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Organizing Your Social Sciences Research Paper

• The Research Problem/Question
• Purpose of Guide
• Design Flaws to Avoid
• Independent and Dependent Variables
• Glossary of Research Terms
• Reading Research Effectively
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Applying Critical Thinking
• Choosing a Title
• Making an Outline
• Paragraph Development
• Research Process Video Series
• Executive Summary
• The C.A.R.S. Model
• Background Information
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Primary Sources
• Secondary Sources
• Tiertiary Sources
• Scholarly vs. Popular Publications
• Qualitative Methods
• Quantitative Methods
• Insiderness
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Writing Concisely
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Generative AI and Writing
• USC Libraries Tutorials and Other Guides
• Bibliography

A research problem is a definite or clear expression [statement] about an area of concern, a condition to be improved upon, a difficulty to be eliminated, or a troubling question that exists in scholarly literature, in theory, or within existing practice that points to a need for meaningful understanding and deliberate investigation. A research problem does not state how to do something, offer a vague or broad proposition, or present a value question. In the social and behavioral sciences, studies are most often framed around examining a problem that needs to be understood and resolved in order to improve society and the human condition.

Bryman, Alan. “The Research Question in Social Research: What is its Role?” International Journal of Social Research Methodology 10 (2007): 5-20; Guba, Egon G., and Yvonna S. Lincoln. “Competing Paradigms in Qualitative Research.” In Handbook of Qualitative Research . Norman K. Denzin and Yvonna S. Lincoln, editors. (Thousand Oaks, CA: Sage, 1994), pp. 105-117; Pardede, Parlindungan. “Identifying and Formulating the Research Problem." Research in ELT: Module 4 (October 2018): 1-13; Li, Yanmei, and Sumei Zhang. "Identifying the Research Problem." In Applied Research Methods in Urban and Regional Planning . (Cham, Switzerland: Springer International Publishing, 2022), pp. 13-21.

Importance of...

The purpose of a problem statement is to:

• Introduce the reader to the importance of the topic being studied . The reader is oriented to the significance of the study.
• Anchors the research questions, hypotheses, or assumptions to follow . It offers a concise statement about the purpose of your paper.
• Place the topic into a particular context that defines the parameters of what is to be investigated.
• Provide the framework for reporting the results and indicates what is probably necessary to conduct the study and explain how the findings will present this information.

In the social sciences, the research problem establishes the means by which you must answer the "So What?" question. This declarative question refers to a research problem surviving the relevancy test [the quality of a measurement procedure that provides repeatability and accuracy]. Note that answering the "So What?" question requires a commitment on your part to not only show that you have reviewed the literature, but that you have thoroughly considered the significance of the research problem and its implications applied to creating new knowledge and understanding or informing practice.

To survive the "So What" question, problem statements should possess the following attributes:

• Clarity and precision [a well-written statement does not make sweeping generalizations and irresponsible pronouncements; it also does include unspecific determinates like "very" or "giant"],
• Demonstrate a researchable topic or issue [i.e., feasibility of conducting the study is based upon access to information that can be effectively acquired, gathered, interpreted, synthesized, and understood],
• Identification of what would be studied, while avoiding the use of value-laden words and terms,
• Identification of an overarching question or small set of questions accompanied by key factors or variables,
• Identification of key concepts and terms,
• Articulation of the study's conceptual boundaries or parameters or limitations,
• Some generalizability in regards to applicability and bringing results into general use,
• Conveyance of the study's importance, benefits, and justification [i.e., regardless of the type of research, it is important to demonstrate that the research is not trivial],
• Does not have unnecessary jargon or overly complex sentence constructions; and,
• Conveyance of more than the mere gathering of descriptive data providing only a snapshot of the issue or phenomenon under investigation.

Bryman, Alan. “The Research Question in Social Research: What is its Role?” International Journal of Social Research Methodology 10 (2007): 5-20; Brown, Perry J., Allen Dyer, and Ross S. Whaley. "Recreation Research—So What?" Journal of Leisure Research 5 (1973): 16-24; Castellanos, Susie. Critical Writing and Thinking. The Writing Center. Dean of the College. Brown University; Ellis, Timothy J. and Yair Levy Nova. "Framework of Problem-Based Research: A Guide for Novice Researchers on the Development of a Research-Worthy Problem." Informing Science: the International Journal of an Emerging Transdiscipline 11 (2008); Thesis and Purpose Statements. The Writer’s Handbook. Writing Center. University of Wisconsin, Madison; Thesis Statements. The Writing Center. University of North Carolina; Tips and Examples for Writing Thesis Statements. The Writing Lab and The OWL. Purdue University; Selwyn, Neil. "‘So What?’…A Question that Every Journal Article Needs to Answer." Learning, Media, and Technology 39 (2014): 1-5; Shoket, Mohd. "Research Problem: Identification and Formulation." International Journal of Research 1 (May 2014): 512-518.

Structure and Writing Style

I.  Types and Content

There are four general conceptualizations of a research problem in the social sciences:

• Casuist Research Problem -- this type of problem relates to the determination of right and wrong in questions of conduct or conscience by analyzing moral dilemmas through the application of general rules and the careful distinction of special cases.
• Difference Research Problem -- typically asks the question, “Is there a difference between two or more groups or treatments?” This type of problem statement is used when the researcher compares or contrasts two or more phenomena. This a common approach to defining a problem in the clinical social sciences or behavioral sciences.
• Descriptive Research Problem -- typically asks the question, "what is...?" with the underlying purpose to describe the significance of a situation, state, or existence of a specific phenomenon. This problem is often associated with revealing hidden or understudied issues.
• Relational Research Problem -- suggests a relationship of some sort between two or more variables to be investigated. The underlying purpose is to investigate specific qualities or characteristics that may be connected in some way.

A problem statement in the social sciences should contain :

• A lead-in that helps ensure the reader will maintain interest over the study,
• A declaration of originality [e.g., mentioning a knowledge void or a lack of clarity about a topic that will be revealed in the literature review of prior research],
• An indication of the central focus of the study [establishing the boundaries of analysis], and
• An explanation of the study's significance or the benefits to be derived from investigating the research problem.

NOTE :   A statement describing the research problem of your paper should not be viewed as a thesis statement that you may be familiar with from high school. Given the content listed above, a description of the research problem is usually a short paragraph in length.

II.  Sources of Problems for Investigation

The identification of a problem to study can be challenging, not because there's a lack of issues that could be investigated, but due to the challenge of formulating an academically relevant and researchable problem which is unique and does not simply duplicate the work of others. To facilitate how you might select a problem from which to build a research study, consider these sources of inspiration:

Deductions from Theory This relates to deductions made from social philosophy or generalizations embodied in life and in society that the researcher is familiar with. These deductions from human behavior are then placed within an empirical frame of reference through research. From a theory, the researcher can formulate a research problem or hypothesis stating the expected findings in certain empirical situations. The research asks the question: “What relationship between variables will be observed if theory aptly summarizes the state of affairs?” One can then design and carry out a systematic investigation to assess whether empirical data confirm or reject the hypothesis, and hence, the theory.

Interdisciplinary Perspectives Identifying a problem that forms the basis for a research study can come from academic movements and scholarship originating in disciplines outside of your primary area of study. This can be an intellectually stimulating exercise. A review of pertinent literature should include examining research from related disciplines that can reveal new avenues of exploration and analysis. An interdisciplinary approach to selecting a research problem offers an opportunity to construct a more comprehensive understanding of a very complex issue that any single discipline may be able to provide.

Interviewing Practitioners The identification of research problems about particular topics can arise from formal interviews or informal discussions with practitioners who provide insight into new directions for future research and how to make research findings more relevant to practice. Discussions with experts in the field, such as, teachers, social workers, health care providers, lawyers, business leaders, etc., offers the chance to identify practical, “real world” problems that may be understudied or ignored within academic circles. This approach also provides some practical knowledge which may help in the process of designing and conducting your study.

Personal Experience Don't undervalue your everyday experiences or encounters as worthwhile problems for investigation. Think critically about your own experiences and/or frustrations with an issue facing society or related to your community, your neighborhood, your family, or your personal life. This can be derived, for example, from deliberate observations of certain relationships for which there is no clear explanation or witnessing an event that appears harmful to a person or group or that is out of the ordinary.

Relevant Literature The selection of a research problem can be derived from a thorough review of pertinent research associated with your overall area of interest. This may reveal where gaps exist in understanding a topic or where an issue has been understudied. Research may be conducted to: 1) fill such gaps in knowledge; 2) evaluate if the methodologies employed in prior studies can be adapted to solve other problems; or, 3) determine if a similar study could be conducted in a different subject area or applied in a different context or to different study sample [i.e., different setting or different group of people]. Also, authors frequently conclude their studies by noting implications for further research; read the conclusion of pertinent studies because statements about further research can be a valuable source for identifying new problems to investigate. The fact that a researcher has identified a topic worthy of further exploration validates the fact it is worth pursuing.

III.  What Makes a Good Research Statement?

A good problem statement begins by introducing the broad area in which your research is centered, gradually leading the reader to the more specific issues you are investigating. The statement need not be lengthy, but a good research problem should incorporate the following features:

1.  Compelling Topic The problem chosen should be one that motivates you to address it but simple curiosity is not a good enough reason to pursue a research study because this does not indicate significance. The problem that you choose to explore must be important to you, but it must also be viewed as important by your readers and to a the larger academic and/or social community that could be impacted by the results of your study. 2.  Supports Multiple Perspectives The problem must be phrased in a way that avoids dichotomies and instead supports the generation and exploration of multiple perspectives. A general rule of thumb in the social sciences is that a good research problem is one that would generate a variety of viewpoints from a composite audience made up of reasonable people. 3.  Researchability This isn't a real word but it represents an important aspect of creating a good research statement. It seems a bit obvious, but you don't want to find yourself in the midst of investigating a complex research project and realize that you don't have enough prior research to draw from for your analysis. There's nothing inherently wrong with original research, but you must choose research problems that can be supported, in some way, by the resources available to you. If you are not sure if something is researchable, don't assume that it isn't if you don't find information right away--seek help from a librarian !

NOTE:   Do not confuse a research problem with a research topic. A topic is something to read and obtain information about, whereas a problem is something to be solved or framed as a question raised for inquiry, consideration, or solution, or explained as a source of perplexity, distress, or vexation. In short, a research topic is something to be understood; a research problem is something that needs to be investigated.

IV.  Asking Analytical Questions about the Research Problem

Research problems in the social and behavioral sciences are often analyzed around critical questions that must be investigated. These questions can be explicitly listed in the introduction [i.e., "This study addresses three research questions about women's psychological recovery from domestic abuse in multi-generational home settings..."], or, the questions are implied in the text as specific areas of study related to the research problem. Explicitly listing your research questions at the end of your introduction can help in designing a clear roadmap of what you plan to address in your study, whereas, implicitly integrating them into the text of the introduction allows you to create a more compelling narrative around the key issues under investigation. Either approach is appropriate.

The number of questions you attempt to address should be based on the complexity of the problem you are investigating and what areas of inquiry you find most critical to study. Practical considerations, such as, the length of the paper you are writing or the availability of resources to analyze the issue can also factor in how many questions to ask. In general, however, there should be no more than four research questions underpinning a single research problem.

Given this, well-developed analytical questions can focus on any of the following:

• Highlights a genuine dilemma, area of ambiguity, or point of confusion about a topic open to interpretation by your readers;
• Yields an answer that is unexpected and not obvious rather than inevitable and self-evident;
• Provokes meaningful thought or discussion;
• Raises the visibility of the key ideas or concepts that may be understudied or hidden;
• Suggests the need for complex analysis or argument rather than a basic description or summary; and,
• Offers a specific path of inquiry that avoids eliciting generalizations about the problem.

NOTE:   Questions of how and why concerning a research problem often require more analysis than questions about who, what, where, and when. You should still ask yourself these latter questions, however. Thinking introspectively about the who, what, where, and when of a research problem can help ensure that you have thoroughly considered all aspects of the problem under investigation and helps define the scope of the study in relation to the problem.

V.  Mistakes to Avoid

Beware of circular reasoning! Do not state the research problem as simply the absence of the thing you are suggesting. For example, if you propose the following, "The problem in this community is that there is no hospital," this only leads to a research problem where:

• The need is for a hospital
• The objective is to create a hospital
• The method is to plan for building a hospital, and
• The evaluation is to measure if there is a hospital or not.

This is an example of a research problem that fails the "So What?" test . In this example, the problem does not reveal the relevance of why you are investigating the fact there is no hospital in the community [e.g., perhaps there's a hospital in the community ten miles away]; it does not elucidate the significance of why one should study the fact there is no hospital in the community [e.g., that hospital in the community ten miles away has no emergency room]; the research problem does not offer an intellectual pathway towards adding new knowledge or clarifying prior knowledge [e.g., the county in which there is no hospital already conducted a study about the need for a hospital, but it was conducted ten years ago]; and, the problem does not offer meaningful outcomes that lead to recommendations that can be generalized for other situations or that could suggest areas for further research [e.g., the challenges of building a new hospital serves as a case study for other communities].

Alvesson, Mats and Jörgen Sandberg. “Generating Research Questions Through Problematization.” Academy of Management Review 36 (April 2011): 247-271 ; Choosing and Refining Topics. Writing@CSU. Colorado State University; D'Souza, Victor S. "Use of Induction and Deduction in Research in Social Sciences: An Illustration." Journal of the Indian Law Institute 24 (1982): 655-661; Ellis, Timothy J. and Yair Levy Nova. "Framework of Problem-Based Research: A Guide for Novice Researchers on the Development of a Research-Worthy Problem." Informing Science: the International Journal of an Emerging Transdiscipline 11 (2008); How to Write a Research Question. The Writing Center. George Mason University; Invention: Developing a Thesis Statement. The Reading/Writing Center. Hunter College; Problem Statements PowerPoint Presentation. The Writing Lab and The OWL. Purdue University; Procter, Margaret. Using Thesis Statements. University College Writing Centre. University of Toronto; Shoket, Mohd. "Research Problem: Identification and Formulation." International Journal of Research 1 (May 2014): 512-518; Trochim, William M.K. Problem Formulation. Research Methods Knowledge Base. 2006; Thesis and Purpose Statements. The Writer’s Handbook. Writing Center. University of Wisconsin, Madison; Thesis Statements. The Writing Center. University of North Carolina; Tips and Examples for Writing Thesis Statements. The Writing Lab and The OWL. Purdue University; Pardede, Parlindungan. “Identifying and Formulating the Research Problem." Research in ELT: Module 4 (October 2018): 1-13; Walk, Kerry. Asking an Analytical Question. [Class handout or worksheet]. Princeton University; White, Patrick. Developing Research Questions: A Guide for Social Scientists . New York: Palgrave McMillan, 2009; Li, Yanmei, and Sumei Zhang. "Identifying the Research Problem." In Applied Research Methods in Urban and Regional Planning . (Cham, Switzerland: Springer International Publishing, 2022), pp. 13-21.

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Academic Experience

How to identify and resolve research problems

Updated July 12, 2023

In this article, we’re going to take you through one of the most pertinent parts of conducting research: a research problem (also known as a research problem statement).

When trying to formulate a good research statement, and understand how to solve it for complex projects, it can be difficult to know where to start.

Not only are there multiple perspectives (from stakeholders to project marketers who want answers), you have to consider the particular context of the research topic: is it timely, is it relevant and most importantly of all, is it valuable?

In other words: are you looking at a research worthy problem?

The fact is, a well-defined, precise, and goal-centric research problem will keep your researchers, stakeholders, and business-focused and your results actionable.

And when it works well, it's a powerful tool to identify practical solutions that can drive change and secure buy-in from your workforce.

Free eBook: The ultimate guide to market research

What is a research problem?

In social research methodology and behavioral sciences , a research problem establishes the direction of research, often relating to a specific topic or opportunity for discussion.

For example: climate change and sustainability, analyzing moral dilemmas or wage disparity amongst classes could all be areas that the research problem focuses on.

As well as outlining the topic and/or opportunity, a research problem will explain:

• why the area/issue needs to be addressed,
• why the area/issue is of importance,
• the parameters of the research study
• the research objective
• the reporting framework for the results and
• what the overall benefit of doing so will provide (whether to society as a whole or other researchers and projects).

Having identified the main topic or opportunity for discussion, you can then narrow it down into one or several specific questions that can be scrutinized and answered through the research process.

What are research questions?

Generating research questions underpinning your study usually starts with problems that require further research and understanding while fulfilling the objectives of the study.

A good problem statement begins by asking deeper questions to gain insights about a specific topic.

For example, using the problems above, our questions could be:

"How will climate change policies influence sustainability standards across specific geographies?"

"What measures can be taken to address wage disparity without increasing inflation?"

Developing a research worthy problem is the first step - and one of the most important - in any kind of research.

It’s also a task that will come up again and again because any business research process is cyclical. New questions arise as you iterate and progress through discovering, refining, and improving your products and processes. A research question can also be referred to as a "problem statement".

Note: good research supports multiple perspectives through empirical data. It’s focused on key concepts rather than a broad area, providing readily actionable insight and areas for further research.

Research question or research problem?

As we've highlighted, the terms “research question” and “research problem” are often used interchangeably, becoming a vague or broad proposition for many.

The term "problem statement" is far more representative, but finds little use among academics.

Instead, some researchers think in terms of a single research problem and several research questions that arise from it.

As mentioned above, the questions are lines of inquiry to explore in trying to solve the overarching research problem.

Ultimately, this provides a more meaningful understanding of a topic area.

It may be useful to think of questions and problems as coming out of your business data – that’s the O-data (otherwise known as operational data) like sales figures and website metrics.

What's an example of a research problem?

Your overall research problem could be: "How do we improve sales across EMEA and reduce lost deals?"

This research problem then has a subset of questions, such as:

"Why do sales peak at certain times of the day?"

"Why are customers abandoning their online carts at the point of sale?"

As well as helping you to solve business problems, research problems (and associated questions) help you to think critically about topics and/or issues (business or otherwise). You can also use your old research to aid future research -- a good example is laying the foundation for comparative trend reports or a complex research project.

(Also, if you want to see the bigger picture when it comes to research problems, why not check out our ultimate guide to market research? In it you'll find out: what effective market research looks like, the use cases for market research, carrying out a research study, and how to examine and action research findings).

The research process: why are research problems important?

A research problem has two essential roles in setting your research project on a course for success.

1. They set the scope

The research problem defines what problem or opportunity you’re looking at and what your research goals are. It stops you from getting side-tracked or allowing the scope of research to creep off-course .

Without a strong research problem or problem statement, your team could end up spending resources unnecessarily, or coming up with results that aren’t actionable - or worse, harmful to your business - because the field of study is too broad.

2. They tie your work to business goals and actions

To formulate a research problem in terms of business decisions means you always have clarity on what’s needed to make those decisions. You can show the effects of what you’ve studied using real outcomes.

Then, by focusing your research problem statement on a series of questions tied to business objectives, you can reduce the risk of the research being unactionable or inaccurate.

It's also worth examining research or other scholarly literature (you’ll find plenty of similar, pertinent research online) to see how others have explored specific topics and noting implications that could have for your research.

Four steps to defining your research problem

Image credit: http://myfreeschooltanzania.blogspot.com/2014/11/defining-research-problem.html

1. Observe and identify

Businesses today have so much data that it can be difficult to know which problems to address first. Researchers also have business stakeholders who come to them with problems they would like to have explored. A researcher’s job is to sift through these inputs and discover exactly what higher-level trends and key concepts are worth investing in.

This often means asking questions and doing some initial investigation to decide which avenues to pursue. This could mean gathering interdisciplinary perspectives identifying additional expertise and contextual information.

Sometimes, a small-scale preliminary study might be worth doing to help get a more comprehensive understanding of the business context and needs, and to make sure your research problem addresses the most critical questions.

This could take the form of qualitative research using a few in-depth interviews , an environmental scan, or reviewing relevant literature.

The sales manager of a sportswear company has a problem: sales of trail running shoes are down year-on-year and she isn’t sure why. She approaches the company’s research team for input and they begin asking questions within the company and reviewing their knowledge of the wider market.

2. Review the key factors involved

As a marketing researcher, you must work closely with your team of researchers to define and test the influencing factors and the wider context involved in your study. These might include demographic and economic trends or the business environment affecting the question at hand. This is referred to as a relational research problem.

To do this, you have to identify the factors that will affect the research and begin formulating different methods to control them.

You also need to consider the relationships between factors and the degree of control you have over them. For example, you may be able to control the loading speed of your website but you can’t control the fluctuations of the stock market.

Doing this will help you determine whether the findings of your project will produce enough information to be worth the cost.

You need to determine:

• which factors affect the solution to the research proposal.
• which ones can be controlled and used for the purposes of the company, and to what extent.
• the functional relationships between the factors.
• which ones are critical to the solution of the research study.

The research team at the running shoe company is hard at work. They explore the factors involved and the context of why YoY sales are down for trail shoes, including things like what the company’s competitors are doing, what the weather has been like – affecting outdoor exercise – and the relative spend on marketing for the brand from year to year.

The final factor is within the company’s control, although the first two are not. They check the figures and determine marketing spend has a significant impact on the company.

3. Prioritize

Once you and your research team have a few observations, prioritize them based on their business impact and importance. It may be that you can answer more than one question with a single study, but don’t do it at the risk of losing focus on your overarching research problem.

Questions to ask:

• Who? Who are the people with the problem? Are they end-users, stakeholders, teams within your business? Have you validated the information to see what the scale of the problem is?
• What? What is its nature and what is the supporting evidence?
• Why? What is the business case for solving the problem? How will it help?
• Where? How does the problem manifest and where is it observed?

To help you understand all dimensions, you might want to consider focus groups or preliminary interviews with external (including consumers and existing customers) and internal (salespeople, managers, and other stakeholders) parties to provide what is sometimes much-needed insight into a particular set of questions or problems.

After observing and investigating, the running shoe researchers come up with a few candidate questions, including:

• What is the relationship between US average temperatures and sales of our products year on year?
• At present, how does our customer base rank Competitor X and Competitor Y’s trail running shoe compared to our brand?
• What is the relationship between marketing spend and trail shoe product sales over the last 12 months?

They opt for the final question, because the variables involved are fully within the company’s control, and based on their initial research and stakeholder input, seem the most likely cause of the dive in sales. The research question is specific enough to keep the work on course towards an actionable result, but it allows for a few different avenues to be explored, such as the different budget allocations of offline and online marketing and the kinds of messaging used.

Get feedback from the key teams within your business to make sure everyone is aligned and has the same understanding of the research problem and questions, and the actions you hope to take based on the results. Now is also a good time to demonstrate the ROI of your research and lay out its potential benefits to your stakeholders.

Different groups may have different goals and perspectives on the issue. This step is vital for getting the necessary buy-in and pushing the project forward.

The running shoe company researchers now have everything they need to begin. They call a meeting with the sales manager and consult with the product team, marketing team, and C-suite to make sure everyone is aligned and has bought into the direction of the research topic. They identify and agree that the likely course of action will be a rethink of how marketing resources are allocated, and potentially testing out some new channels and messaging strategies .

Can you explore a broad area and is it practical to do so?

A broader research problem or report can be a great way to bring attention to prevalent issues, societal or otherwise, but are often undertaken by those with the resources to do so.

Take a typical government cybersecurity breach survey, for example. Most of these reports raise awareness of cybercrime, from the day-to-day threats businesses face to what security measures some organizations are taking. What these reports don't do, however, is provide actionable advice - mostly because every organization is different.

The point here is that while some researchers will explore a very complex issue in detail, others will provide only a snapshot to maintain interest and encourage further investigation. The "value" of the data is wholly determined by the recipients of it - and what information you choose to include.

To summarize, it can be practical to undertake a broader research problem, certainly, but it may not be possible to cover everything or provide the detail your audience needs. Likewise, a more systematic investigation of an issue or topic will be more valuable, but you may also find that you cover far less ground.

It's important to think about your research objectives and expected findings before going ahead.

Ensuring your research project is a success

A complex research project can be made significantly easier with clear research objectives, a descriptive research problem, and a central focus. All of which we've outlined in this article.

If you have previous research, even better. Use it as a benchmark

Remember: what separates a good research paper from an average one is actually very simple: valuable, empirical data that explores a prevalent societal or business issue and provides actionable insights.

And we can help.

Sophisticated research made simple with Qualtrics

Trusted by the world's best brands, our platform enables researchers from academic to corporate to tackle the hardest challenges and deliver the results that matter.

Our CoreXM platform supports the methods that define superior research and delivers insights in real-time. It's easy to use (thanks to drag-and-drop functionality) and requires no coding, meaning you'll be capturing data and gleaning insights in no time.

It also excels in flexibility; you can track consumer behavior across segments , benchmark your company versus competitors , carry out complex academic research, and do much more, all from one system.

It's one platform with endless applications, so no matter your research problem, we've got the tools to help you solve it. And if you don't have a team of research experts in-house, our market research team has the practical knowledge and tools to help design the surveys and find the respondents you need.

Of course, you may want to know where to begin with your own market research . If you're struggling, make sure to download our ultimate guide using the link below.

It's got everything you need and there’s always information in our research methods knowledge base.

Scott Smith

Scott Smith, Ph.D. is a contributor to the Qualtrics blog.

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Research Writing and Analysis

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Problem statement overview.

The dissertation problem needs to be very focused because everything else from the dissertation research logically flows from the problem. You may say that the problem statement is the very core of a dissertation research study. If the problem is too big or too vague, it will be difficult to scope out a purpose that is manageable for one person, given the time available to execute and finish the dissertation research study.

Through your research, your aim is to obtain information that helps address a problem so it can be resolved. Note that the researcher does not actually solve the problem themselves by conducting research but provides new knowledge that can be used toward a resolution. Typically, the problem is solved (or partially solved) by practitioners in the field, using input from researchers.

Given the above, the problem statement should do three things :

• Specify and describe the problem (with appropriate citations)
• Explain the consequences of NOT solving the problem
• Explain the knowledge needed to solve the problem (i.e., what is currently unknown about the problem and its resolution – also referred to as a gap )

What is a problem?

The world is full of problems! Not all problems make good dissertation research problems, however, because they are either too big, complex, or risky for doctorate candidates to solve. A proper research problem can be defined as a specific, evidence-based, real-life issue faced by certain people or organizations that have significant negative implications to the involved parties.

Example of a proper, specific, evidence-based, real-life dissertation research problem:

“Only 6% of CEOs in Fortune 500 companies are women” (Center for Leadership Studies, 2019).

Specific refers to the scope of the problem, which should be sufficiently manageable and focused to address with dissertation research. For example, the problem “terrorism kills thousands of people each year” is probably not specific enough in terms of who gets killed by which terrorists, to work for a doctorate candidate; or “Social media use among call-center employees may be problematic because it could reduce productivity,” which contains speculations about the magnitude of the problem and the possible negative effects.

Evidence-based here means that the problem is well-documented by recent research findings and/or statistics from credible sources. Anecdotal evidence does not qualify in this regard. Quantitative evidence is generally preferred over qualitative ditto when establishing a problem because quantitative evidence (from a credible source) usually reflects generalizable facts, whereas qualitative evidence in the form of research conclusions tend to only apply to the study sample and may not be generalizable to a larger population. Example of a problem that isn’t evidence-based: “Based on the researcher’s experience, the problem is that people don’t accept female leaders;” which is an opinion-based statement based on personal (anecdotal) experience.

Real-life means that a problem exists regardless of whether research is conducted or not. This means that “lack of knowledge” or “lack of research” cannot be used as the problem for a dissertation study because it’s an academic issue or a gap; and not a real-life problem experienced by people or organizations.  Example of a problem that doesn’t exist in real life: “There is not enough research on the reasons why people distrust minority healthcare workers.” This type of statement also reveals the assumption that people actually do mistrust minority healthcare workers; something that needs to be supported by actual, credible evidence to potentially work as an underlying research problem.

What are consequences?

Consequences are negative implications experienced by a group of people or organizations, as a result of the problem. The negative effects should be of a certain magnitude to warrant research. For example, if fewer than 1% of the stakeholders experience a negative consequence of a problem and that consequence only constitutes a minor inconvenience, research is probably not warranted. Negative consequences that can be measured weigh stronger than those that cannot be put on some kind of scale.

In the example above, a significant negative consequence is that women face much larger barriers than men when attempting to get promoted to executive jobs; or are 94% less likely than men to get to that level in Corporate America.

What is a gap?

To establish a complete basis for a dissertation research study, the problem has to be accompanied by a gap . A gap is missing knowledge or insights about a particular issue that contributes to the persistence of the problem. We use gaps to “situate” new research in the existing literature by adding to the knowledge base in the business research field, in a specific manner (determined by the purpose of the research). Identifying gaps requires you to review the literature in a thorough fashion, to establish a complete understanding of what is known and what isn’t known about a certain problem.  In the example from above about the underrepresentation of female CEOs, a gap may be that male-dominated boards have not been studied extensively in terms of their CEO hiring decisions, which might then warrant a study of such boards, to uncover implicit biases and discriminatory practices against female candidates.

How to Write a Problem Statement

How to write a problem statement.

• Here is one way to construct a problem section (keep in mind you have a 250-300 word limit, but you can write first and edit later):

It is helpful to begin the problem statement with a sentence :  “The problem to be addressed through this study is… ”  Then, fill out the rest of the paragraph with elaboration of that specific problem, making sure to “document” it, as NU reviewers will look for research-based evidence that it is indeed a problem (emphasis also on timeliness of the problem, supported by citations within the last 5 years).

Next, write a paragraph explaining the consequences of NOT solving the problem. Who will be affected? How will they be affected? How important is it to fix the problem? Again, NU reviewers will want to see research-based citations and statistics that indicate the negative implications are significant.

In the final paragraph, you will explain what information (research) is needed in order to fix the problem. This paragraph shows that the problem is worthy of doctoral-level research. What isn’t known about the problem? Ie, what is the gap? Presumably, if your problem and purpose are aligned, your research will try to close or minimize this gap by investigating the problem. Have other researchers investigated the issue? What has their research left unanswered?

• Another way to tackle the Statement of the Problem:

The Statement of the Problem section is a very clear, concise identification of the problem. It must stay within the template guidelines of 250-300 words but more importantly, must contain four elements as outlined below. A dissertation worthy problem should be able to address all of the following points:

-->identification of the problem itself--what is "going wrong" (Ellis & Levy, 2008)

-->who is affected by the problem

-->the consequences that will result from a continuation of the problem

-->a brief discussion of 1) at least 3 authors’ research related to the problem; and 2)   their stated suggestion/recommendation for further research related to the problem

Use the following to work on the Statement of the Problem by first outlining the section as follows:

1. One clear, concise statement that tells the reader what is not working, what is “going wrong”. Be specific and support it with current studies.

2. Tell who is affected by the problem identified in #1. 

3. Briefly tell what will happen if the problem isn’t addressed.

4. Find at least 3 current studies and write a sentence or two for each study that

i. briefly discusses the author(s)’ work, what they studied, and

ii. state their recommendation for further research about the problem

• Finally, you can follow this simple 3-part outline when writing the statement of the problem section:

Your problem statement is a short (250-300 words), 3 paragraph section, in which you

• Explain context and state problem (“the problem is XYZ”), supported by statistics and/or recent research findings
• Explain the negative consequences of the problem to stakeholders, supported by statistics and/or recent research findings
• Explain the gap in the literature.

Example of a problem statement that follows the 3-part outline (295 words):

The problem to be addressed by this study is the decline of employee well-being for followers of novice mid-level managers and the corresponding rise in employee turnover faced by business leaders across the financial services industry (Oh et al., 2014).  Low levels of employee well-being are toxic for morale and result in expensive turnover costs, dysfunctional work environments, anemic corporate cultures, and poor customer service (Compdata, 2018; Oh et al., 2014).  According to Ufer (2017), the financial services industry suffers from one of the highest turnover rates among millennial-aged employees in all industries in the developed world, at 18.6% annually.  Starkman (2015) reported that 50% of those surveyed in financial services were not satisfied with a single one of the four key workplace aspects: job, firm, pay or career path. 

Low levels of employee well-being interrupt a financial services’ company’s ability to deliver outstanding customer service in a world increasingly dependent on that commodity (Wladawsky-Berger, 2018).Mid-level managers play an essential role in support of the success of many of top businesses today (Anicich & Hirsh, 2017). 

The current body of literature does not adequately address the well-being issue in the financial services industry from the follower’s perspective (Uhl-Bien, Riggio, Lowe, & Carsten, 2014). Strategic direction flows top-down from senior executives and passes through mid-level leadership to individual contributors at more junior grades.  The mid-level managers’ teams are tasked with the achievement of core tasks and the managers themselves are expected to maintain the workforce’s morale, motivation and welfare (Anicich & Hirsh, 2017).  Unless industry leaders better understand the phenomenon of employee well-being from the follower perspective and its role in positioning employees to provide a premium client experience, they may be handicapped from preserving their most significant principal market differentiator: customer service (Wladawsky-Berger, 2018). 

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QuickTips: The Blog @ Evidence Explained

How To Solve a Research Problem

Elizabeth Shown Mills

It’s doable. Really. All it takes are two nevers and three  always. 

1. Never  rely on a single document for any point, even when it tells you exactly what you want to know. Records often err and we won’t know it until and unless we test their assertions against other records. With any piece of research our goal should be to use all relevant records and to make certain that anything we use to “corroborate” something else has totally independent origins.

2. Never assume any type of record is reliable. Record types are like people. Some are totally dependable. Some make us cringe or roll our eyeballs. Most are a mixture. We love what’s good about them. We’re wise to look warily at the flaws.

3. Always  test each finding—no matter how small it may be—against the Evidence Analysis Process Map .  The ultimate “fact” in all projects is this:  Our conclusion can never be better than the evidence on which we base it.

4. Always  use each finding to lead you to something else. No fact is an absolute. No record is an end to itself.  Facts and records are always part of something much bigger. To understand the fragment we’ve found and interpret it correctly, we need the rest of what went on.

5. Always  contrast, compare, and challenge. Each new piece of information needs to be scrutinized rigorously. We study not just the details in a record but the construction of the record and the record set. We watch for anomalies in the records and discrepancies between them.  

We study the behavior of the people who created each record. We study the laws that governed the record—and the degree to which participants and their communities  c omplied with those laws. We constantly look for ways to measure differences and similarities—and ways to quantify actions. We watch for behavior that is aberrant to community norms—which means we may also have to study the community and its records deeply enough to define those norms.

Yes. It’s doable. I didn’t say it’s quick 'n easy. But it’s doable. The issue now is this: How badly do you want to solve that research problem?

PHOTO CREDITS: "5 Star Solution," CanStockPhoto (http://www.canstockphoto.com/images-photos/solution.html#file_view.php?id=16887728 : downloaded 7 April 2015), image  csp16887728, uploaded by drcmarx, 20 November 2013; used under license.

Posted 8 April 2015

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• Evidence analysis
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© Evidence Explained  2011-2024.

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Overview of the Problem-Solving Mental Process

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

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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Original research article, creative problem solving as overcoming a misunderstanding.

• Department of Psychology, University of Milano-Bicocca, Milan, Italy

Solving or attempting to solve problems is the typical and, hence, general function of thought. A theory of problem solving must first explain how the problem is constituted, and then how the solution happens, but also how it happens that it is not solved; it must explain the correct answer and with the same means the failure. The identification of the way in which the problem is formatted should help to understand how the solution of the problems happens, but even before that, the source of the difficulty. Sometimes the difficulty lies in the calculation, the number of operations to be performed, and the quantity of data to be processed and remembered. There are, however, other problems – the insight problems – in which the difficulty does not lie so much in the complexity of the calculations, but in one or more critical points that are susceptible to misinterpretation , incompatible with the solution. In our view, the way of thinking involved in insight problem solving is very close to the process involved in the understanding of an utterance, when a misunderstanding occurs. In this case, a more appropriate meaning has to be selected to resolve the misunderstanding (the “impasse”), the default interpretation (the “fixation”) has to be dropped in order to “restructure.” to grasp another meaning which appears more relevant to the context and the speaker’s intention (the “aim of the task”). In this article we support our view with experimental evidence, focusing on how a misunderstanding is formed. We have studied a paradigmatic insight problem, an apparent trivial arithmetical task, the Ties problem. We also reviewed other classical insight problems, reconsidering in particular one of the most intriguing one, which at first sight appears impossible to solve, the Study Window problem. By identifying the problem knots that alter the aim of the task, the reformulation technique has made it possible to eliminate misunderstanding, without changing the mathematical nature of the problem. With the experimental versions of the problems exposed we have obtained a significant increase in correct answers. Studying how an insight problem is formed, and not just how it is solved, may well become an important topic in education. We focus on undergraduate students’ strategies and their errors while solving problems, and the specific cognitive processes involved in misunderstanding, which are crucial to better exploit what could be beneficial to reach the solution and to teach how to improve the ability to solve problems.

Introduction

“A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action, then there has to be recourse to thinking. (…) Such thinking has the task of devising some action which may mediate between the existing and the desired situations.” ( Duncker, 1945 , p. 1). We agree with Duncker’s general description of every situation we call a problem: the problem solving activity takes a central role in the general function of thought, if not even identifies with it.

So far, psychologists have been mainly interested in the solution and the solvers. But the formation of the problem remained in the shadows.

Let’s consider for example the two fundamental theoretical approaches to the study of problem solving. “What questions should a theory of problem solving answer? First, it should predict the performance of a problem solver handling specified tasks. It should explain how human problem solving takes place: what processes are used, and what mechanisms perform these processes.” ( Newell et al., 1958 , p. 151). In turn, authors of different orientations indicate as central in their research “How does the solution arise from the problem situation? In what ways is the solution of a problem attained?” ( Duncker, 1945 , p. 1) or that of what happens when you solve a problem, when you suddenly see the point ( Wertheimer, 1959 ). It is obvious, and it was inevitable, that the formation of the problem would remain in the shadows.

A theory of problem solving must first explain how the problem is constituted, and then how the solution happens, but also how it happens that it is not solved; it must explain the correct answer and with the same means the failure. The identification of the way in which the problem is constituted – the formation of the problem – and the awareness that this moment is decisive for everything that follows imply that failures are considered in a new way, the study of which should help to understand how the solution of the problems happens, but even before that, the source of the difficulty.

Sometimes the difficulty lies in the calculation, the number of operations to be performed, and the quantity of data to be processed and remembered. Take the well-known problems studied by Simon, Crypto-arithmetic task, for example, or the Cannibals and Missionaries problem ( Simon, 1979 ). The difficulty in these problems lies in the complexity of the calculation which characterizes them. But, the text and the request of the problem is univocally understood by the experimenter and by the participant in both the explicit ( said )and implicit ( implied ) parts. 1 As Simon says, “Subjects do not initially choose deliberately among problem representations, but almost always adopt the representation suggested by the verbal problem statement” ( Kaplan and Simon, 1990 , p. 376). The verbal problem statement determines a problem representation, implicit presuppositions of which are shared by both.

There are, however, other problems where the usual (generalized) interpretation of the text of the problem (and/or the associated figure) prevents and does not allow a solution to be found, so that we are soon faced with an impasse. We’ll call this kind of problems insight problems . “In these cases, where the complexity of the calculations does not play a relevant part in the difficulty of the problem, a misunderstanding would appear to be a more appropriate abstract model than the labyrinth” ( Mosconi, 2016 , p. 356). Insight problems do not arise from a fortuitous misunderstanding, but from a deliberate violation of Gricean conversational rules, since the implicit layer of the discourse (the implied ) is not shared both by experimenter and participant. Take for example the problem of how to remove a one-hundred dollar bill without causing a pyramid balanced atop the bill to topple: “A giant inverted steel pyramid is perfectly balanced on its point. Any movement of the pyramid will cause it to topple over. Underneath the pyramid is a $100 bill. How would you remove the bill without disturbing the pyramid?” ( Schooler et al., 1993 , p. 183). The solution is burn or tear the dollar bill but people assume that the 100 dollar bill must not be damaged, but contrary to his assumption, this is in fact the solution. Obviously this is not a trivial error of understanding between the two parties, but rather a misunderstanding due to social conventions, and dictated by conversational rules. It is the essential condition for the forming of the problem and the experimenter has played on the very fact that the condition was not explicitly stated (see also Bulbrook, 1932 ).

When insight problems are used in research, it could be said that the researcher sets a trap, more or less intentionally, inducing an interpretation that appears to be pertinent to the data and to the text; this interpretation is adopted more or less automatically because it has been validated by use but the default interpretation does not support understanding, and misunderstanding is inevitable; as a result, sooner or later we come up against an impasse. The theory of misunderstanding is supported by experimental evidence obtained by Mosconi in his research on insight problem solving ( Mosconi, 1990 ), and by Bagassi and Macchi on problem solving, decision making and probabilistic reasoning ( Bagassi and Macchi, 2006 , 2016 ; Macchi and Bagassi, 2012 , 2014 , 2015 , 2020 ; Macchi, 1995 , 2000 ; Mosconi and Macchi, 2001 ; Politzer and Macchi, 2000 ).

The implication of the focus on problem forming for education is remarkable: everything we say generates a communicative and therefore interpretative context, which is given by cultural and social assumptions, default interpretations, and attribution of intention to the speaker. Since the text of the problem is expressed in natural language, it is affected, it shares the characteristics of the language itself. Natural language is ambiguous in itself, differently from specialized languages (i.e., logical and statistical ones), which presuppose a univocal, unambiguous interpretation. The understanding of what a speaker means requires a disambiguation process centered on the intention attribution.

Restructuring as Reinterpreting

Traditionally, according to the Gestaltists, finding the solution to an insight problem is an example of “productive thought.” In addition to the reproductive activities of thought, there are processes which create, “produce” that which does not yet exist. It is characterized by a switch in direction which occurs together with the transformation of the problem or a change in our understanding of an essential relationship. The famous “aha!” experience of genuine insight accompanies this change in representation, or restructuring. As Wertheimer says: “… Solution becomes possible only when the central features of the problem are clearly recognized, and paths to a possible approach emerge. Irrelevant features must be stripped away, core features must become salient, and some representation must be developed that accurately reflects how various parts of the problem fit together; relevant relations among parts, and between parts and whole, must be understood, must make sense” ( Wertheimer, 1985 , p. 23).

The restructuring process circumscribed by the Gestaltists to the representation of the perceptual stimulus is actually a general feature of every human cognitive activity and, in particular, of communicative interaction, which allows the understanding, the attribution of meaning, thus extending to the solution of verbal insight problems. In this sense, restructuring becomes a process of reinterpretation.

We are able to get out of the impasse by neglecting the default interpretation and looking for another one that is more pertinent to the situation and which helps us grasp the meaning that matches both the context and the speaker’s intention; this requires continuous adjustments until all makes sense.

In our perspective, this interpretative function is a characteristic inherent to all reasoning processes and is an adaptive characteristic of the human cognitive system in general ( Levinson, 1995 , 2013 ; Macchi and Bagassi, 2019 ; Mercier and Sperber, 2011 ; Sperber and Wilson, 1986/1995 ; Tomasello, 2009 ). It guarantees cognitive economy when meanings and relations are familiar, permitting recognition in a “blink of an eye.” This same process becomes much more arduous when meanings and relations are unfamiliar, obliging us to face the novel. When this happens, we have to come to terms with the fact that the usual, default interpretation will not work, and this is a necessary condition for exploring other ways of interpreting the situation. A restless, conscious and unconscious search for other possible relations between the parts and the whole ensues until everything falls into place and nothing is left unexplained, with an interpretative heuristic-type process. Indeed, the solution restructuring – is a re -interpretation of the relationship between the data and the aim of the task, a search for the appropriate meaning carried out at a deeper level, not by automaticity. If this is true, then a disambiguant reformulation of the problem that eliminates the trap into which the subject has fallen, should produce restructuring and the way to the solution.

Insight Problem Solving as the Overcoming of a Misunderstanding: The Effect of Reformulation

In this article we support our view with experimental evidence, focusing on how a misunderstanding is formed, and how a pragmatic reformulation of the problem, more relevant to the aim of the task, allows the text of the problem to be interpreted in accordance with the solution.

We consider two paradigmatic insight problems, the intriguing Study Window problem, which at first sight appears impossible to solve, and an apparent trivial arithmetical task, the Ties problem ( Mosconi and D’Urso, 1974 ).

The Study Window problem

The study window measures 1 m in height and 1 m wide. The owner decides to enlarge it and calls in a workman. He instructs the man to double the area of the window without changing its shape and so that it still measures 1 m by 1 m. The workman carried out the commission. How did he do it?

This problem was investigated in a previous study ( Macchi and Bagassi, 2015 ). For all the participants the problem appeared impossible to solve, and nobody actually solved it. The explanation we gave for the difficulty was the following: “The information provided regarding the dimensions brings a square form to mind. The problem solver interprets the window to be a square 1 m high by 1 m wide, resting on one side. Furthermore, the problem states “without changing its shape,” intending geometric shape of the two windows (square, independently of the orientation of the window), while the problem solver interprets this as meaning the phenomenic shape of the two windows (two squares with the same orthogonal orientation)” ( Macchi and Bagassi, 2015 , p. 156). And this is where the difficulty of the problem lies, in the mental representation of the window and the concurrent interpretation of the text of the problem. Actually, spatial orientation is a decisive factor in the perception of forms. “Two identical shapes seen from different orientations take on a different phenomenic identity” ( Mach, 1914 ).

The solution is to be found in a square (geometric form) that “rests” on one of its angles, thus becoming a rhombus (phenomenic form). Now the dimensions given are those of the two diagonals of the represented rhombus (ABCD).

Figure 1. The study window problem solution.

The “inverted” version of the problem gave less trouble:

[…] The owner decides to make it smaller and calls in a workman. He instructs the man to halve the area of the window […].

Figure 2. The inverted version.

With this version, 30% of the participants solved the problem ( n = 30). They started from the representation of the orthogonal square (ABCD) and looked for the solution within the square, trying to respect the required height and width of the window, and inevitably changing the orientation of the internal square. This time the height and width are the diagonals, rather than the side (base and height) of the square.

Eventually, in another version (the “orientation” version) it was explicit that orientation was not a mandatory attribute of the shape, and this time 66% of the participants found the solution immediately ( n = 30). This confirms the hypothesis that an inappropriate representation of the relation between the orthogonal orientation of the square and its geometric shape is the origin of the misunderstanding .

The “orientation” version:

A study window measures 1 m in height and 1 m wide. The owner decides to make it smaller and calls in a workman. He instructs the man to halve the area of the window: the workman can change the orientation of the window, but not its shape and in such a way that it still measures one meter by one meter. The workman carries out the commission. How did he do it?

While with the Study window problem the subjects who do not arrive at the solution, and who are the totality, know they are wrong, with the problem we are now going to examine, the Ties problem, those who are wrong do not realize it at all and the solution they propose is experienced as the correct solution.

The Ties Problem ( Mosconi and D’Urso, 1974 )

Peter and John have the same number of ties.

Peter gives John five of his ties.

How many ties does John have now more than Peter?

We believe that the seemingly trivial problem is actually the result of the simultaneous activation and mutual interference of complex cognitive processes that prevent its solution.

The problem has been submitted to 50 undergraduate students of the Humanities Faculty of the University of Milano-Bicocca. The participants were tested individually and were randomly assigned to three groups: control version ( n = 50), experimental version 2 ( n = 20), and experimental version 3 ( n = 23). All groups were tested in Italian. Each participant was randomly assigned to one of the conditions and received a form containing only one version of the two assigned problems. There was no time limit. They were invited to think aloud and their spontaneous justifications were recorded and then transcribed.

The correct answer is obviously “ten,” but it must not be so obvious if it is given by only one third of the subjects (32%), while the remaining two thirds give the wrong answer “five,” which is so dominant.

If we consider the text of the problem from the point of view of the information explicitly transmitted ( said ), we have that it only theoretically provides the necessary information to reach the solution and precisely that: (a) the number of ties initially owned by P. and J. is equal, (b) P. gives J. five of his ties. However, the subjects are wrong. What emerges, however, from the spontaneous justifications given by the subjects who give the wrong answer is that they see only the increase of J. and not the consequent loss of P. by five ties. We report two typical justifications: “P. gives five of his to J., J. has five more ties than P., the five P. gave him” and also “They started from the same number of ties, so if P. gives J. five ties, J. should have five more than P.”

Slightly different from the previous ones is the following recurrent answer, in which the participants also consider the decrease of P. as well as the increase of J.: “I see five ties at stake, which are the ones that move,” or also “There are these five ties that go from one to the other, so one has five ties less and the other has five more,” reaching however the conclusion similar to the previous one that “J. has five ties more, because the other gave them to him.” 2

Almost always the participants who answer “five” use a numerical example to justify the answer given or to find a solution to the problem, after some unsuccessful attempts. It is paradoxical how many of these participants accept that the problem has two solutions, one “five ties” obtained by reasoning without considering a concrete number of initial ties, owned by P. and J., the other “ten ties” obtained by using a numerical example. So, for example, we read in the protocol of a participant who, after having answered “five more ties,” using a numerical example, finds “ten” of difference between the ties of P. and those of J.: “Well! I think the “five” is still more and more exact; for me this one has five more, period and that’s it.” “Making the concrete example: “ten” – he chases another subject on an abstract level. I would be more inclined to another formula, to five.”

About half of the subjects who give the answer “five,” in fact, at first refuse to answer because “we don’t know the initial number and therefore we can’t know how many ties J. has more than P.,” or at the most they answer: “J. has five ties more, P. five less, more we can’t know, because a data is missing.”

Even before this difficulty, so to speak, operational, the text of the problem is difficult because in it the quantity relative to the decrease of P. remains implicit (−5). The resulting misunderstanding is that if the quantity transferred is five ties, the resulting difference is only five ties: if the ties that P. gives to J. are five, how can J. have 10 ties more than P.?

So the difficulty of the problem lies in the discrepancy between the quantity transferred and the bidirectional effect that this quantity determines with its displacement. Resolving implies a restructuring of the sentence: “Peter gives John five of his ties (and therefore he loses five).” And this is precisely the reasoning carried out by those subjects who give the right answer “ten.”

We have therefore formulated a new version in which a pair of verbs should make explicit the loss of P.:

Peter loses five of his ties and John takes them.

However, the results obtained with this version, submitted to 20 other subjects, substantially confirm the results obtained with the original version: the correct answers are 17% (3/20) and the wrong ones 75% (15/20). From a Chi-square test (χ 2 = 2,088 p = 0.148) it results no significant difference between the two versions.

If we go to read the spontaneous justifications, we find that the subjects who give the answer “five” motivate it in a similar way to the subjects of the original version. So, for example: “P. loses five, J. gets them, so J. has five ties more than P.”

The decrease of P. is still not perceived, and the discrepancy between the lost amount of ties and the double effect that this quantity determines with its displacement persists.

Therefore, a new version has been realized in which the amount of ties lost by P. has nothing to do with J’s acquisition of five ties, the two amounts of ties are different and then they are perceived as decoupled, so as to neutralize the perceptual-conceptual factor underlying it.

Peter loses five of his ties and John buys five new ones.

It was submitted to 23 participants. Of them, 17 (74%) gave the answer “ten” and only 3 (13%) the answer “five.” There was a significant difference (χ 2 = 16,104 p = 0.000) between the results obtained using the present experimental version and the results from the control version. The participants who give the correct solution “ten” mostly motivate their answer as follows: “P. loses five and therefore J. has also those five that P. lost; he buys another five, there are ten,” declaring that he “added to the five that P. had lost the five that J. had bought.” The effectiveness of the experimental manipulation adopted is confirmed. 3

The satisfactory results obtained with this version cannot be attributed to the use of two different verbs, which proved to be ineffective (see version 2), but to the splitting, and consequent differentiation (J. has in addition five new ties), of the two quantities.

This time, the increase of J. and the decrease of P. are grasped as simultaneous and distinct and their combined effect is not identified with one or the other, but is equal to the sum of +5 and −5 in absolute terms.

The hypothesis regarding the effect of reformulation has also been confirmed in classical insight problems such as the Square and the Parallelogram ( Wertheimer, 1925 ), the Pigs in a Pen ( Schooler et al., 1993 ), the Bat & Ball ( Frederick, 2005 ) in recent studies ( Macchi and Bagassi, 2012 , 2015 ) which showed a dramatic increase in the number of solutions.

In their original version these problems are true brain teasers, and the majority of participants in these studies needed them to be reformulated in order to reach the solution. In Appendix B we present in detail the results obtained (see Table 1 ). Below we report, for each problem, the text of the original version in comparison with the reformulated experimental version.

Table 1. Percentages of correct solutions with reformulated experimental versions.

Square and Parallelogram Problem ( Wertheimer, 1925 )

Given that AB = a and AG = b, find the sum of the areas of square ABCD and parallelogram EBGD ( Figures 3 , 4 ).

Figure 3. The square and parallelogram problem.

Figure 4. Solution.

Experimental Version

Given that AB = a and AG = b , find the sum of the areas of the two partially overlapping figures .

Pigs in a Pen Problem ( Schooler et al., 1993 )

Nine pigs are kept in a square pen . Build two more square enclosures that would put each pig in a pen by itself ( Figures 5 , 6 ).

Figure 5. The pigs in a pen problem.

Figure 6. Solution.

Nine pigs are kept in a square pen. Build two more squares that would put each pig in a by itself .

Bat and Ball Problem ( Frederick, 2005 )

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. How much does the ball cost? ___cents.

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. Find the cost of the bat and of the ball .

Once the problem knots that alter the aim of the task have been identified, the reformulation technique can be a valid didactic tool, as it allows to reveal the misunderstanding and to eliminate it without changing the mathematical nature of the problem. The training to creativity would consist in this sense in training to have interpretative keys different from the usual, when the difficulty cannot be addressed through computational techniques.

Closing Thoughts

By identifying the misunderstanding in problem solving, the reformulation technique has made it possible to eliminate the problem knots, without changing the mathematical nature of the problem. With the experimental reformulated versions of paradigmatic problems, both apparent trivial tasks or brain teasers have obtained a significant increase in correct answers.

Studying how an insight problem is formed, and not just how it is solved, may well become an important topic in education. We focus on undergraduate students’ strategies and their errors while solving problems, and the specific cognitive processes involved in misunderstanding, which are crucial to better exploit what could be beneficial to reach the solution and to teach how to improve the ability to solve problems.

Without violating the need for the necessary rigor of a demonstration, for example, it is possible to organize the problem-demonstration discourse according to a different criterion, precisely by favoring the psychological needs of the subject to whom the explanation discourse is addressed, taking care to organize the explanation with regard to the way his mind works, to what can favor its comprehension and facilitate its memory.

On the other hand, one of the criteria traditionally followed by mathematicians in constructing, for example, demonstrations, or at least in explaining them, is to never make any statement that is not supported by the elements provided above. In essence, in the course of the demonstration nothing is anticipated, and indeed it happens frequently that the propositions directly relevant and relevant to the development of the reasoning (for example, the steps of a geometric demonstration) are preceded by digressions intended to introduce and deal with the elements that legitimize them. As a consequence of such an expositive formalism, the recipient of the speech (the student) often finds himself in the situation of being led to the final conclusion a bit like a blind man who, even though he knows the goal, does not see the way, but can only control step by step the road he is walking along and with difficulty becomes aware of the itinerary.

The text of every problem, if formulated in natural language, has a psychorhetoric dimension, in the sense that in every speech, that is in the production and reception of every speech, there are aspects related to the way the mind works – and therefore psychological and rhetorical – that are decisive for comprehensibility, expressive adequacy and communicative effectiveness. It is precisely to these aspects that we refer to when we talk about the psychorhetoric dimension. Rhetoric, from the point of view of the broadcaster, has studied discourse in relation to the recipient, and therefore to its acceptability, comprehensibility and effectiveness, so that we can say that rhetoric has studied discourse “psychologically.”

Adopting this perspective, the commonplace that the rhetorical dimension only concerns the common discourse, i.e., the discourse that concerns debatable issues, and not the scientific discourse (logical-mathematical-demonstrative), which would be exempt from it, is falling away. The matter dealt with, the truth of what is actually said, is not sufficient to guarantee comprehension.

Data Availability Statement

The datasets generated for this study are available on request to the corresponding author.

Ethics Statement

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.

Author Contributions

LM and MB devised the project, developed the theory, carried out the experiment and wrote the manuscript. Both authors contributed to the article and approved the submitted version.

Conflict of Interest

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.

• ^ The theoretical framework assumed here is Paul Grice’s theory of communication (1975) based on the existence in communication of the explicit layer ( said ) and of the implicit ( implied ), so that the recognition of the communicative intention of the speaker by the interlocutor is crucial for comprehension.
• ^ A participant who after having given the solution “five” corrects himself in “ten” explains the first answer as follows: “it is more immediate, in my opinion, to see the real five ties that are moved, because they are five things that are moved; then as a more immediate answer is ‘five,’ because it is something more real, less mathematical.”
• ^ The factor indicated is certainly the main responsible for the answer “five,” but not the only one (see the Appendix for a pragmatic analysis of the text).
• ^ Versions and results of the problems exposed are already published in Macchi e Bagassi 2012, 2014, 2015.

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Pragmatic analysis of the problematic loci of the Ties problem, which emerged from the spontaneous verbalizations of the participants:

- “the same number of ties”

This expression is understood as a neutral information, a kind of base or sliding plane on which the transfer of the five ties takes place and, in fact, these subjects motivate their answer “five” with: “there is this transfer of five ties from P. to J. ….”

- “5 more, 5 less”

We frequently resort to similar expressions in situations where, if I have five units more than another, the other has five less than me and the difference between us is five.

Consider, for example, the case of the years: say that J. is five years older than P. means to say that P. is five years younger than J. and that the difference in years between the two is five, not ten.

In comparisons, we evaluate the difference with something used as a term of reference, for example the age of P., which serves as a basis, the benchmark, precisely.

- “he gives”

The verb “to give” conveys the concept of the growth of the recipient, not the decrease of the giver, therefore, contributes to the crystallization of the “same number,” preventing to grasp the decrease of P.

Appendix B 4

Given that AB = a and AG = b, find the sum of the areas of square ABCD and parallelogram EBGD .

Typically, problem solvers find the problem difficult and fail to see that a is also the altitude of parallelogram EBGD. They tend to calculate its area with onerous and futile methods, while the solution can be reached with a smart method, consisting of restructuring the entire given shape into two partially overlapping triangles ABG and ECD. The sum of their areas is 2 x a b /2 = a b . Moreover, by shifting one of the triangles so that DE coincides with GB, the answer is “ a b ,” which is the area of the resultant rectangle. Referring to a square and a parallelogram fixes a favored interpretation of the perceptive stimuli, according to those principles of perceptive organization thoroughly studied by the Gestalt Theory. It firmly sets the calculation of the area on the sum of the two specific shapes dealt with in the text, while, the problem actually requires calculation of the area of the shape, however organized, as the sum of two triangles rectangles, or the area of only one rectangle, as well as the sum of square and parallelogram. Hence, the process of restructuring is quite difficult.

To test our hypotheses we formulated an experimental version:

In this formulation of the problem, the text does not impose constraints on the interpretation/organization of the figure, and the spontaneous, default interpretation is no longer fixed. Instead of asking for “the areas of square and parallelogram,” the problem asks for the areas of “the two partially overlapping figures.” We predicted that the experimental version would allow the subjects to see and consider the two triangles also.

Actually, we found that 80% of the participants (28 out of 35) gave a correct answer, and most of them (21 out of 28) gave the smart “two triangles” solution. In the control version, on the other hand, only 19% (9 out of 47) gave the correct response, and of these only two gave the “two triangles” solution.

The findings were replicated in the “Pigs in a pen” problem:

Nine pigs are kept in a square pen . Build two more square enclosures that would put each pig in a pen by itself.

The difficulty of this problem lies in the interpretation of the request, nine pigs each individually enclosed in a square pen, having only two more square enclosures. This interpretation is supported by the favored, orthogonal reference scheme, with which we represent the square. This privileged organization, according to our hypothesis, is fixed by the text which transmits the implicature that the pens in which the piglets are individually isolated must be square in shape too. The function of enclosure wrongfully implies the concept of a square. The task, on the contrary, only requires to pen each pig.

Once again, we created an experimental version by reformulating the problem, eliminating the word “enclosure” and the phrase “in a pen.” The implicit inference that the pen is necessarily square is not drawn.

The experimental version yielded 87% correct answers (20 out of 23), while the control version yielded only 38% correct answers (8 out of 25).

The formulation of the experimental versions was more relevant to the aim of the task, and allowed the perceptual stimuli to be interpreted in accordance with the solution.

The relevance of text and the re-interpretation of perceptual stimuli, goal oriented to the aim of the task, were worked out in unison in an interrelated interpretative “game.”

We further investigated the interpretative activity of thinking, by studying the “Bat and ball” problem, which is part of the CRT. Correct performance is usually considered to be evidence of reflective cognitive ability (correlated with high IQ scores), versus intuitive, erroneous answers to the problem ( Frederick, 2005 ).

Bat and Ball problem

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. How much does the ball cost?___cents

Of course the answer which immediately comes to mind is 10 cents, which is incorrect as, in this case, the difference between $ 1.00 and 10 cents is only 90 cents, not $1.00 as the problem stipulates. The correct response is 5 cents.

Number physiognomics and the plausibility of the cost are traditionally considered responsible for this kind of error ( Frederick, 2005 ; Kahneman, 2003 ).

These factors aside, we argue that if the rhetoric structure of the text is analyzed, the question as formulated concerns only the ball, implying that the cost of the bat is already known. The question gives the key to the interpretation of what has been said in each problem and, generally speaking, in every discourse. Given data, therefore, is interpreted in the light of the question. Hence, “The bat costs $ 1.00 more than” becomes “The bat costs $ 1.00,” by leaving out “more than.”

According to our hypothesis, independently of the different cognitive styles, erroneous responses could be the effect of the rhetorical structure of the text, where the question is not adequate to the aim of the task. Consequently, we predicted that if the question were to be reformulated to become more relevant, the subjects would find it easier to grasp the correct response. In the light of our perspective, the cognitive abilities involved in the correct response were also reinterpreted. Consequently, we reformulated the text as follows in order to eliminate this misleading inference:

This time we predicted an increase in the number of correct answers. The difference in the percentages of correct solutions was significant: in the experimental version 90% of the participants gave a correct answer (28 out of 31), and only 10% (2 out of 20) answered correctly in the control condition.

The simple reformulation of the question, which expresses the real aim of the task (to find the cost of both items), does not favor the “short circuit” of considering the cost of the bat as already known (“$1,” by leaving out part of the phrase “more than”).

It still remains to be verified if those subjects who gave the correct response in the control version have a higher level of cognitive reflexive ability compared to the “intuitive” respondents. This has been the general interpretation given in the literature to the difference in performance.

We think it is a matter of a particular kind of reflexive ability, due to which the task is interpreted in the light of the context and not abstracting from it. The difficulty which the problem implicates does not so much involve a high level of abstract reasoning ability as high levels of pragmatic competence, which disambiguates the text. So much so that, intervening only on the pragmatic level, keeping numbers physiognomics and maintaining the plausible costs identical, the problem becomes a trivial arithmetical task.

Keywords : creative problem solving, insight, misunderstanding, pragmatics, language and thought

Citation: Bagassi M and Macchi L (2020) Creative Problem Solving as Overcoming a Misunderstanding. Front. Educ. 5:538202. doi: 10.3389/feduc.2020.538202

Received: 26 February 2020; Accepted: 29 October 2020; Published: 03 December 2020.

Reviewed by:

Copyright © 2020 Bagassi and Macchi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Laura Macchi, [email protected]

This article is part of the Research Topic

Psychology and Mathematics Education

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Problem solving through values: A challenge for thinking and capability development

• • This paper introduces the 4W framework of consistent problem solving through values.
• • The 4W suggests when, how and why the explication of values helps to solve a problem.
• • The 4W is significant to teach students to cope with problems having crucial consequences.
• • The paper considers challenges using such framework of thinking in different fields of education.

The paper aims to introduce the conceptual framework of problem solving through values. The framework consists of problem analysis, selection of value(s) as a background for the solution, the search for alternative ways of the solution, and the rationale for the solution. This framework reveals when, how, and why is important to think about values when solving problems. A consistent process fosters cohesive and creative value-based thinking during problem solving rather than teaching specific values. Therefore, the framework discloses the possibility for enabling the development of value-grounded problem solving capability.The application of this framework highlights the importance of responsibility for the chosen values that are the basis for the alternatives which determine actions. The 4W framework is meaningful for the people’s lives and their professional work. It is particularly important in the process of future professionals’ education. Critical issues concerning the development of problem solving through values are discussed when considering and examining options for the implementation of the 4W framework in educational institutions.

1. Introduction

The core competencies necessary for future professionals include problem solving based on complexity and collaborative approaches ( OECD, 2018 ). Currently, the emphasis is put on the development of technical, technological skills as well as system thinking and other cognitive abilities (e.g., Barber, 2018 ; Blanco, Schirmbeck, & Costa, 2018 ). Hence, education prepares learners with high qualifications yet lacking in moral values ( Nadda, 2017 ). Educational researchers (e.g., Barnett, 2007 ; Harland & Pickering, 2010 ) stress that such skills and abilities ( the how? ), as well as knowledge ( the what? ), are insufficient to educate a person for society and the world. The philosophy of education underlines both the epistemological and ontological dimensions of learning. Barnett (2007) points out that the ontological dimension has to be above the epistemological one. The ontological dimension encompasses the issues related to values that education should foster ( Harland & Pickering, 2010 ). In addition, values are closely related to the enablement of learners in educational environments ( Jucevičienė et al., 2010 ). For these reasons, ‘ the why ?’ based on values is required in the learning process. The question arises as to what values and how it makes sense to educate them. Value-based education seeks to address these issues and concentrates on values transfer due to their integration into the curriculum. Yazdani and Akbarilakeh (2017) discussed that value-based education could only convey factual knowledge of values and ethics. However, such education does not guarantee the internalization of values. Nevertheless, value-based education indicates problem solving as one of the possibilities to develop values.

Values guide and affect personal behavior encompassing the ethical aspects of solutions ( Roccas, Sagiv, & Navon, 2017 ; Schwartz, 1992 , 2012 ; Verplanken & Holland, 2002 ). Therefore, they represent the essential foundation for solving a problem. Growing evidence indicates the creative potential of values ( Dollinger, Burke, & Gump, 2007 ; Kasof, Chen, Himsel, & Greenberger, 2007 ; Lebedeva et al., 2019) and emphasizes their significance for problem solving. Meanwhile, research in problem solving pays little attention to values. Most of the problem solving models (e.g., Newell & Simon, 1972 ; Jonassen, 1997 ) utilize a rational economic approach. Principally, the research on the mechanisms of problem solving have been conducted under laboratory conditions performing simple tasks ( Csapó & Funke, 2017 ). Moreover, some of the decision-making models share the same steps as problem solving (c.f., Donovan, Guss, & Naslund, 2015 ). This explains why these terms are sometimes used interchangeably ( Huitt, 1992 ). Indeed, decision-making is a part of problem solving, which emerges while choosing between alternatives. Yet, values, moral, and ethical issues are more common in decision-making research (e.g., Keeney, 1994 ; Verplanken & Holland, 2002 ; Hall & Davis, 2007 ; Sheehan & Schmidt, 2015 ). Though, research by Shepherd, Patzelt, and Baron (2013) , Baron, Zhao, and Miao (2015) has affirmed that contemporary business decision makers rather often leave aside ethical issues and moral values. Thus, ‘ethical disengagement fallacy’ ( Sternberg, 2017, p.7 ) occurs as people think that ethics is more relevant to others. In the face of such disengagement, ethical issues lose their prominence.

The analysis of the literature revealed a wide field of problem solving research presenting a range of more theoretical insights rather empirical evidence. Despite this, to date, a comprehensive model that reveals how to solve problems emphasizing thinking about values is lacking. This underlines the relevance of the chosen topic, i.e. a challenge for thinking and for the development of capabilities addressing problems through values. To address this gap, the following issues need to be investigated: When, how, and why a problem solver should take into account values during problem solving? What challenges may occur for using such framework of thinking in different fields of education? Aiming this, the authors of the paper substantiated the conceptual framework of problem solving grounded in consistent thinking about values. The substantiation consists of several parts. First, different approaches to solving problems were examined. Second, searching to reveal the possibilities of values integration into problem solving, value-based approaches significant for problem solving were critically analyzed. Third, drawing on the effect of values when solving a problem and their creative potential, the authors of this paper claim that the identification of values and their choice for a solution need to be specified in the process of problem solving. As a synthesis of conclusions coming from the literature review and conceptual extensions regarding values, the authors of the paper created the coherent framework of problem solving through values (so called 4W).

The novelty of the 4W framework is exposed by several contributions. First, the clear design of overall problem solving process with attention on integrated thinking about values is used. Unlike in most models of problem solving, the first stage encompass the identification of a problem, an analysis of a context and the perspectives that influence the whole process, i.e. ‘What?’. The stage ‘What is the basis for a solution?’ focus on values identification and their choice. The stage ‘Ways how?’ encourages to create alternatives considering values. The stage ‘Why?’ represent justification of a chosen alternative according particular issues. Above-mentioned stages including specific steps are not found in any other model of problem solving. Second, even two key stages nurture thinking about values. The specificity of the 4W framework allows expecting its successful practical application. It may help to solve a problem more informed revealing when and how the explication of values helps to reach the desired value-based solution. The particular significance is that the 4W framework can be used to develop capabilities to solve problems through values. The challenges to use the 4W framework in education are discussed.

2. Methodology

To create the 4W framework, the integrative literature review was chosen. According to Snyder (2019) , this review is ‘useful when the purpose of the review is not to cover all articles ever published on the topic but rather to combine perspectives to create new theoretical models’ (p.334). The scope of this review focused on research disclosing problem solving process that paid attention on values. The following databases were used for relevant information search: EBSCO/Hostdatabases (ERIC, Education Source), Emerald, Google Scholar. The first step of this search was conducted using integrated keywords problem solving model , problem solving process, problem solving steps . These keywords were combined with the Boolean operator AND with the second keywords values approach, value-based . The inclusion criteria were used to identify research that: presents theoretical backgrounds and/or empirical evidences; performed within the last 5 years; within an educational context; availability of full text. The sources appropriate for this review was very limited in scope (N = 2).

We implemented the second search only with the same set of the integrated keywords. The inclusion criteria were the same except the date; this criterion was extended up to 10 years. This search presented 85 different sources. After reading the summaries, introductions and conclusions of the sources found, the sources that do not explicitly provide the process/models/steps of problem solving for teaching/learning purposes and eliminates values were excluded. Aiming to see a more accurate picture of the chosen topic, we selected secondary sources from these initial sources.

Several important issues were determined as well. First, most researchers ground their studies on existing problem solving models, however, not based on values. Second, some of them conducted empirical research in order to identify the process of studies participants’ problem solving. Therefore, we included sources without date restrictions trying to identify the principal sources that reveal the process/models/steps of problem solving. Third, decision-making is a part of problem solving process. Accordingly, we performed a search with the additional keywords decision-making AND values approach, value-based decision-making . We used such inclusion criteria: presents theoretical background and/or empirical evidence; no date restriction; within an educational context; availability of full text. These all searches resulted in a total of 16 (9 theoretical and 7 empirical) sources for inclusion. They were the main sources that contributed most fruitfully for the background. We used other sources for the justification the wholeness of the 4W framework. We present the principal results of the conducted literature review in the part ‘The background of the conceptual framework’.

3. The background of the conceptual framework

3.1. different approaches of how to solve a problem.

Researchers from different fields focus on problem solving. As a result, there still seems to be a lack of a conventional definition of problem solving. Regardless of some differences, there is an agreement that problem solving is a cognitive process and one of the meaningful and significant ways of learning ( Funke, 2014 ; Jonassen, 1997 ; Mayer & Wittrock, 2006 ). Differing in approaches to solving a problem, researchers ( Collins, Sibthorp, & Gookin, 2016 ; Jonassen, 1997 ; Litzinger et al., 2010 ; Mayer & Wittrock, 2006 ; O’Loughlin & McFadzean, 1999 ; ect.) present a variety of models that differ in the number of distinct steps. What is similar in these models is that they stress the procedural process of problem solving with the focus on the development of specific skills and competences.

For the sake of this paper, we have focused on those models of problem solving that clarify the process and draw attention to values, specifically, on Huitt (1992) , Basadur, Ellspermann, and Evans (1994) , and Morton (1997) . Integrating the creative approach to problem solving, Newell and Simon (1972) presents six phases: phase 1 - identifying the problem, phase 2 - understanding the problem, phase 3 - posing solutions, phase 4 - choosing solutions, phase 5 - implementing solutions, and phase 6 - final analysis. The weakness of this model is that these phases do not necessarily follow one another, and several can coincide. However, coping with simultaneously occurring phases could be a challenge, especially if these are, for instance, phases five and six. Certainly, it may be necessary to return to the previous phases for further analysis. According to Basadur et al. (1994) , problem solving consists of problem generation, problem formulation, problem solving, and solution implementation stages. Huitt (1992) distinguishes four stages in problem solving: input, processing, output, and review. Both Huitt (1992) and Basadur et al. (1994) four-stage models emphasize a sequential process of problem solving. Thus, problem solving includes four stages that are used in education. For example, problem-based learning employs such stages as introduction of the problem, problem analysis and learning issues, discovery and reporting, solution presentation and evaluation ( Chua, Tan, & Liu, 2016 ). Even PISA 2012 framework for problem solving composes four stages: exploring and understanding, representing and formulating, planning and executing, monitoring and reflecting ( OECD, 2013 ).

Drawing on various approaches to problem solving, it is possible to notice that although each stage is named differently, it is possible to reveal some general steps. These steps reflect the essential idea of problem solving: a search for the solution from the initial state to the desirable state. The identification of a problem and its contextual elements, the generation of alternatives to a problem solution, the evaluation of these alternatives according to specific criteria, the choice of an alternative for a solution, the implementation, and monitoring of the solution are the main proceeding steps in problem solving.

3.2. Value-based approaches relevant for problem solving

Huitt (1992) suggests that important values are among the criteria for the evaluation of alternatives and the effectiveness of a chosen solution. Basadur et al. (1994) point out to visible values in the problem formulation. Morton (1997) underlines that interests, investigation, prevention, and values of all types, which may influence the process, inspire every phase of problem solving. However, the aforementioned authors do not go deeper and do not seek to disclose the significance of values for problem solving.

Decision-making research shows more possibilities for problem solving and values integration. Sheehan and Schmidt (2015) model of ethical decision-making includes moral sensitivity, moral judgment, moral motivation, and moral action where values are presented in the component of moral motivation. Another useful approach concerned with values comes from decision-making in management. It is the concept of Value-Focused Thinking (VFT) proposed by Keeney (1994) . The author argues that the goals often are merely means of achieving results in traditional models of problem solving. Such models frequently do not help to identify logical links between the problem solving goals, values, and alternatives. Thus, according to Keeney (1994) , the decision-making starts with values as they are stated in the goals and objectives of decision-makers. VFT emphasizes the core values of decision-makers that are in a specific context as well as how to find a way to achieve them by using means-ends analysis. The weakness of VFT is its restriction to this means-ends analysis. According to Shin, Jonassen, and McGee (2003) , in searching for a solution, such analysis is weak as the problem solver focuses simply on removing inadequacies between the current state and the goal state. The strengths of this approach underline that values are included in the decision before alternatives are created. Besides, values help to find creative and meaningful alternatives and to assess them. Further, they include the forthcoming consequences of the decision. As VFT emphasizes the significant function of values and clarifies the possibilities of their integration into problem solving, we adapt this approach in the current paper.

3.3. The effect of values when solving a problem

In a broader sense, values provide a direction to a person’s life. Whereas the importance of values is relatively stable over time and across situations, Roccas et al. (2017) argue that values differ in their importance to a person. Verplanken and Holland (2002) investigated the relationship between values and choices or behavior. The research revealed that the activation of a value and the centrality of a value to the self, are the essential elements for value-guided behavior. The activation of values could happen in such cases: when values are the primary focus of attention; if the situation or the information a person is confronted with implies values; when the self is activated. The centrality of a particular value is ‘the degree to which an individual has incorporated this value as part of the self’ ( Verplanken & Holland, 2002, p.436 ). Thus, the perceived importance of values and attention to them determine value-guided behavior.

According to Argandoña (2003) , values can change due to external (changing values in the people around, in society, changes in situations, etc.) and internal (internalization by learning) factors affecting the person. The research by Hall and Davis (2007) indicates that the decision-makers’ applied value profile temporarily changed as they analyzed the issue from multiple perspectives and revealed the existence of a broader set of values. The study by Kirkman (2017) reveal that participants noticed the relevance of moral values to situations they encountered in various contexts.

Values are tightly related to personal integrity and identity and guide an individual’s perception, judgment, and behavior ( Halstead, 1996 ; Schwartz, 1992 ). Sheehan and Schmidt (2015) found that values influenced ethical decision-making of accounting study programme students when they uncovered their own values and grounded in them their individual codes of conduct for future jobs. Hence, the effect of values discloses by observing the problem solver’s decision-making. The latter observations could explain the abundance of ethics-laden research in decision-making rather than in problem solving.

Contemporary researchers emphasize the creative potential of values. Dollinger et al. (2007) , Kasof et al. (2007) , Lebedeva, Schwartz, Plucker, & Van De Vijver, 2019 present to some extent similar findings as they all used Schwartz Value Survey (respectively: Schwartz, 1992 ; ( Schwartz, 1994 ), Schwartz, 2012 ). These studies disclosed that such values as self-direction, stimulation and universalism foster creativity. Kasof et al. (2007) focused their research on identified motivation. Stressing that identified motivation is the only fully autonomous type of external motivation, authors define it as ‘the desire to commence an activity as a means to some end that one greatly values’ (p.106). While identified motivation toward specific values (italic in original) fosters the search for outcomes that express those specific values, this research demonstrated that it could also inhibit creative behavior. Thus, inhibition is necessary, especially in the case where reckless creativity could have painful consequences, for example, when an architect creates a beautiful staircase without a handrail. Consequently, creativity needs to be balanced.

Ultimately, values affect human beings’ lives as they express the motivational goals ( Schwartz, 1992 ). These motivational goals are the comprehensive criteria for a person’s choices when solving problems. Whereas some problem solving models only mention values as possible evaluation criteria, but they do not give any significant suggestions when and how the problem solver could think about the values coming to the understanding that his/her values direct the decision how to solve the problem. The authors of this paper claim that the identification of personal values and their choice for a solution need to be specified in the process of problem solving. This position is clearly reflected in humanistic philosophy and psychology ( Maslow, 2011 ; Rogers, 1995 ) that emphasize personal responsibility for discovering personal values through critical questioning, honest self-esteem, self-discovery, and open-mindedness in the constant pursuit of the truth in the path of individual life. However, fundamental (of humankind) and societal values should be taken into account. McLaughlin (1997) argues that a clear boundary between societal and personal values is difficult to set as they are intertwined due to their existence in complex cultural, social, and political contexts at a particular time. A person is related to time and context when choosing values. As a result, a person assumes existing values as implicit knowledge without as much as a consideration. This is particularly evident in the current consumer society.

Moreover, McLaughlin (1997) stresses that if a particular action should be tolerated and legitimated by society, it does not mean that this action is ultimately morally acceptable in all respects. Education has possibilities to reveal this. One such possibility is to turn to the capability approach ( Sen, 1990 ), which emphasizes what people are effectively able to do and to be. Capability, according to Sen (1990) , reflects a person’s freedom to choose between various ways of living, i.e., the focus is on the development of a person’s capability to choose the life he/she has a reason to value. According to Webster (2017) , ‘in order for people to value certain aspects of life, they need to appreciate the reasons and purposes – the whys – for certain valuing’ (italic in original; p.75). As values reflect and foster these whys, education should supplement the development of capability with attention to values ( Saito, 2003 ). In order to attain this possibility, a person has to be aware of and be able to understand two facets of values. Argandoña (2003) defines them as rationality and virtuality . Rationality refers to values as the ideal of conduct and involves the development of a person’s understanding of what values and why he/she should choose them when solving a problem. Virtuality approaches values as virtues and includes learning to enable a person to live according to his/her values. However, according to McLaughlin (1997) , some people may have specific values that are deep or self-evidently essential. These values are based on fundamental beliefs about the nature and purpose of the human being. Other values can be more or less superficial as they are based on giving priority to one or the other. Thus, virtuality highlights the depth of life harmonized to fundamentally rather than superficially laden values. These approaches inform the rationale for the framework of problem solving through values.

4. The 4W framework of problem solving through values

Similar to the above-presented stages of the problem solving processes, the introduced framework by the authors of this paper revisits them (see Fig. 1 ). The framework is titled 4W as its four stages respond to such questions: Analyzing the Problem: W hat ? → Choice of the value(s): W hat is the background for the solution? → Search for the alternative w ays of the solution: How ? → The rationale for problem solution: W hy is this alternative significant ? The stages of this framework cover seven steps that reveal the logical sequence of problem solving through values.

The 4 W framework: problem solving through values.

Though systematic problem solving models are criticized for being linear and inflexible (e.g., Treffinger & Isaksen, 2005 ), the authors of this paper assume a structural view of the problem solving process due to several reasons. First, the framework enables problem solvers to understand the thorough process of problem solving through values. Second, this framework reveals the depth of each stage and step. Third, problem solving through values encourages tackling problems that have crucial consequences. Only by understanding and mastering the coherence of how problems those require a value-based approach need to be addressed, a problem solver will be able to cope with them in the future. Finally, this framework aims at helping to recognize, to underline personal values, to solve problems through thinking about values, and to take responsibility for choices, even value-based. The feedback supports a direct interrelation between stages. It shapes a dynamic process of problem solving through values.

The first stage of problem solving through values - ‘ The analysis of the problem: What? ’- consists of three steps (see Fig. 1 ). The first step is ‘ Recognizing the problematic situation and naming the problem ’. This step is performed in the following sequence. First, the problem solver should perceive the problematic situation he/she faces in order to understand it. Dostál (2015) argues that the problematic situation has the potential to become the problem necessary to be addressed. Although each problem is limited by its context, not every problematic situation turns into a problem. This is related to the problem solver’s capability and the perception of reality: a person may not ‘see’ the problem if his/her capability to perceive it is not developed ( Dorst, 2006 ; Dostál, 2015 ). Second, after the problem solver recognizes the existence of the problematic situation, the problem solver has to identify the presence or absence of the problem itself, i.e. to name the problem. This is especially important in the case of the ill-structured problems since they cannot be directly visible to the problem solver ( Jonassen, 1997 ). Consequently, this step allows to determine whether the problem solver developed or has acquired the capability to perceive the problematic situation and the problem (naming the problem).

The second step is ‘ Analysing the context of the problem as a reason for its rise ’. At this step, the problem solver aims to analyse the context of the problem. The latter is one of the external issues, and it determines the solution ( Jonassen, 2011 ). However, if more attention is paid to the solution of the problem, it diverts attention from the context ( Fields, 2006 ). The problem solver has to take into account both the conveyed and implied contextual elements in the problematic situation ( Dostál, 2015 ). In other words, the problem solver has to examine it through his/her ‘contextual lenses’ ( Hester & MacG, 2017 , p.208). Thus, during this step the problem solver needs to identify the elements that shape the problem - reasons and circumstances that cause the problem, the factors that can be changed, and stakeholders that are involved in the problematic situation. Whereas the elements of the context mentioned above are within the problematic situation, the problem solver can control many of them. Such control can provide unique ways for a solution.

Although the problem solver tries to predict the undesirable results, some criteria remain underestimated. For that reason, it is necessary to highlight values underlying the various possible goals during the analysis ( Fields, 2006 ). According to Hester and MacG (2017) , values express one of the main features of the context and direct the attention of the problem solver to a given problematic situation. Hence, the problem solver should explore the value-based positions that emerge in the context of the problem.

The analysis of these contextual elements focus not only on a specific problematic situation but also on the problem that has emerged. This requires setting boundaries of attention for an in-depth understanding ( Fields, 2006 ; Hester & MacG, 2017 ). Such understanding influences several actions: (a) the recognition of inappropriate aspects of the problematic situation; (b) the emergence of paths in which identified aspects are expected to change. These actions ensure consistency and safeguard against distractions. Thus, the problem solver can now recognize and identify the factors that influence the problem although they are outside of the problematic situation. However, the problem solver possesses no control over them. With the help of such context analysis, the problem solver constructs a thorough understanding of the problem. Moreover, the problem solver becomes ready to look at the problem from different perspectives.

The third step is ‘ Perspectives emerging in the problem ’. Ims and Zsolnai (2009) argue that problem solving usually contains a ‘problematic search’. Such a search is a pragmatic activity as the problem itself induces it. Thus, the problem solver searches for a superficial solution. As a result, the focus is on control over the problem rather than a deeper understanding of the problem itself. The analysis of the problem, especially including value-based approaches, reveals the necessity to consider the problem from a variety of perspectives. Mitroff (2000) builds on Linstone (1989) ideas and claims that a sound foundation of both naming and solving any problem lays in such perspectives: the technical/scientific, the interpersonal/social, the existential, and the systemic (see Table 1 ).

The main characteristics of four perspectives for problem solving

Whereas all problems have significant aspects of each perspective, disregarding one or another may lead to the wrong way of solving the problem. While analysing all four perspectives is essential, this does not mean that they all are equally important. Therefore, it is necessary to justify why one or another perspective is more relevant and significant in a particular case. Such analysis, according to Linstone (1989) , ‘forces us to distinguish how we are looking from what we are looking at’ (p.312; italic in original). Hence, the problem solver broadens the understanding of various perspectives and develops the capability to see the bigger picture ( Hall & Davis, 2007 ).

The problem solver aims to identify and describe four perspectives that have emerged in the problem during this step. In order to identify perspectives, the problem solver search answers to the following questions. First, regarding the technical/scientific perspective: What technical/scientific reasons are brought out in the problem? How and to what extent do they influence a problem and its context? Second, regarding the interpersonal/social perspective: What is the impact of the problem on stakeholders? How does it influence their attitudes, living conditions, interests, needs? Third, regarding the existential perspective: How does the problem affect human feelings, experiences, perception, and/or discovery of meaning? Fourth, regarding the systemic perspective: What is the effect of the problem on the person → community → society → the world? Based on the analysis of this step, the problem solver obtains a comprehensive picture of the problem. The next stage is to choose the value(s) that will address the problem.

The second stage - ‘ The choice of value(s): What is the background for the solution?’ - includes the fourth and the fifth steps. The fourth step is ‘ The identification of value(s) as a base for the solution ’. During this step, the problem solver should activate his/her value(s) making it (them) explicit. In order to do this, the problem solver proceeds several sub-steps. First, the problem solver reflects taking into account the analysis done in previous steps. He/she raises up questions revealing values that lay in the background of this analysis: What values does this analyzed context allow me to notice? What values do different perspectives of the problem ‘offer’? Such questioning is important as values are deeply hidden ( Verplanken & Holland, 2002 ) and they form a bias, which restricts the development of the capability to see from various points of view ( Hall & Paradice, 2007 ). In the 4W framework, this bias is relatively eliminated due to the analysis of the context and exploration of the perspectives of a problem. As a result, the problem solver discovers distinct value-based positions and gets an opportunity to identify the ‘value uncaptured’ ( Yang, Evans, Vladimirova, & Rana, 2017, p.1796 ) within the problem analyzed. The problem solver observes that some values exist in the context (the second step) and the disclosed perspectives (the third step). Some of the identified values do not affect the current situation as they are not required, or their potential is not exploited. Thus, looking through various value-based lenses, the problem solver can identify and discover a congruence between the opportunities offered by the values in the problem’s context, disclosed perspectives and his/her value(s). Consequently, the problem solver decides what values he/she chooses as a basis for the desired solution. Since problems usually call for a list of values, it is important to find out their order of priority. Thus, the last sub-step requires the problem solver to choose between fundamentally and superficially laden values.

In some cases, the problem solver identifies that a set of values (more than one value) can lead to the desired solution. If a person chooses this multiple value-based position, two options emerge. The first option is concerned with the analysis of each value-based position separately (from the fifth to the seventh step). In the second option, a person has to uncover which of his/her chosen values are fundamentally laden and which are superficially chosen, considering the desired outcome in the current situation. Such clarification could act as a strategy where the path for the desired solution is possible going from superficially chosen value(s) to fundamentally laden one. When a basis for the solution is established, the problem solver formulates the goal for the desired solution.

The fifth step is ‘ The formulation of the goal for the solution ’. Problem solving highlights essential points that reveal the structure of a person’s goals; thus, a goal is the core element of problem solving ( Funke, 2014 ). Meantime, values reflect the motivational content of the goals ( Schwartz, 1992 ). The attention on the chosen value not only activates it, but also motivates the problem solver. The motivation directs the formulation of the goal. In such a way, values explicitly become a basis of the goal for the solution. Thus, this step involves the problem solver in formulating the goal for the solution as the desired outcome.

The way how to take into account value(s) when formulating the goal is the integration of value(s) chosen by the problem solver in the formulation of the goal ( Keeney, 1994 ). For this purpose the conjunction of a context for a solution (it is analyzed during the second step) and a direction of preference (the chosen value reveals it) serves for the formulation of the goal (that represents the desired solution). In other words, a value should be directly included into the formulation of the goal. The goal could lose value, if value is not included into the goal formulation and remains only in the context of the goal. Let’s take the actual example concerning COVID-19 situation. Naturally, many countries governments’ preference represents such value as human life (‘it is important of every individual’s life’). Thus, most likely the particular country government’s goal of solving the COVID situation could be to save the lifes of the country people. The named problem is a complex where the goal of its solution is also complex, although it sounds simple. However, if the goal as desired outcome is formulated without the chosen value, this value remains in the context and its meaning becomes tacit. In the case of above presented example - the goal could be formulated ‘to provide hospitals with the necessary equipment and facilities’. Such goal has the value ‘human’s life’ in the context, but eliminates the complexity of the problem that leads to a partial solution of the problem. Thus, this step from the problem solver requires caution when formulating the goal as the desired outcome. For this reason, maintaining value is very important when formulating the goal’s text. To avoid the loss of values and maintain their proposed direction, is necessary to take into account values again when creating alternatives.

The third stage - ‘ Search for the alternative ways for a solution: How? ’ - encompasses the sixth step, which is called ‘ Creation of value-based alternatives ’. Frequently problem solver invokes a traditional view of problem identification, generation of alternatives, and selection of criteria for evaluating findings. Keeney (1994) ; Ims and Zsolnai (2009) criticize this rational approach as it supports a search for a partial solution where an active search for alternatives is neglected. Moreover, a problematic situation, according to Perkins (2009) , can create the illusion of a fully framed problem with some apparent weighting and some variations of choices. In this case, essential and distinct alternatives to the solution frequently become unnoticeable. Therefore, Perkins (2009) suggest to replace the focus on the attempts to comprehend the problem itself. Thinking through the ‘value lenses’ offers such opportunities. The deep understanding of the problem leads to the search for the alternative ways of a solution.

Thus, the aim of this step is for the problem solver to reveal the possible alternative ways for searching a desired solution. Most people think they know how to create alternatives, but often without delving into the situation. First of all, the problem solver based on the reflection of (but not limited to) the analysis of the context and the perspectives of the problem generates a range of alternatives. Some of these alternatives represent anchored thinking as he/she accepts the assumptions implicit in generated alternatives and with too little focus on values.

The chosen value with the formulated goal indicates direction and encourages a broader and more creative search for a solution. Hence, the problem solver should consider some of the initial alternatives that could best support the achievement of the desired solution. Values are the principles for evaluating the desirability of any alternative or outcome ( Keeney, 1994 ). Thus, planned actions should reveal the desirable mode of conduct. After such consideration, he/she should draw up a plan setting out the actions required to implement each of considered alternatives.

Lastly, after a thorough examination of each considered alternative and a plan of its implementation, the problem solver chooses one of them. If the problem solver does not see an appropriate alternative, he/she develops new alternatives. However, the problem solver may notice (and usually does) that more than one alternative can help him/her to achieve the desired solution. In this case, he/she indicates which alternative is the main one and has to be implemented in the first place, and what other alternatives and in what sequence will contribute in searching for the desired solution.

The fourth stage - ‘ The rationale for the solution: Why ’ - leads to the seventh step: ‘ The justification of the chosen alternative ’. Keeney (1994) emphasizes the compatibility of alternatives in question with the values that guide the action. This underlines the importance of justifying the choices a person makes where the focus is on taking responsibility. According to Zsolnai (2008) , responsibility means a choice, i.e., the perceived responsibility essentially determines its choice. Responsible justification allows for discovering optimal balance when choosing between distinct value-based alternatives. It also refers to the alternative solution that best reflects responsibility in a particular value context, choice, and implementation.

At this stage, the problem solver revisits the chosen solution and revises it. The problem solver justifies his/her choice based on the following questions: Why did you choose this? Why is this alternative significant looking from the technical/scientific, the interpersonal/social, the existential, and the systemic perspectives? Could you take full responsibility for the implementation of this alternative? Why? How clearly do envisaged actions reflect the goal of the desired solution? Whatever interests and for what reasons do this alternative satisfies in principle? What else do you see in the chosen alternative?

As mentioned above, each person gives priority to one aspect or another. The problem solver has to provide solid arguments for the justification of the chosen alternative. The quality of arguments, according to Jonassen (2011) , should be judged based on the quality of the evidence supporting the chosen alternative and opposing arguments that can reject solutions. Besides, the pursuit of value-based goals reflects the interests of the individual or collective interests. Therefore, it becomes critical for the problem solver to justify the level of responsibility he/she takes in assessing the chosen alternative. Such a complex evaluation of the chosen alternative ensures the acceptance of an integral rather than unilateral solution, as ‘recognizing that, in the end, people benefit most when they act for the common good’ ( Sternberg, 2012, p.46 ).

5. Discussion

The constant emphasis on thinking about values as explicit reasoning in the 4W framework (especially from the choice of the value(s) to the rationale for problem solution) reflects the pursuit of virtues. Virtues form the features of the character that are related to the choice ( Argandoña, 2003 ; McLaughlin, 2005 ). Hence, the problem solver develops value-grounded problem solving capability as the virtuality instead of employing rationality for problem solving.

Argandoña (2003) suggests that, in order to make a sound valuation process of any action, extrinsic, transcendent, and intrinsic types of motives need to be considered. They cover the respective types of values. The 4W framework meets these requirements. An extrinsic motive as ‘attaining the anticipated or expected satisfaction’ ( Argandoña, 2003, p.17 ) is reflected in the formulation of the goal of the solution, the creation of alternatives and especially in the justification of the chosen alternative way when the problem solver revisits the external effect of his/her possible action. Transcendent motive as ‘generating certain effects in others’ ( Argandoña, 2003, p.17 ) is revealed within the analysis of the context, perspectives, and creating alternatives. When the learner considers the creation of alternatives and revisits the chosen alternative, he/she pays more attention to these motives. Two types of motives mentioned so far are closely related to an intrinsic motive that emphasizes learning development within the problem solver. These motives confirm that problem solving is, in fact, lifelong learning. In light of these findings, the 4W framework is concerned with some features of value internalization as it is ‘a psychological outcome of conscious mind reasoning about values’ ( Yazdani & Akbarilakeh, 2017, p.1 ).

The 4W framework is complicated enough in terms of learning. One issue is concerned with the educational environments ( Jucevičienė, 2008 ) required to enable the 4W framework. First, the learning paradigm, rather than direct instruction, lies at the foundation of such environments. Second, such educational environments include the following dimensions: (1) educational goal; (2) learning capacity of the learners; (3) educational content relevant to the educational goal: ways and means of communicating educational content as information presented in advance (they may be real, people among them, as well as virtual); (5) methods and means of developing educational content in the process of learners’ performance; (6) physical environment relevant to the educational goal and conditions of its implementation as well as different items in the environment; (7) individuals involved in the implementation of the educational goal.

Another issue is related to exercising this framework in practice. Despite being aware of the 4W framework, a person may still not want to practice problem solving through values, since most of the solutions are going to be complicated, or may even be painful. One idea worth looking into is to reveal the extent to which problem solving through values can become a habit of mind. Profound focus on personal values, context analysis, and highlighting various perspectives can involve changes in the problem solver’s habit of mind. The constant practice of problem solving through values could first become ‘the epistemic habit of mind’ ( Mezirow, 2009, p.93 ), which means a personal way of knowing things and how to use that knowledge. This echoes Kirkman (2017) findings. The developed capability to notice moral values in situations that students encountered changed some students’ habit of mind as ‘for having “ruined” things by making it impossible not to attend to values in such situations!’ (the feedback from one student; Kirkman, 2017, p.12 ). However, this is not enough, as only those problems that require a value-based approach are addressed. Inevitably, the problem solver eventually encounters the challenges of nurturing ‘the moral-ethical habit of mind’ ( Mezirow, 2009, p.93 ). In pursuance to develop such habits of mind, the curriculum should include the necessity of the practising of the 4W framework.

Thinking based on values when solving problems enables the problem solver to engage in thoughtful reflection in contrast to pragmatic and superficial thinking supported by the consumer society. Reflection begins from the first stage of the 4W framework. As personal values are the basis for the desired solution, the problem solver is also involved in self-reflection. The conscious and continuous reflection on himself/herself and the problematic situation reinforce each step of the 4W framework. Moreover, the fourth stage (‘The rationale for the solution: Why’) involves the problem solver in critical reflection as it concerned with justification of ‘the why , the reasons for and the consequences of what we do’ (italic, bold in original; Mezirow, 1990, p.8 ). Exercising the 4W framework in practice could foster reflective practice. Empirical evidence shows that reflective practice directly impacts knowledge, skills and may lead to changes in personal belief systems and world views ( Slade, Burnham, Catalana, & Waters, 2019 ). Thus, with the help of reflective practice it is possible to identify in more detail how and to what extent the 4W framework has been mastered, what knowledge gained, capabilities developed, how point of views changed, and what influence the change process.

Critical issues related to the development of problem solving through values need to be distinguished when considering and examining options for the implementation of the 4W framework at educational institutions. First, the question to what extent can the 4W framework be incorporated into various subjects needs to be answered. Researchers could focus on applying the 4W framework to specific subjects in the humanities and social sciences. The case is with STEM subjects. Though value issues of sustainable development and ecology are of great importance, in reality STEM teaching is often restricted to the development of knowledge and skills, leaving aside the thinking about values. The special task of the researchers is to help practitioners to apply the 4W framework in STEM subjects. Considering this, researchers could employ the concept of ‘dialogic space’ ( Wegerif, 2011, p.3 ) which places particular importance of dialogue in the process of education emphasizing both the voices of teachers and students, and materials. In addition, the dimensions of educational environments could be useful aligning the 4W framework with STEM subjects. As STEM teaching is more based on solving various special tasks and/or integrating problem-based learning, the 4W framework could be a meaningful tool through which content is mastered, skills are developed, knowledge is acquired by solving pre-prepared specific tasks. In this case, the 4W framework could act as a mean addressing values in STEM teaching.

Second is the question of how to enable the process of problem solving through values. In the current paper, the concept of enabling is understood as an integral component of the empowerment. Juceviciene et al. (2010) specify that at least two perspectives can be employed to explain empowerment : a) through the power of legitimacy (according to Freire, 1996 ); and b) through the perspective of conditions for the acquisition of the required knowledge, capabilities, and competence, i.e., enabling. In this paper the 4W framework does not entail the issue of legitimacy. This issue may occur, for example, when a teacher in economics is expected to provide students with subject knowledge only, rather than adding tasks that involve problem solving through values. Yet, the issue of legitimacy is often implicit. A widespread phenomenon exists that teaching is limited to certain periods that do not have enough time for problem solving through values. The issue of legitimacy as an organizational task that supports/or not the implementation of the 4W framework in any curriculum is a question that calls for further discussion.

Third (if not the first), the issue of an educator’s competence to apply such a framework needs to be addressed. In order for a teacher to be a successful enabler, he/she should have the necessary competence. This is related to the specific pedagogical knowledge and skills, which are highly dependent on the peculiarities of the subject being taught. Nowadays actualities are encouraging to pay attention to STEM subjects and their teacher training. For researchers and teacher training institutions, who will be interested in implementing the 4W framework in STEM subjects, it would be useful to draw attention to ‘a material-dialogic approach to pedagogy’ ( Hetherington & Wegerif, 2018, p.27 ). This approach creates the conditions for a deep learning of STEM subjects revealing additional opportunities for problem solving through values in teaching. Highlighting these opportunities is a task for further research.

In contrast to traditional problem solving models, the 4W framework is more concerned with educational purposes. The prescriptive approach to teaching ( Thorne, 1994 ) is applied to the 4W framework. This approach focuses on providing guidelines that enable students to make sound decisions by making explicit value judgements. The limitation is that the 4W framework is focused on thinking but not executing. It does not include the fifth stage, which would focus on the execution of the decision how to solve the problem. This stage may contain some deviation from the predefined process of the solution of the problem.

6. Conclusions

The current paper focuses on revealing the essence of the 4W framework, which is based on enabling the problem solver to draw attention to when, how, and why it is essential to think about values during the problem solving process from the perspective of it’s design. Accordingly, the 4W framework advocates the coherent approach when solving a problem by using a creative potential of values.

The 4W framework allows the problem solver to look through the lens of his/her values twice. The first time, while formulating the problem solving goal as the desired outcome. The second time is when the problem solver looks deeper into his/her values while exploring alternative ways to solve problems. The problem solver is encouraged to reason about, find, accept, reject, compare values, and become responsible for the consequences of the choices grounded on his/her values. Thus, the problem solver could benefit from the 4W framework especially when dealing with issues having crucial consequences.

An educational approach reveals that the 4W framework could enable the development of value-grounded problem solving capability. As problem solving encourages the development of higher-order thinking skills, the consistent inclusion of values enriches them.

The 4W framework requires the educational environments for its enablement. The enablement process of problem solving through values could be based on the perspective of conditions for the acquisition of the required knowledge and capability. Continuous practice of this framework not only encourages reflection, but can also contribute to the creation of the epistemic habit of mind. Applying the 4W framework to specific subjects in the humanities and social sciences might face less challenge than STEM ones. The issue of an educator’s competence to apply such a framework is highly important. The discussed issues present significant challenges for researchers and educators. Caring that the curriculum of different courses should foresee problem solving through values, both practicing and empirical research are necessary.

Declaration of interests

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Both authors have approved the final article.

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How to Solve Problems

• Laura Amico

To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

• Laura Amico is a former senior editor at Harvard Business Review.

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35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

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Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

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Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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Many studies have incorporated concept maps into digital games to enable learners to make connections between subject concepts in the game. However, most learners do not associate spontaneously with the thematic concepts in the game but need to be facilitated by effective scaffolding mechanisms to reconceptualize the learning process and content. Therefore, this study proposed a knowledge check-based concept map-guided gaming strategy for chemistry learning for secondary-level learners. Specifically, the knowledge check-based concept map-guided gaming strategy was employed as a learning strategy while playing digital games. The knowledge check mechanismwas developed based on the notation of two-tier testing. Moreover, the learning environment was a self-developed chemical classification-based digital game, in which learners learned through concept mapping guided gaming tasks with factual and conceptual questions to confirm that they can actually learn content and conceptual understanding in the game. To understand the effects of the proposed strategy, a quasi-experimental design was adopted to measure compare two groups’ learning achievement, problem-solving awareness, critical thinking tendency, and germane cognitive load of seventh-grade students using the knowledge check-based concept map-guided gaming strategy and the conventional concept map-guided gaming strategy. The results of the study showed that learners’ learning achievement, problem-solving awareness, critical thinking tendency, and germane cognitive load in chemistry learning were effectively improved by the knowledge check-based concept map-guided gaming strategy. Furthermore, this study implies that teachers can adjust their teaching scaffolds and provide strategies according to learners’ learning behaviors in digital game-based learning.

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Comprehending complex chemistry problems in a structured and enjoyable manner: A concept mapping-based contextual gaming approach

Implementation of Game-transformed Inquiry-based Learning to Promote the Understanding of and Motivation to Learn Chemistry

Essentials of Gamification in Education: A Game-Based Learning

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The datasets generated and analyzed during the current study are not publicly available due to privacy and ethical considerations concerning student data. However, the manuscript provides a comprehensive account of the data used, the methodologies employed in data collection, and the analytical processes applied. Researchers interested in replicating the study or inquiring further into the data may contact the corresponding author. Access to the data will be granted following an assessment of the request and ensuring compliance with privacy regulations and institutional policies.

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Acknowledgements

This study is supported in part by the National Science and Technology Council of Taiwan under contract numbers NSTC 112-2410-H-011-012-MY3 and MOST 111-2410-H-011 -007 -MY3. The study is also supported by the “Empower Vocational Education Research Center” of National Taiwan University of Science and Technology (NTUST) from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

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Chen, KF., Hwang, GJ. & Chen, MR.A. Knowledge check-based concept mapping in digital games: impacts on students’ learning performance and behaviors. Education Tech Research Dev (2024). https://doi.org/10.1007/s11423-024-10378-6

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Gabriel Filippelli, Ph.D., is a Chancellor’s Professor of Earth and Environmental Sciences and Executive Director of the Indiana University Environmental Resilience Institute . Dr. Filippelli is a biogeochemist with broad training in climate change, exposure science, and environmental health. Author of over 200 publications, in 2022 Dr. Filippelli also published the book Climate Change and Life with Elsevier and edited Climate Resilience in Indiana and Beyond with Indiana University Press . He was the Editor-in-Chief for the journal GeoHealth , a Fellow of the International Association of Geochemistry, a 2022, Fulbright Distinguished Chair, and a former National Academy of Sciences Jefferson Science Fellow, where he served as a Senior Science Advisor for the U.S. Department of State.

In his free time, Dr. Filippelli loves to travel, which his job frequently allows him to do, and he enjoys exercising on a daily basis. He also loves to cook and have friends over to his home to share delicious meals and lively conversation.

I am particularly interested in engaging communities to help them identify and overcome environmental challenges that face them. Dr. Gabriel Filippelli

Top photo: Dr. Gabriel Filippelli appeared on a WFYI Indiana Lawmakers episode in March 2024. He discussed climate change, policy, and the need for valuing natural resources as much as profit. Bottom left and right photos: Dr. Gabriel Filippelli talks with Sunday Morning correspondent, Mo Rocca, about the dangers of wearing shoes inside your home. 

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Q and A with Dr. Gabriel Filippelli

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I always liked science and history, and when I was very young I wanted to be an astronomer or an astronaut. But growing up in the mountains, surrounded by rocks, I became interested in the history of the Earth, and first pursued climate history and more recently, the history of environmental contaminants, and the present horrors of human exposures to pollutants.

What problem(s) are you trying to solve/alleviate with your research?

I am particularly interested in engaging communities to help them identify and overcome environmental challenges that face them. This includes my citizen-science work on lead exposure as well as my public speaking and writing activities revolving around the climate crisis. For the first topic, I am working to alleviate lead poisoning, a tragic and avoidable harm that often brings a lifetime of cognitive challenges. Lead is present in soils, dust, paint, and water pipes, but we collectively have done a terrible job of identifying lead hotspots in communities and dealing with them. This is where my community science approach comes in—by providing some guidance, participants collect environmental samples which we analyze for free to identity lead and other heavy metals. If values are normal, then they can carry on with their lives, but when we find elevated values, we provide guidance on low-cost mitigation strategies that participants can use to reduce their risk of exposure. For the second topic, I try to highlight the unjust impacts of climate change and climate-fueled disasters, and place climate change in the geologic context so that people can better understand the forces at play, and can be assured that their individual and collective actions can bend the climate needle to reduce current and future harm. I try to amplify this message by being a frequent media contributor and speaker, and have authored and edited books on the topic.

How is your research making an impact in the local and/or global community?

My impact is due to the timeliness of the topics that I research—lead poisoning and the climate crisis—and to my attempts to explain these issues in terms that everyday people can understand, and thus take action on. The ivory tower (academic institutions) is no place from which to engage society on important and thorny issues—academics are wise to become more public scholars, sharing their ideas and solutions so that they can be incorporated into policy and practice.

What is your favorite part about your research?

I love speaking and writing, as the act of research translation is just so interesting to me. I get the most energy from engaging with students and community members. Oh—and I don’t mind solving geeky technical issues in the lab, either!

How are students involved in your research?

Students are involved from start to finish, particularly those who are interested in not just the technical lab stuff but also in working with the community and presenting results. Students inspire some of my own research ideas, and I love to see them “out in the wild” making an impact in the world in small and big ways.

How are community members engaged in your research?

Community members are my primary research partners. Because the issues that I confront in my research have strong community relevance, I rely on the community members themselves to help co-create feasible, place-appropriate, and equitable research plans so that the results are useful and impactful. Several of my current research practices have been informed by input and creativity of community members, including some approaches to soil lead remediation that I am now working with the United States Environmental Protection Agency (US EPA) to institute as national best practices!

What are the next steps in your research?

I am working on a novel “green soil bank” to introduce to Indianapolis, which will be used to mitigate soil lead contaminations, increase green-ness and climate resilience of the city, fight environmental injustice, and train new generations in the green circular economy.  I am also looking into writing another book on chemistry and climate. I have too many possible ideas at the moment, so I need to whittle them down. And of course, I still actively recruit and train students, who are the engines in my research machine!

Conversation with Dr. Gabriel Filippelli

On Friday, April 26, 2024. from 12 noon to 1 p.m., Dr. Gabriel Filippelli will talk about  “Building Environmental Optimism from the Ground Up.”

Many communities are plagued by long-standing environmental injustices, many of them deeply embedded in the fabric of neighborhoods due to redlining and other systemic practices. These injustices include widespread contamination by lead (a neurotoxin), poor air quality, and lack of climate resilience. Dr. Filippelli will share in-depth examples of these issues, and his own approach to community-based research that strives to provide data, resources, and agency for communities to tip the balance toward equity. Join our conversation to learn how to build healthier and more sustainable communities.

Interested in Becoming an IUPUI TRIP Scholar?

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IUPUI faculty member conducting translational community-based research

• Valued member of an extensive network of researchers/collaborators
• Opportunities to showcase work

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Differentiation by Design

Blending human-centered design research and methodologies with a strategic focus on creative problem solving, dan brown helps made students seek, conceive, and create compelling solutions for the marketplace..

In the Segal Design Institute’s most recent Manufacturing and Design Engineering (MaDE) capstone, all five student teams secured provisional patents for their class projects.

But that result alone is not what brings a smile to Dan Brown ’s face.

“What’s most exciting is watching the students push themselves beyond their comfort zones and work in teams to strategically solve problems through design with distinct differentiations that create advantage,” said Brown, a clinical professor at Segal.

Brown has long championed the concept of “Differentiation by Design” – a trademarked term he has long used to describe his design process – to strategically create innovative solutions to real-world problems in a competitively advantaged way. Through their three-quarter capstone work, MaDE students put Brown’s design thinking doctrine into action.

“It’s fundamentally working smarter, not harder in a ‘designerly’ way,” Brown said.

Pursuing a competitive edge through design

Brown has lived the “Differentiation by Design” mantra over four decades in product design and entrepreneurship. A serial inventor and design engineering professional, the Chicago native boasts nearly 45 US patents as well as numerous international patents and awards for design and innovation. He’s developed celebrated, game-changing products like the Bionic Wrench and founded LoggerHead Tools in 2005.  

Brown joined the Segal faculty in 2008 after receiving a Master of Product Design and Development Management from Northwestern and subsequently pursuing a PhD at Coventry University in the UK. In the classroom, Brown leaned into his practical experiences and graduate research to educate students and demonstrate the value of strategically baking competitive advantage into the design process.

Brown defines design as “how people seek, conceive, and create new knowledge” and innovation as “how new knowledge competes with existing knowledge.” The competitive advantage, then, is innovation’s key metric – and the target Brown actively promotes with students as they pursue novel solutions.

“We’re teaching beyond the skills of research, data collection, and analysis. Our capstone focus is the application and practice of strategic critical thinking, research, and process rigor applied to real, right-now problems in a professionally appropriate way,” he said.

While promoting core elements of human-ce ntered design, such as stakeholder research and iterative testing, Brown also provides students with deep instruction on how to design with strong intellectual property in mind. Specifically, he trumpets the importance of patents and other forms of intellectual property to protecting one’s competitive edge. He also incorporates patent research as primary research to guide strategic design.

“If you’re going to invest your time, effort, and money, you need to be able to protect it and essentially design the strategy to protect your IP as you create it. Without protection, you will simply lose the control of who benefits from your efforts,” said Brown, who recently completed a three-year term on the United States Patent and Trademark Office’s Patent Public Advisory Committee. The US Secretary of Commerce appointed him to the committee to represent the voices of independent inventors.

Providing students a powerful experience

Brown’s Differentiation by Design ethos is evident in the MaDE capstone he leads alongside fellow Segal clinical professor David Gatchell, director of the MaDE undergraduate program.  

Together, Brown and Gatchell reject handing students a defined problem or a design process with strict checkpoints. Rather, they encourage exploratory research, creative critical thinking, and rigorous evidence-based reasoning and validation to propel unique design solutions to the real-world problems students identify.

Brown recalls one MaDE team designing a restaurant highchair that could be easily broken down and placed in the standard commercial dishwasher for cleaning, thereby eliminating a pain point for restaurant guests with young children.

“Both Dave and I fondly remember at one point the team, frustrated by the challenges, insisting it was physically impossible to accomplish, but we insisted they push towards a solution,” Brown said. “We often reflect and share the story of how excited the team was having proven themselves wrong.”

Brown has also watched others launch startups from products they designed at Northwestern and then gain marketplace traction given their focus on distinctive IP that allowed for investor interest.

Along the way, Brown has witnessed students’ persistence and confidence grow as they imagine new possibilities and seize compelling opportunities. Even better, they begin to see competitive advantage as an attainable goal when they marry the foundational disciplinary design knowledge of creative problem solving and critical strategic thinking alongside the technical skills and experience gained in their engineering courses.  

“In the MaDE Capstone, we want to prepare students for real-world problem solving and push them beyond what they think they can do,” Brown said. “When we embrace design as a discipline through the lens of how humans seek, conceive, and create new knowledge solutions, and focus them on ethical and responsible competitive outcomes, we are all in better positions for success in society.”

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Center for Undergraduate Research

CUGR Announces Summer 2024 EPIC Fellowship Awardees

The University of Maine’s Center for Undergraduate Research (CUGR) is pleased to announce Summer 2024 EPIC fellowship winners. 

Experiential Programs Innovation Central (EPIC) aspires to provide integrated experiential learning and high-impact, student-centered education opportunities through hands-on exposure to research practices, emerging technologies, design thinking, interdisciplinary experiences, and innovative problem-solving.  

Students interested in pursuing any CUGR fellowship are encouraged to enroll in the EPIC course, INT 125, to support their preparation for undergraduate research beyond the classroom in any discipline.  To learn more, visit umaine.edu/epic. 

Recipients of the EPIC fellowship will receive $4,000 to put towards their research and experiential learning project. 

This year’s recipients are: 

• Robert Atwater , Engineering Physics, “Characterizing the Effects of Defect Doping on BaTiO3,” advised by Nicholas Bingham
• Jenna Cox , Psychology, “The Friendship Machine: Fast Friends And Its Effects Across Time In a University Setting,” advised by Jordan LaBouff
• Katie Davison , Communication Sciences and Disorders and Sociology, “Exploring Social-Communication, Health, and Educational Experiences of Children with Brain Injury,” advised by Jessica Riccardi
• Myles Harrison , Finance and Financial Economics, “A Maine Equity Index: How Have Maine Stocks Fared Over Time? Performance and Characteristics,” advised by Sebastian Lobe
• Matthew Patterson , New Media and Computer Science, “Our ClassXRoom,” advised by Justin Dimmel
• Arrow Smith , Anthropology and English, “Anonymity in Public Space Graffiti: Gender Differences in Public Restrooms across The University of Maine,” advised by Heather Falconer

UGC NET 2024 Paper 1: List of topics you must prepare for

Apr 26, 2024

Teaching Aptitude

Teaching methods encompass various strategies such as lectures, discussions, and demonstrations, each suited to different learning objectives and audiences. A good teacher possesses qualities like patience, effective communication skills, and adaptability to engage and inspire learners.

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Classroom Management

Effective classroom management techniques are essential for maintaining a productive learning environment. This includes establishing clear expectations, managing behavior, and fostering positive relationships among students.

Evaluation Methods

Assessment methods such as assignments and tests are crucial for measuring students' understanding and progress. Choosing appropriate evaluation techniques aligned with learning objectives ensures fair and accurate assessment.

Learner's Characteristics

Understanding Piaget's stages of cognitive development helps educators tailor instruction to meet students' cognitive abilities. Recognizing diverse learning styles, including auditory, visual, and kinesthetic, allows for differentiated instruction to cater to individual needs.

Individual Differences

Every learner is unique, with varying abilities, backgrounds, and motivations. Acknowledging and addressing these differences is vital for creating inclusive learning environments and fostering student success.

Factors Affecting Teaching

Effective curriculum design is fundamental to facilitating meaningful learning experiences. Integrating teaching aids and technology enhances engagement and understanding, while the learning environment and external influences like parental involvement play significant roles in shaping learning outcomes.

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Infrastructure & learning environment.

The physical and social environment in which learning occurs significantly impacts student engagement and achievement. Providing adequate infrastructure and cultivating a supportive learning atmosphere are essential for maximizing learning potential

Teaching Methods

Utilising e-learning platforms like SWAYAM and MOOCs expands access to educational resources and promotes self-directed learning. Group discussions and collaborative learning activities foster critical thinking, communication skills, and peer interaction.

Problem-Solving and Critical Thinking

Encouraging problem-solving methods and critical thinking skills development empowers learners to analyze situations, explore alternatives, and make informed decisions. Balancing learner-centered and teacher-centered approaches fosters active engagement and deep understanding.

Research Aptitude

Differentiating between quantitative and qualitative research methodologies informs effective research design and data collection techniques. Upholding research ethics and avoiding plagiarism ensures the integrity and credibility of scholarly inquiry.

Thanks For Reading!

Next: Meet Nilkrishna Gajare: A Farmer's Son Who Topped JEE Main 2024