( Wallas, 1926 , as cited in Gabora, 2002 , p. 1; Boden, 1990 ).

The Geneplore model ( Finke et al., 1992 ) explicitly models this idea; after stages in which objects are merely generated, follow phases in which an object’s utility is explored and estimated. The generation phase brings forth pre inventive objects, imaginary objects that are generated without any constraints in mind. In exploration, these objects are evaluated for their possible functionalities. In anticipating the functional characteristics of generated ideas, convergent thinking is needed to apprehend the situation, make evaluations ( Kozbelt, 2008 ), and consider the consequences of a chosen solution ( Goel and Pirolli, 1992 ). Convergent reasoning in creativity tasks invokes criteria of functionality and appropriateness ( Halpern, 2003 ; Kaufmann, 2003 ), goal directedness and adaptive behavior ( Sternberg, 1982 ), as well as the abilities of planning and attention. Convergent thinking stages may even require divergent thinking sub processes to identify restrictions on proposed new ideas and suggest requisite revision strategies ( Mumford et al., 2007 ). Hence, evaluation, which is considered to belong to the construct of intelligence, is also functional in creative processes.

In contrast, the ability of flexibility , which is considered to belong to the construct of creativity and denotes an openness of mind that ensures the generation of ideas from different domains, showed, as a factor component for latent divergent thinking, a relationship with intelligence ( Silvia, 2008 ). Flexibility was also found to play an important role in intelligent behavior where it enables us to do novel things smartly in new situations ( Colunga and Smith, 2008 ). These authors studied children’s generalizations of novel nouns and concluded that if we are to understand human intelligence, we must understand the processes that make inventiveness. They propose to include the construct of flexibility within that of intelligence. Therefore, definitions of the constructs we are to measure affect test construction and the resulting data. However, an overlap between definitions, as discussed, yields a test diversity that makes it impossible to interpret the different findings across studies with any confidence ( Arden et al., 2010 ). Also Kim (2005) concluded that because of differences in tests and administration methods, the observed correlation between intelligence and creativity was negligible. As the various definitions of the constructs of intelligence and creativity show problematic overlap, we propose to circumvent the discussion about which cognitive abilities are assessed by which construct, and to consider both constructs as being involved in one design process. This approach allows us to study the contribution to this process of the various defined abilities, without one construct excluding the other.

Reasoning Abilities

The CRT is a psychometrical tool constructed on the basis of an alternative construct of human cognitive functioning that considers creative reasoning as a thinking process understood as the cooperation between cognitive abilities related to intelligent and creative thinking.

In generating relationships for a matrix, reasoning and more specifically the ability of rule invention is applied. The ability of rule invention could be considered as an extension of the sequence of abilities of rule learning, rule inference, and rule application, implying that creativity is an extension of intelligence ( Shye and Goldzweig, 1999 ). According to this model, we could expect different results between a task assessing abilities of rule learning and rule inference, and a task assessing abilities of rule application. In two studies rule learning and rule inference was assessed with the RPM and rule application was assessed with the CRT. Results showed that from Grades 1 to 4, the frequencies of relationships applied did not correlate with those solved ( Jaarsveld et al., 2010 , 2012 ). Results showed that performance in the CRT allows an insight of cognitive abilities operating on relationships among components that differs from the insight based on performance within the same knowledge domain in a matrix solving task. Hence, reasoning abilities lead to different performances when applied in solving closed as to open problems.

We assume that reasoning abilities are more clearly reflected when one formulates a matrix from scratch; in the process of thinking and drawing one has, so to speak, to solve one’s own matrix. In doing so one explains to oneself the relationship(s) realized so far and what one would like to attain. Drawing is thinking aloud a problem and aids the designer’s thinking processes in providing some “talk-back” ( Cross and Clayburn Cross, 1996 ). Explanatory activity enhances learning through increased depth of processing ( Siegler, 2005 ). Analyzing explanations of examples given with physics problems showed that they clarify and specify the conditions and consequences of actions, and that they explicate tacit knowledge; thereby enhancing and completing an individual’s understanding of principles relevant to the task ( Chi and VanLehn, 1991 ). Constraint of the CRT is that the matrix, in principle, can be solved by another person. Therefore, in a kind of inner explanatory discussion, the designer makes observations of progress, and uses evaluations and decisions to answer this constraint. Because of this, open problems where certain constraints have to be met, constitute a powerful mechanism for promoting understanding and conceptual advancement ( Chi and VanLehn, 1991 ; Mestre, 2002 ; Siegler, 2005 ).

Convergent and divergent thinking processes have been studied with a variety of intelligence and creativity tests, respectively. Relationships between performances on these tests have been demonstrated and a large number of research questions have been addressed. However, the fact that intelligence and creativity tests vary in the definition of their construct, in their problem space, and in their knowledge domain, poses methodological problems regarding the validity of comparisons of test results. When we want to focus on one cognitive process, e.g., intelligent thinking, and on its different performances in well or ill-defined problem situations, we need pairs of tasks that are constructed along identical definitions of the construct to be assessed, that differ, however, in the description of their constraints but are identical regarding their knowledge domain.

One such possible pair, the Progressive Matrices Test and the CRT was suggested here. The CRT was developed on the basis of creative reasoning , a construct that assumes the intertwining of intelligent and creativity related abilities when looking for original and applicable solutions. Matched with the Matrices test, results indicated that, besides similarities, intelligent thinking also yielded considerable differences for both problem spaces. Hence, with knowledge domain controlled, and only differences in problem space remaining, comparison of data yielded new results on intelligence’s operations. Data gathered from intelligence and creativity tests, whether they are performance scores or physiological measurements on the basis of, e.g., EEG, and fMRI methods, are reflections of cognitive processes performing on a certain test that was constructed on the basis of a certain definition of the construct it was meant to measure. Data are also reflections of the processes evolving within a certain problem space and of cognitive abilities operating on a certain knowledge domain.

Data can unhide brain networks that are involved in the performance of certain tasks, e.g., traditional intelligence and creativity tests, but data will always be related to the characteristics of the task. The characteristics of the task, such as problem space and knowledge domain originated at the construction of the task, and the construction, on its turn, is affected by the definition of the construct the task is meant to measure.

Here we present the CRT as one possible solution for the described problems in cognition research. However, for research on relationships among test scores other pairs of tests are imaginable, e.g., pairs of tasks operating on the same domain where one task has a defined problem space and the other one an ill-defined space. It is conceivable that pairs of test could operate, besides on the domain of mathematics, on content of e.g., visuo-spatial, verbal, and musical domains. Pairs of test have been constructed by changing the instruction of a task; instructions instigated a more convergent or a more a divergent mode of response ( Razumnikova et al., 2009 ; Limb, 2010 ; Jauk et al., 2012 ; Beaty et al., 2013 ).

The CRT involves the creation of components and their relationships for a 3 × 3 matrix. Hence, matrices created in the CRT are original in the sense that they all bear individual markers and they are applicable in the sense, that they can, in principle, be solved by another person. We showed that the CRT instigates a real design process; creators’ cognitive abilities are wrapped up in a process that should produce a closed problem within an ill-defined problem space.

For research on the relationship among convergent and divergent thinking, we need pairs of test that differ in the problem spaces related to each test but are identical in the knowledge domain on which cognition operates. The test pair of RPM and CRT provides such a pair. For research on the intertwining of convergent and divergent thinking, we need tasks that measure more than tests assessing each construct alone. We need tasks that are developed on the definition of intertwining cognitive abilities; the CRT is one such test.

Hence, we hope to have sufficiently discussed and demonstrated the importance of the three test features, construct definition, problem space, and knowledge domain, for research questions in creative cognition research.

Author Contributions

All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00134/full#supplementary-material

• Abraham A., Bubic A. (2015). Semantic memory as the root of imagination. Front. Psychol. 6 : 325 10.3389/fpsyg.2015.00325 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Abraham A., Windmann S. (2007). Creative cognition: the diverse operations and the prospect of applying a cognitive neuroscience perspective. Methods 42 38–48. 10.1016/j.ymeth.2006.12.007 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Akin O. (1986). Psychology of Architectural Design London: Pion. [ Google Scholar ]
• Anderson J. R. (1983). The Architecture of Cognition Cambridge, MA: Harvard University Press. [ Google Scholar ]
• Arden R., Chavez R. S., Grazioplene R., Jung R. E. (2010). Neuroimaging creativity: a psychometric view. Behav. Brain Res. 214 143–156. 10.1016/j.bbr.2010.05.015 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Arnheim R. (1962/1974). Picasso’s Guernica Berkeley: University of California Press. [ Google Scholar ]
• Barsalou L. W. (1992). Cognitive Psychology: An Overview for Cognitive Scientists Hillsdale, NJ: LEA. [ Google Scholar ]
• Beaty R. E., Benedek M., Silvia P. J., Schacter D. L. (2016). Creative cognition and brain network dynamics. Trends Cogn. Sci. 20 87–95. 10.1016/j.tics.2015.10.004 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Beaty R. E., Kaufman S. B., Benedek M., Jung R. E., Kenett Y. N., Jauk E., et al. (2015). Personality and complex brain networks: the role of openness to experience in default network efficiency. Hum. Brain Mapp. 37 773–777. 10.1002/hbm.23065 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Beaty R. E., Nusbaum E. C., Silvia P. J. (2014). Does insight problem solving predict real-world creativity? Psychol. Aesthet. Creat. Arts 8 287–292. 10.1037/a0035727 [ CrossRef ] [ Google Scholar ]
• Beaty R. E., Silvia R. E. (2013). Metaphorically speaking: cognitive abilities and the production of figurative language. Mem. Cognit. 41 255–267. 10.3758/s13421-012-0258-5 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Beaty R. E., Smeekens B. A., Silvia P. J., Hodges D. A., Kane M. J. (2013). A first look at the role of domain-general cognitive and creative abilities in jazz improvisation. Psychomusicology 23 262–268. 10.1037/a0034968 [ CrossRef ] [ Google Scholar ]
• Benedek M., Bergner S., Konen T., Fink A., Neubauer A. C. (2011). EEG alpha synchronization is related to top-down processing in convergent and divergent thinking. Neuropsychologia 49 3505–3511. 10.1016/j.neuropsychologia.2011.09.004 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Benedek M., Franz F., Heene M., Neubauer A. C. (2012). Differential effects of cognitive inhibition and intelligence on creativity. Pers. Individ. Dif. 53 480–485. 10.1016/j.paid.2012.04.014 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Benedek M., Jauk E., Sommer M., Arendasy M., Neubauer A. C. (2014). Intelligence, creativity, and cognitive control: the common and differential involvement of executive functions in intelligence and creativity. Intelligence 46 73–83. 10.1016/j.intell.2014.05.007 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Boden M. A. (1990). The Creative Mind: Myths and Mechanisms London: Abacus. [ Google Scholar ]
• Boden M. A. (1996). Artificial Intelligence New York, NY: Academic. [ Google Scholar ]
• Buschman T. J., Miller E. K. (2007). Top-down versus bottom-up control of attention in the prefrontal and posterior parietal cortices. Science 315 1860–1862. 10.1126/science.1138071 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Carroll J. B. (1982). “The measurement of Intelligence,” in Handbook of Human Intelligence , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 29–120. [ Google Scholar ]
• Cattell R. B. (1967). The theory of fluid and crystallized general intelligence checked at the 5-6 year-old level. Br. J. Educ. Psychol. 37 209–224. 10.1111/j.2044-8279.1967.tb01930.x [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Chi M. T. H. (1997). “ Creativity: Shifting across ontological categories flexibly ,” in Creative Thought: An Investigation of Conceptual Structures and Processes , eds Ward T., Smith S., Vaid J. (Washington, DC: American Psychological Association; ), 209–234. [ Google Scholar ]
• Chi M. T. H., VanLehn K. A. (1991). The content of physics self-explanations. J. Learn. Sci. 1 69–105. 10.1207/s15327809jls0101_4 [ CrossRef ] [ Google Scholar ]
• Christensen B. T. (2007). The relationship of analogical distance to analogical function and preinventive structure: the case of engineering design. Mem. Cogn. 35 29–38. 10.3758/BF03195939 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Colom R., Haier R. J., Head K., Álvarez-Linera J., Quiroga M. A., Shih P. C., et al. (2009). Gray matter correlates of fluid, crystallized, and spatial intelligence: testing the P-FIT model. Intelligence 37 124–135. 10.1016/j.intell.2008.07.007 [ CrossRef ] [ Google Scholar ]
• Colunga E., Smith L. B. (2008). Flexibility and variability: essential to human cognition and the study of human cognition. New Ideas Psychol. 26 158–192. 10.1016/j.newideapsych.2007.07.012 [ CrossRef ] [ Google Scholar ]
• Cooper N. R., Croft R. J., Dominey S. J. J., Burgess A. P., Gruzelier J. H. (2003). Paradox lost? Exploring the role of alpha oscillations during externally vs. internally directed attention and the implications for idling and inhibition hypotheses. Int. J. Psychophysiol. 47 65–74. 10.1016/S0167-8760(02)00107-1 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Cropley A. (2006). In praise of convergent thinking. Creat. Res. J. 18 391–404. 10.1207/s15326934crj1803_13 [ CrossRef ] [ Google Scholar ]
• Cropley A., Cropley D. (2008). Resolving the paradoxes of creativity: an extended phase model. Camb. J. Educ. 38 355–373. 10.1080/03057640802286871 [ CrossRef ] [ Google Scholar ]
• Cross N., Clayburn Cross A. (1996). Winning by design: the methods of Gordon Murray, racing car designer. Des. Stud. 17 91–107. 10.1016/0142-694X(95)00027-O [ CrossRef ] [ Google Scholar ]
• Dennett D. (1978). Brainstorms: Philosophical Essays on Mind and Psychology Montgomery, VT: Bradford Books. [ Google Scholar ]
• Dietrich A. (2007). Who’s afraid of a cognitive neuroscience of creativity? Methods 42 22–27. 10.1016/j.ymeth.2006.12.009 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Dorst K. (2004). The problem of design problems: Problem solving and design expertise. J. Design Res. 4 10.1504/JDR.2004.009841 [ CrossRef ] [ Google Scholar ]
• Dorst K. (2011). The core of ‘design thinking’ and its application. Des. Stud. 32 521–532. 10.1016/j.destud.2011.07.006 [ CrossRef ] [ Google Scholar ]
• Eysenck H. J. (2003). “Creativity, personality and the convergent-divergent continuum,” in Critical Creative Processes , ed. Runco M. A. (Cresskill, NJ: Hampton Press; ), 95–114. [ Google Scholar ]
• Fink A., Benedek M. (2014). EEG alpha power and creative ideation. Neurosci. Biobehav. Rev. 44 111–123. 10.1016/j.neubiorev.2012.12.002 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Fink A., Benedek M., Grabner R. H., Staudt B., Neubauer A. C. (2007). Creativity meets neuroscience: experimental tasks for the neuroscientific study of creative thinking. Methods 42 68–76. 10.1016/j.ymeth.2006.12.001 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Fink A., Grabner R. H., Benedek M., Reishofer G., Hauswirth V., Fally M., et al. (2009). The creative brain: investigation of brain activity during creative problem solving by means of EEG and FMRI. Hum. Brain Mapp. 30 734–748. 10.1002/hbm.20538 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Finke R. A., Ward T. B., Smith S. M. (1992). Creative Cognition: Theory, Research, and Applications Cambridge, MA: MIT Press. [ Google Scholar ]
• Fuster J. M. (1997). Network memory. Trends Neurosci. 20 451–459. 10.1016/S0166-2236(97)01128-4 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Gabora L. (2002). “Cognitive mechanisms underlying the creative process,” in Proceedings of the Fourth International Conference on Creativity and Cognition , eds Hewett T., Kavanagh T. (Loughborough: Loughborough University; ), 126–133. [ Google Scholar ]
• Gabora L. (2010). Revenge of the ‘neurds’: Characterizing creative thought in terms of the structure and dynamics of human memory. Creat. Res. J. 22 1–13. 10.1080/10400410903579494 [ CrossRef ] [ Google Scholar ]
• Gabora L., Kaufman S. B. (2010). “Evolutionary approaches to creativity,” in The Cambridge Handbook of Creativity , eds Kaufman J. S., Sternberg R. J. (Cambridge: Cambridge University Press; ), 279–300. [ Google Scholar ]
• Gabora L., Ranjan A. (2013). “How insight emerges in a distributed, content-addressable memory,” in The Neuroscience of Creativity , eds Bristol A., Vartanian O., Kaufman J. (Cambridge: MIT Press; ), 19–43. [ Google Scholar ]
• Gabora L., Saab A. (2011). “Creative inference and states of potentiality in analogy problem solving,” in Proceedings of the Annual Meeting of the Cognitive Science Society , Boston, MA, 3506–3511. [ Google Scholar ]
• Gentner D. (1983). Structure mapping: a theoretical framework for analogy. Cogn. Sci. 7 155–170. 10.1207/s15516709cog0702_3 [ CrossRef ] [ Google Scholar ]
• Getzels J. W. (1975). Problem finding and the inventiveness of solutions. J. Creat. Behav. 9 12–18. 10.1002/j.2162-6057.1975.tb00552.x [ CrossRef ] [ Google Scholar ]
• Getzels J. W. (1987). “Creativity, intelligence, and problem finding: retrospect and prospect,” in Frontiers of Creativity Research: Beyond the Basics , ed. Isaksen S. G. (Buffalo, NY: Bearly Limited; ), 88–102. [ Google Scholar ]
• Getzels J. W., Csikszentmihalyi M. (1976). The Creative Vision: A Longitudinal Study of Problem Finding in Art New York, NY: Wiley. [ Google Scholar ]
• Ghiselin B. (ed.) (1952/1985). The Creative Process Los Angeles: University of California. [ Google Scholar ]
• Goel V., Pirolli P. (1992). The structure of design problem spaces. Cogn. Sci. 16 395–429. 10.1207/s15516709cog1603_3 [ CrossRef ] [ Google Scholar ]
• Goldschmidt G. (2013). “A micro view of design reasoning: two-way shifts between embodiment and rationale,” in Creativity and Rationale: Enhancing Human Experience by Design, Human-Computer Interaction Series , ed. Carroll J. M. (London: Springer Verlag; ). 10.1007/978-1-4471-2_3 [ CrossRef ] [ Google Scholar ]
• Goldschmidt G. (2014). Linkography: Unfolding the Design Process Cambridge, MA: MIT Press. [ Google Scholar ]
• Grube H. E., Davis S. N. (1988). “Inching our way up mount Olympus: The evolving-systems approach to creative thinking,” in The Nature of Creativity , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 243–270. [ Google Scholar ]
• Guilford J. P. (1950). Creativity. Am. Psychol. 5 444–454. 10.1037/h0063487 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Guilford J. P. (1956). The structure of intellect model. Psychol. Bull. 53 267–293. 10.1037/h0040755 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Guilford J. P. (1959). “Traits of creativity,” in Creativity and its Cultivation , ed. Anderson H. H. (New York: Harper; ), 142–161. [ Google Scholar ]
• Guilford J. P. (1967). The Nature of Human Intelligence New York, NY: McGraw-Hill, Inc. [ Google Scholar ]
• Guilford J. P., Christensen P. R., Merrifield P. R., Wilson R. C. (1978). Alternate Uses: Manual of Instructions and Interpretation Orange, CA: Sheridan Psychological Services. [ Google Scholar ]
• Halpern D. F. (2003). “Thinking critically about creative thinking,” in Critical Creative Processes , ed. Runco M. A. (Cresskill, NJ: Hampton Press; ), 189–208. [ Google Scholar ]
• Hayes J. R., Flowers L. S. (1986). Writing research and the writer. Am. Psychol. 41 1106–1113. 10.1037/0003-066X.41.10.1106 [ CrossRef ] [ Google Scholar ]
• Jaarsveld S. (2007). Creative Cognition: New Perspectives on Creative Thinking Kaiserslautern: University of Kaiserslautern Press. [ Google Scholar ]
• Jaarsveld S., Fink A., Rinner M., Schwab D., Benedek M., Lachmann T. (2015). Intelligence in creative processes; an EEG study. Intelligence 49 171–178. 10.1016/j.ijpsycho.2012.02.012 [ CrossRef ] [ Google Scholar ]
• Jaarsveld S., Lachmann T., Hamel R., van Leeuwen C. (2010). Solving and creating Raven Progressive Matrices: reasoning in well and ill defined problem spaces. Creat. Res. J. 22 304–319. 10.1080/10400419.2010.503541 [ CrossRef ] [ Google Scholar ]
• Jaarsveld S., Lachmann T., van Leeuwen C. (2012). Creative reasoning across developmental levels: convergence and divergence in problem creation. Intelligence 40 172–188. 10.1016/j.intell.2012.01.002 [ CrossRef ] [ Google Scholar ]
• Jaarsveld S., Lachmann T., van Leeuwen C. (2013). “The impact of problem space on reasoning: Solving versus creating matrices,” in Proceedings of the 35th Annual Conference of the Cognitive Science Society , eds Knauff M., Pauen M., Sebanz N., Wachsmuth I. (Austin, TX: Cognitive Science Society; ), 2632–2638. [ Google Scholar ]
• Jaarsveld S., van Leeuwen C. (2005). Sketches from a design process: creative cognition inferred from intermediate products. Cogn. Sci. 29 79–101. 10.1207/s15516709cog2901_4 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Jauk E., Benedek M., Dunst B., Neubauer A. C. (2013). The relationship between intelligence and creativity: new support for the threshold hypothesis by means of empirical breakpoint detection. Intelligence 41 212–221. 10.1016/j.intell.2013.03.003 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Jauk E., Benedek M., Neubauer A. C. (2012). Tackling creativity at its roots: evidence for different patterns of EEG alpha activity related to convergent and divergent modes of task processing. Int. J. Psychophysiol. 84 219–225. 10.1016/j.ijpsycho.2012.02.012 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Jaušovec N. (1999). “Brain biology and brain functioning,” in Encyclopedia of Creativity , eds Runco M. A., Pritzker S. R. (San Diego, CA: Academic Press; ), 203–212. [ Google Scholar ]
• Jaušovec N. (2000). Differences in cognitive processes between gifted, intelligent, creative, and average individuals while solving complex problems: an EEG Study. Intelligence 28 213–237. 10.1016/S0160-2896(00)00037-4 [ CrossRef ] [ Google Scholar ]
• Jung R. E. (2014). Evolution, creativity, intelligence, and madness: “here be dragons”. Front. Psychol 5 : 784 10.3389/fpsyg.2014.00784 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Jung R. E., Haier R. J. (2013). “Creativity and intelligence,” in Neuroscience of Creativity , eds Vartanian O., Bristol A. S., Kaufman J. C. (Cambridge, MA: MIT Press; ), 233–254. [ Google Scholar ]
• Jung R. E., Segall J. M., Bockholt H. J., Flores R. A., Smith S. M., Chavez R. S., et al. (2010). Neuroanatomy of creativity. Hum. Brain Mapp. 31 398–409. 10.1002/hbm.20874 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Karmiloff-Smith A. (1992). Beyond Modularity: A Developmental Perspective on Cognitive Science Cambridge, MA: MIT Press. [ Google Scholar ]
• Kaufman J. C. (2015). Why creativity isn’t in IQ tests, why it matters, and why it won’t change anytime soon probably. Intelligence 3 59–72. 10.3390/jintelligence303005 [ CrossRef ] [ Google Scholar ]
• Kaufmann G. (2003). What to measure? A new look at the concept of creativity. Scand. J. Educ. Res. 47 235–251. 10.1080/00313830308604 [ CrossRef ] [ Google Scholar ]
• Kim K. H. (2005). Can only intelligent people be creative? J. Second. Gift. Educ. 16 57–66. [ Google Scholar ]
• Koestler A. (1964). The Act of Creation London: Penguin. [ Google Scholar ]
• Kozbelt A. (2008). Hierarchical linear modeling of creative artists’ problem solving behaviors. J. Creat. Behav. 42 181–200. 10.1002/j.2162-6057.2008.tb01294.x [ CrossRef ] [ Google Scholar ]
• Kulkarni D., Simon H. A. (1988). The processes of scientific discovery: the strategy of experimentation. Cogn. Sci. 12 139–175. 10.1016/j.coph.2009.08.004 [ CrossRef ] [ Google Scholar ]
• Limb C. J. (2010). Your Brain on Improve Available at: http://www.ted.com/talks/charles_limb_your_brain_on_improv [ Google Scholar ]
• Lubart T. I. (2001). Models of the creative process: past, present and future. Creat. Res. J. 13 295–308. 10.1207/S15326934CRJ1334_07 [ CrossRef ] [ Google Scholar ]
• Lubart T. I. (2003). Psychologie de la Créativité. Cursus. Psychologie Paris: Armand Colin. [ Google Scholar ]
• Martindale C. (1999). “Biological basis of creativity,” in Handbook of Creativity , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 137–152. [ Google Scholar ]
• Mednick S. A. (1962). The associative basis of the creative process. Psychol. Rev. 69 220–232. 10.1037/h0048850 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Mendelssohn G. A. (1976). Associational and attentional processes in creative performance. J. Pers. 44 341–369. 10.1111/j.1467-6494.1976.tb00127.x [ CrossRef ] [ Google Scholar ]
• Mestre J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Appl. Dev. Psychol. 23 9–50. 10.1016/S0193-3973(01)00101-0 [ CrossRef ] [ Google Scholar ]
• Miller E. K., Cohen J. D. (2001). An integrative theory of prefrontal cortex function. Annu. Rev. Neurosci. 24 167–202. 10.1146/annurev.neuro.24.1.167 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Mumford M. D., Hunter S. T., Eubanks D. L., Bedell K. E., Murphy S. T. (2007). Developing leaders for creative efforts: a domain-based approach to leadership development. Hum. Res. Manag. Rev. 17 402–417. 10.1016/j.hrmr.2007.08.002 [ CrossRef ] [ Google Scholar ]
• Newell A., Simon H. A. (1972). “The theory of human problem solving,” in Human Problem Solving , eds Newell A., Simon H. (Englewood Cliffs, NJ: Prentice Hall; ), 787–868. [ Google Scholar ]
• Nusbaum E. C., Silvia P. J. (2011). Are intelligence and creativity really so different? Intelligence 39 36–40. 10.1016/j.intell.2010.11.002 [ CrossRef ] [ Google Scholar ]
• Palmiero M., Nori R., Aloisi V., Ferrara M., Piccardi L. (2015). Domain-specificity of creativity: a study on the relationship between visual creativity and visual mental imagery. Front. Psychol. 6 : 1870 10.3389/fpsyg.2015.01870 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Piaget J., Montangero J., Billeter J. (1977). “La formation des correlats,” in Recherches sur L’abstraction Reflechissante I , ed. Piaget J. (Paris: Presse Universitaires de France; ), 115–129. [ Google Scholar ]
• Plucker J. (1999). Is the proof in the pudding? Reanalyses of torrance’s (1958 to present) longitudinal study data. Creat. Res. J. 12 103–114. 10.1207/s15326934crj1202_3 [ CrossRef ] [ Google Scholar ]
• Raven J. C. (1938/1998). Standard Progressive Matrices, Sets A, B, C, D & E Oxford: Oxford Psychologists Press. [ Google Scholar ]
• Razumnikova O. M., Volf N. V., Tarasova I. V. (2009). Strategy and results: sex differences in electrographic correlates of verbal and figural creativity. Hum. Physiol. 35 285–294. 10.1134/S0362119709030049 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Runco M. A. (1991). The evaluative, valuative, and divergent thinking of children. J. Creat. Behav. 25 311–319. 10.1177/1073858414568317 [ CrossRef ] [ Google Scholar ]
• Runco M. A. (2003). “Idea evaluation, divergent thinking, and creativity,” in Critical Creative Processes , ed. Runco M. A. (Cresskill, NJ: Hampton Press; ), 69–94. [ Google Scholar ]
• Runco M. A. (2007). Creativity, Theories and Themes: Research, Development, and Practice New York, NY: Elsevier. [ Google Scholar ]
• Runco M. A. (2008). Commentary: divergent thinking is not synonymous with creativity. Psychol. Aesthet. Creat. Arts 2 93–96. 10.1037/1931-3896.2.2.93 [ CrossRef ] [ Google Scholar ]
• Sakar P., Chakrabarti A. (2013). Support for protocol analyses in design research. Des. Issues 29 70–81. 10.1162/DESI_a_00231 [ CrossRef ] [ Google Scholar ]
• Saraç S., Önder A., Karakelle S. (2014). The relations among general intelligence, metacognition and text learning performance. Educ. Sci. 39 40–53. [ Google Scholar ]
• Shye S., Goldzweig G. (1999). Creativity as an extension of intelligence: Faceted definition and structural hypotheses. Megamot 40 31–53. [ Google Scholar ]
• Shye S., Yuhas I. (2004). Creativity in problem solving. Tech. Rep. 10.13140/2.1.1940.0643 [ CrossRef ] [ Google Scholar ]
• Siegler R. S. (1998). Children’s Thinking , 3rd Edn Upper Saddle River, NJ: Prentice Hall, 28–50. [ Google Scholar ]
• Siegler R. S. (2005). Children’s learning. Am. Psychol. 60 769–778. 10.1037/0003-066X.60.8.769 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Silvia P. J. (2008). Creativity and intelligence revisited: a reanalysis of Wallach and Kogan (1965). Creat. Res. J. 20 34–39. 10.1080/10400410701841807 [ CrossRef ] [ Google Scholar ]
• Silvia P. J., Beaty R. E., Nussbaum E. C. (2013). Verbal fluency and creativity: general and specific contributions of broad retrieval ability (Gr) factors to divergent thinking. Intelligence 41 328–340. 10.1016/j.intell.2013.05.004 [ CrossRef ] [ Google Scholar ]
• Simon H. A. (1973). The structure of ill structured problems. Artif. Intell. 4 1012–1021. 10.1016/0004-3702(73)90011-8 [ CrossRef ] [ Google Scholar ]
• Simon H. A., Newell A. (1971). Human problem solving: state of theory in 1970. Am. Psychol. 26 145–159. 10.1037/h0030806 [ CrossRef ] [ Google Scholar ]
• Sligh A. C., Conners F. A., Roskos-Ewoldsen B. (2005). Relation of creativity to fluid and crystallized intelligence. J. Creat. Behav. 39 123–136. 10.1002/j.2162-6057.2005.tb01254.x [ CrossRef ] [ Google Scholar ]
• Spearman C. (1904). ‘General intelligence,’ objectively determined and measured. Am. J. Psychol. 15 201–293. 10.2307/1412107 [ CrossRef ] [ Google Scholar ]
• Spearman C. (1927). The Abilities of Man London: Macmillan. [ Google Scholar ]
• Sternberg R. J. (1982). “Conceptions of intelligence,” in Handbook of Human Intelligence , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 3–28. [ Google Scholar ]
• Sternberg R. J. (2005). “The WICS model of giftedness,” in Conceptions of Giftedness , 2nd Edn, eds Sternberg R. J., Davidson J. E. (New York, NY: Cambridge University Press; ), 237–243. [ Google Scholar ]
• Sternberg R. J., Lubart T. I. (1999). “The concept of creativity: Prospects and paradigms,” in Handbook of Creativity , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 3–15. [ Google Scholar ]
• Sternberg R. J., Salter W. (1982). “The nature of intelligence and its measurements,” in Handbook of Human Intelligence , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 3–24. [ Google Scholar ]
• Thagard P., Verbeurgt K. (1998). Coherence as constraint satisfaction. Cogn. Sci. 22 l–24. 10.1207/s15516709cog2201_1 [ CrossRef ] [ Google Scholar ]
• Torrance E. P. (1988). “The nature of creativity as manifest in its testing,” in The Nature of Creativity: Contemporary Psychological Perspectives , ed. Sternberg R. J. (New York, NY: Cambridge University Press; ), 43–75. [ Google Scholar ]
• Urban K. K., Jellen H. G. (1995). Test of Creative Thinking – Drawing Production Frankfurt: Swets Test Services. [ Google Scholar ]
• van Leeuwen C., Verstijnen I. M., Hekkert P. (1999). “Common unconscious dynamics underlie uncommon conscious effect: a case study in the iterative nature of perception and creation,” in Modeling Consciousness Across the Disciplines , ed. Jordan J. S. (Lanham, MD: University Press of America; ), 179–218. [ Google Scholar ]
• Vernon P. E. (ed.) (1970). Creativity London: Penguin. [ Google Scholar ]
• Verstijnen I. M., Heylighen A., Wagemans J., Neuckermans H. (2001). “Sketching, analogies, and creativity,” in Visual and Spatial Reasoning in Design, II. Key Centre of Design Computing and Cognition , eds Gero J. S., Tversky B., Purcell T. (Sydney, NSW: University of Sydney; ). [ Google Scholar ]
• Wallas G. (1926). The Art of Thought New York, NY: Harcourt, Brace & World. [ Google Scholar ]
• Ward T. B. (2007). Creative cognition as a window on creativity. Methods 42 28–37. 10.1016/j.ymeth.2006.12.002 [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Webb Young J. (1939/2003). A Technique for Producing Ideas New York, NY: McGraw-Hill. [ Google Scholar ]
• Welter M. M., Jaarsveld S., Lachmann T. Problem space matters: development of creativity and intelligence in primary school children. Creat. Res. J. (in press) [ Google Scholar ]
• Welter M. M., Jaarsveld S., van Leeuwen C., Lachmann T. (2016). Intelligence and creativity; over the threshold together? Creat. Res. J. 28 212–218. 10.1080/10400419.2016.1162564 [ CrossRef ] [ Google Scholar ]
• Wertheimer M. (1945/1968). Productive Thinking (Enlarged Edition) London: Tavistock. [ Google Scholar ]
• Yamamoto Y., Nakakoji K., Takada S. (2000). Hand on representations in two dimensional spaces for early stages of design. Knowl. Based Syst. 13 357–384. 10.1016/S0950-7051(00)00078-2 [ CrossRef ] [ Google Scholar ]

7 Types of Critical Thinking: A Guide to Analyzing Problems

Critical thinking is the ability to think clearly and rationally about various issues and situations. It involves applying different types of thinking skills to different problems and challenges. Some of the main types of critical thinking are: Analytical Thinking, Creative Thinking, Decision-Making, Problem-Solving, Reflection , Open-mindedness, Good communication

Sanju Pradeepa

Have you ever had a problem that was too big to solve right away? Or perhaps you just couldn’t figure out how to approach it? Whether it’s a personal, academic, or professional problem, having the right set of critical thinking skills can help.

Critical thinking is all about carefully evaluating data and making rational decisions. In other words, it’s the skill of analyzing information from many different points of view before drawing a conclusion. It’s an ongoing process that involves gathering information, asking questions, and considering various solutions.

In this guide, we’ll go over different types of critical thinking skills and provide examples of how to apply these skills when approaching a problem from any angle. We’ll also look at ways to sharpen your critical thinking skills so you can tackle any challenge with ease. So let’s get started.

Table of Contents

What is “critical thinking”.

Critical thinking is the ability to analyze a problem or situation and come up with a rational, informed solution. It’s an essential skill for all kinds of processes, from problem solving to decision-making to creative thinking.

In order to tackle complex problems, you need to be able to think critically and evaluate the information at your disposal in order to come up with the best solution.

Critical thinking involves breaking down a problem into its component parts and analyzing it systematically to determine how best to proceed. It requires the ability to think objectively and make informed judgments based on facts and evidence rather than just guesswork or opinion. It also involves the use of several different types of critical thinking skills, such as:

• Analytical Thinking : This type of critical thinking skill involves analyzing data or information in order to draw logical conclusions or find solutions. It’s important for problem-solving and decision-making since it helps you find solutions through careful analysis.
• Creative Thinking: This type of critical thinking skill requires imagination and open-mindedness in order to come up with innovative ideas and solutions. It can help you identify new ways of looking at a situation or find different solutions to a problem.
• Problem-Solving Thinking : This type of critical thinking skill involves developing strategies in order to solve problems quickly and effectively.

Different Types of Critical Thinking

Critical thinking involves analyzing and evaluating information in order to come to a conclusion or make decisions. But did you know that there are different types of critical thinking?

Let’s break down those types of critical thinking skills into 7 different titles and learn them one by one:

1. Analytical Thinking

It is all about taking the pieces of a problem, digging into them, and methodically finding a solution. Analytical thinking is a key element in working through problems and coming up with the best plan of action for success.

So, what does analytical thinking involve? It involves being able to break a problem down into smaller bits and pieces, understanding how each piece interconnects, and developing strategies for solving each individual piece by gathering information relating to it.

Analyzing how each piece of the puzzle affects the next requires you to really understand how they connect together, and using this approach can help you come up with better solutions that can help improve the overall situation.

You’ll also need to make sure any strategies or solutions you come up with are grounded in evidence-based research so that your conclusions are reliable.

Here are some key skills necessary for effective analytical thinking:

• Evaluating: being able to review facts and make judgments about them depending on the situation at hand
• Investigating means asking questions about various aspects of a problem and doing research so that you can identify its root causes.
• Synthesizing: Combining different pieces of data or information together to create new solutions or approaches to existing problems
• Reasoning logically means connecting bits of data together in order to evaluate different possibilities that could help solve the problem or issue at hand.

With these analytical thinking skills, you can start breaking down any problem into smaller, manageable parts, think logically through how they connect together, assess what evidence is needed to make decisions, and draw conclusions based on facts rather than just opinions or hunches.

2. Creative Thinking and Idea Generation

Do you ever feel like your thoughts are stuck in a rut ? Creative thinking and idea generation can help you come up with fresh solutions to problems and break out of that rut.

Creative thinking is an essential critical thinking tool. It can help you look at an issue from a different point of view or think of new ways to approach the problem. Here are some tips for giving your creative thinking skills an extra boost:

• Challenge assumptions.    Even if something seems obvious, take some time to question it and consider other possibilities.
• Brainstorm different solutions . Try writing down potential solutions, no matter how wild they may seem, then look for patterns between them or ideas that can be combined into something new.
• Consider different perspectives. Even if the issue seems cut and dry from one perspective, try to imagine it from other angles and think about how the issue appears from those views.
• Take a break and come back later with fresh eyes: sometimes taking a step away from the problem is enough to give you the necessary distance to discover new ideas or paths of exploration.

These strategies will help dramatically improve your ability to generate new ideas and jumpstart your creative thinking process whenever you need it.

3. Decision-Making

When it comes to critical thinking, decision-making is an essential skill. It’s not just about being able to evaluate a situation; it’s about being able to make a well-informed decision that will bring the best results.

Here are four key components of decision-making:

• Goal Setting : Take time to first identify what you want to accomplish with your decision.
• Analyzing Alternatives: Evaluate the pros and cons of potential solutions before choosing one.
• Risk assessment: estimate the possible risks associated with each potential solution, based on current evidence.
• Implementation: Once the decision is made, start working on implementation tasks and track results for ongoing improvement or refinement.

By following these steps, you’ll be in a better position to make decisions that have positive outcomes for you and those involved in the decision-making process.

The ability to think critically and make sound decisions can not only help you solve problems quickly but can also lead to more successful long-term strategies for your business or organization.

4. Problem-Solving

It is one of the most essential types of critical thinking skills. Problem-solving involves taking all the pieces of a problem and figuring out how to resolve it. This can involve coming up with new solutions, making decisions, devising strategies, and identifying patterns and trends.

It’s an invaluable skill in many aspects of life and can help you create effective solutions to a wide range of problems. To use your problem-solving skills effectively, keep these tips in mind:

• Break the problem down into smaller, manageable parts . Breaking down a problem into smaller chunks makes it easier to work on and understand.
• Look for connections between pieces. Try to identify any connections between different aspects or pieces of the problem to gain insights that may help you solve it more efficiently.
• Don’t get overwhelmed by the scope of the challenge at hand; take it one step at a time and remember that even small victories can help move you closer to finding a solution.
• Think creatively when coming up with possible solutions or strategies; often the best solution is not obvious at first glance.
• Keep track of what works and what doesn’t ; this will give you valuable insights for future problem-solving endeavors as well as feedback on your progress towards resolving the current one at hand.

5. Reflection and Assessing Evidence

Now it’s time to take a look at your own cognitive activity. Reflection and assessing evidence are two types of critical thinking skills that help you make sure you’re not jumping to conclusions without considering the pros and cons of a situation.

When it comes to reflection, this involves being honest with yourself and taking a deep look at the way your thoughts, feelings, and beliefs are informing your decisions. At its core, reflection allows you to objectively evaluate the evidence that’s in front of you so that you can make an informed assessment about what the best next step is for a given problem or situation.

Assessing evidence is also critical for coming up with effective solutions. This means carefully examining the available data and making sure you have all of the necessary information before reaching an opinion or making a decision. It involves looking at multiple perspectives and interpretations of any given issue so that you can form an educated conclusion about how best to solve it.

6. Open-mindedness

It is a critical thinking skill that is all about trying to understand something from different perspectives and being able to appreciate the difference in opinions. Open-mindedness allows you to analyze a problem from multiple angles and consider different solutions or ways of approaching it.

Here are some tips for developing open-mindedness as a critical thinking skill:

• Listen carefully and actively to others ; rather than just hearing words, try to understand their point of view.
• Ask questions without judgmen t and without assuming your own opinion is the right one.
• Pay attention to how other people view the same situation differently than you do.
• Think critically and evaluate arguments objectively, without assumptions or preconceived ideas about what the answer should be or which course of action should be taken.
• Suspend judgment until you have enough information about a topic or situation; don’t jump to conclusions too quickly.
• Prioritize respect when engaging with others who have different perspectives. Be willing to put in the effort required to understand why they think that way and why that might be important to them in their lives or work.
• Avoid making assumptions about what someone else believes; find out more first before passing judgment on someone’s opinion or actions.

By developing this type of open-mindedness, you can become more aware of how your personal biases may impact your ability to think critically, improving your overall decision-making skills over time and helping you become a more valuable asset as part of any team or organization.

7. Good communication

Good communication is an important part of the critical thinking process. That’s because having good communication skills helps you be more persuasive, helping you convince people of ideas and solutions that are well thought-out. It also allows you to better explain and justify your reasoning to others, which is essential when looking at complex problems.

To have strong communication skills, it’s important to think before you speak. You should also take the time to clearly articulate your thoughts, using simple yet powerful language. Additionally, having an open mind is key. It allows you to consider different angles and perspectives on any issue or problem that you might face.

Here are some tips for good communication:

• Take a moment to succinctly formulate your thoughts before speaking or writing them down.
• Ask questions when necessary, and listen carefully to what others have to say.
• Stay open-minded in conversations, as this will help broaden your knowledge of the situation.
• Speak clearly and use accurate language so that your message won’t be misunderstood.

While it’s true that critical thinking skills can’t be taught in just a few days, plenty of work and practice can go a long way toward equipping you to think critically about the problems in your life. With the right practice and guidance, you can become a master at analyzing issues, discerning cause and effect, and integrating facts to formulate your strategy.

If you’re looking to hone your critical thinking skills, start by breaking down a problem into its component parts. Assess the evidence, identify assumptions, and determine the best course of action. With practice and dedication, you can develop the analytical skills to resolve complex problems and make better decisions in the future.

• 6 Main Types of Critical Thinking Skills (With Examples) by Jamie Birt (2022) from Indeed.com
• Critical thinking From Wikipedia, the free encyclopedia
• Critical thinking is the one skillset you can’t afford not to master By  Maggie Wooll (2022) from BetterUp (https://www.betterup.com/)

Call to Action

If you want to improve yourself and achieve your goals, you need to take action. Don’t wait for the perfect moment or the right opportunity. Start today with one small step and build momentum.

Let’s boost your self-growth with Believe in Mind.

Interested in self-reflection tips, learning hacks, and knowing ways to calm down your mind? We offer you the best content which you have been looking for.

Follow Me on

You May Like Also

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.