7.3 Problem-Solving
Learning objectives.
By the end of this section, you will be able to:
- Describe problem solving strategies
- Define algorithm and heuristic
- Explain some common roadblocks to effective problem solving
People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.
PROBLEM-SOLVING STRATEGIES
When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.
Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.
A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.
Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
- When one is faced with too much information
- When the time to make a decision is limited
- When the decision to be made is unimportant
- When there is access to very little information to use in making the decision
- When an appropriate heuristic happens to come to mind in the same moment
Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.
Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.
Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.
Additional Problem Solving Strategies :
- Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
- Analogy – is using a solution that solves a similar problem.
- Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
- Divide and conquer – breaking down large complex problems into smaller more manageable problems.
- Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
- Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
- Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
- Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
- Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
- Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
- Reduction – adapting the problem to be as similar problems where a solution exists.
- Research – using existing knowledge or solutions to similar problems to solve the problem.
- Root cause analysis – trying to identify the cause of the problem.
The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.
One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :
Missionary-Cannibal Problem
Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.
Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.
The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:
- 1. Only one disk can be moved at a time.
- 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
- 3. No disc may be placed on top of a smaller disk.
Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.
Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.
The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.
GESTALT PSYCHOLOGY AND PROBLEM SOLVING
As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.
As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage (1990) suggesting that while collecting data for what would later be his book The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.
While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).
While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.
Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground. Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).
Solving puzzles.
Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.
How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)
Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:
Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.
Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).
What steps did you take to solve this puzzle? You can read the solution at the end of this section.
Pitfalls to problem solving.
Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.
Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.
Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).
In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.
The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.
Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.
Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.
Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.
References:
Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology
Review Questions:
1. A specific formula for solving a problem is called ________.
a. an algorithm
b. a heuristic
c. a mental set
d. trial and error
2. Solving the Tower of Hanoi problem tends to utilize a ________ strategy of problem solving.
a. divide and conquer
b. means-end analysis
d. experiment
3. A mental shortcut in the form of a general problem-solving framework is called ________.
4. Which type of bias involves becoming fixated on a single trait of a problem?
a. anchoring bias
b. confirmation bias
c. representative bias
d. availability bias
5. Which type of bias involves relying on a false stereotype to make a decision?
6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.
a. social adjustment
b. student load payment options
c. emotional learning
d. insight learning
7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.
a. functional fixedness
c. working memory
Critical Thinking Questions:
1. What is functional fixedness and how can overcoming it help you solve problems?
2. How does an algorithm save you time and energy when solving a problem?
Personal Application Question:
1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?
anchoring bias
availability heuristic
confirmation bias
functional fixedness
hindsight bias
problem-solving strategy
representative bias
trial and error
working backwards
Answers to Exercises
algorithm: problem-solving strategy characterized by a specific set of instructions
anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution
availability heuristic: faulty heuristic in which you make a decision based on information readily available to you
confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs
functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended
heuristic: mental shortcut that saves time when solving a problem
hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t
mental set: continually using an old solution to a problem without results
problem-solving strategy: method for solving problems
representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment
trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found
working backwards: heuristic in which you begin to solve a problem by focusing on the end result
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Thinking and Intelligence
Problem Solving
OpenStaxCollege
[latexpage]
Learning Objectives
By the end of this section, you will be able to:
- Describe problem solving strategies
- Define algorithm and heuristic
- Explain some common roadblocks to effective problem solving
People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
PROBLEM-SOLVING STRATEGIES
When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.
A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.
Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
- When one is faced with too much information
- When the time to make a decision is limited
- When the decision to be made is unimportant
- When there is access to very little information to use in making the decision
- When an appropriate heuristic happens to come to mind in the same moment
Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.
Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.
Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.
Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:
Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).
PITFALLS TO PROBLEM SOLVING
Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.
Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.
Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.
Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).
In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.
The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.
Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .
Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.
Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).
Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.
Review Questions
A specific formula for solving a problem is called ________.
- an algorithm
- a heuristic
- a mental set
- trial and error
A mental shortcut in the form of a general problem-solving framework is called ________.
Which type of bias involves becoming fixated on a single trait of a problem?
- anchoring bias
- confirmation bias
- representative bias
- availability bias
Which type of bias involves relying on a false stereotype to make a decision?
Critical Thinking Questions
What is functional fixedness and how can overcoming it help you solve problems?
Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.
How does an algorithm save you time and energy when solving a problem?
An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.
Personal Application Question
Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?
Problem Solving by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.
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Overview of the Problem-Solving Mental Process
Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
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Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.
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- 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.
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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 Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
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Thinking and Intelligence
Solving problems, learning objectives.
- Describe problem solving strategies, including algorithms and heuristics
People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
Problem-Solving Strategies
When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.
A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them. For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.
Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
- When one is faced with too much information
- When the time to make a decision is limited
- When the decision to be made is unimportant
- When there is access to very little information to use in making the decision
- When an appropriate heuristic happens to come to mind in the same moment
Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.
You can view the transcript for “Can you solve “Einstein’s Riddle”? – Dan Van der Vieren” here (opens in new window) .
Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.
Everyday Connections: Solving Puzzles
Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 1) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.
Figure 1 . How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)
Here is another popular type of puzzle that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:
Figure 2 . Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.
Take a look at the “Puzzling Scales” logic puzzle below (Figure 3). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).
Figure 3 . The puzzle reads, “Since the scales now balance…and balance when arranged this way, then how many marbles will it require to balance with that top?
Were you able to determine how many marbles are needed to balance the scales in the Puzzling Scales? You need nine. Were you able to solve the other problems above? Here are the answers:
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- Can you solve Einsteinu2019s Riddle? . Authored by : Dan Van der Vieren. Provided by : Ted-Ed. Located at : https://www.youtube.com/watch?v=1rDVz_Fb6HQ&index=3&list=PLUmyCeox8XCwB8FrEfDQtQZmCc2qYMS5a . License : Other . License Terms : Standard YouTube License
4 Main problem-solving strategies
In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.
Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.
Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.
Problem-solving stages
What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.
To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:
- Initial state
The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).
For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.
In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?
It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.
Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.
Initial theory in problem-solving
When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.
But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.
Problem-solving strategies
These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:
- Trial and error
1. Algorithms
When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.
Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.
2. Heuristics
Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.
You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.
If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.
When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.
Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.
3. Trial and error
When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.
Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.
This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.
Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.
When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.
I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.
You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.
Pilot problem-solving
No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.
Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.
This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.
Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.
Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.
Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.
Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.
The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.
If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.
Getting your causal thinking right
Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.
All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.
As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.
I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:
“What caused this?” (Projecting present into the past)
“What will this cause?” (Projecting present into the future)
The first question is more relevant to problem-solving and the second to goal-accomplishing.
If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.
Hi, I’m Hanan Parvez (MBA, MA Psychology), founder and author of PsychMechanics. PsychMechanics has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .
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What is problem solving (a definition), why problem solving is important.
- Substance use disorder
- Alcohol use disorder
- Low back pain
- Improving mood in children, adults, and elderly adults
- Emotional distress due to cancer and divorce
Problem Solving vs Critical Thinking
Problem Solving Theory (in Psychology)
Video: the psychology of problem-solving.
Problem Solving Skills
Video: figure it out - the art of problem solving.
Problem-Solving Process & Steps
- Attempting to identify a problem when it occurs
- Defining a problem
- Attempting to understand the problem
- Setting goals related to the problem
- Generating alternative solutions
- Evaluating and choosing the best alternatives
- Implementing the chosen alternatives
- Evaluating the efficacy of the effort at problem-solving
Examples of Problem Solving
- Solution #1: Tanya decides to tackle the problem head-on and decides to change the tire by herself. She lets her work know she might be late, reads the owner’s manual, and successfully changes the tire on her own.
- Solution #2: Tanya decides she doesn’t feel comfortable changing a tire on the busy highway. She lets her work know that she will miss the morning meeting and calls her brother to come and help her change the tire.
- Solution #1: Yasmin decides to modify her workout to a 15-minute stretch on the days she is sick. This way she sticks to her commitment and allows her body to rest.
- Solution #2: Yasmin decides she really doesn’t feel well enough to get out of bed. She takes care of her body by drinking plenty of water and resting. She resumes her routine as soon as she feels better and doesn't beat herself up about the lapse in routine.
- Solution #1: Kai was prepared for this situation because he has seen how bad the technology in the classroom is. He hands out printed copies of his presentation to the professor and class.
- Solution #2: Kai decides to do an oral presentation instead of using his digital materials. He uses notes he prepared to do the presentation without the aid of his slides.
Problem Solving Strategies
Video: problem solving through perspective change.
Problem Solving Methods
Problem-Solving Games & Activities
- Crossword puzzles
- Escape rooms
- Rubik’s cube
- 20 dry spaghetti noodles
- Roll of masking tape
- Yard of string
- 1 marshmallow
- Each team will need a set of materials listed above.
- Instruct each team they have ten minutes to construct the tallest spaghetti tower capable of supporting a marshmallow on top using only the materials provided.
- Once complete, stick a single marshmallow on top of the tower.
- The team whose tower is the tallest and can support a marshmallow wins.
Video: How to Teach Kids Better Problem Solving
Articles Related to Problem Solving
- Self-Management: Definition, Skills & Strategies
- Life Skills: Definition, Examples, & Skills to Build
- Overthinking: Definition, Causes, & How to Stop
Books Related to Problem Solving
- Bulletproof Problem Solving: The One Skill That Changes Everything
- Critical thinking, Logic & Problem Solving: The Ultimate Guide to Better Thinking, Systematic Problem Solving and Making Impeccable Decisions with Secret Tips to Detect Logical Fallacies
- Solve It!: The Mindset and Tools of Smart Problem Solvers
- Think Like a Programmer: An Introduction to Creative Problem Solving
Final Thoughts on Problem Solving
Don't forget to grab our free ebook to learn how to grow your wellness business exponentially.
- Dostál, J. (2015). Theory of problem-solving . Procedia - Social and Behavioral Sciences, 174, 2798–2805.
- D'Zurilla, T. J., & Goldfried, M. R. (1971). Problem-solving and behavior modification . Journal of Abnormal Psychology, 78(1), 107–126.
- Malouff, J., Thorsteinsson, E., & Schutte, N. (2007). The efficacy of problem-solving therapy in reducing mental and physical health problems: A meta-analysis . Clinical Psychology Review, 27(1), 46–57.
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Cognitive Psychology: Different Problem-solving Strategies
From the Lecture Series: Introduction to Psychology
July 20, 2022 Psychology
By Catherine A. Sanderson , Amherst College
The field of psychology has identified a variety of mental shortcuts which we all tend to use when thinking and trying to solve our many problems. however, unfortunately at times, these very helpful shortcuts can lead us into making certain characteristic errors. then, should we avoid them altogether or, tread with caution.
Using an Algorithm
Cognitive psychology has identified various strategies for solving problems. One approach is to use an algorithm, meaning a logical rule or procedure that guarantees solving a type of problem. So, if one is asked to divide 500 by 4, we could use the algorithm we’ve learned to solve long division problems—a process that would work for any numbers, no matter how complex.
This is also a very distinct advantage of an algorithm: it will always work to get us a correct answer. But it also has a downside; it’s time-consuming, and it may be very inefficient.
Let’s take an example where an algorithm is not the best choice. Take a series of letters that can be rearranged to form a word—SPL-OY-OC-HYG. Feel free to pause briefly, about 10 seconds, and try to figure out what this word is. The answer is PSYCHOLOGY.
Shortcuts in Our Thinking
One can solve this without the use of an algorithm. Why? Because a few seconds is not enough time to use an algorithm. With unlimited time, one could solve this problem using an algorithm, which in this case, might involve trying every single combination of each letter in each position. This process would generate 907,208 different combinations, making it time-consuming and inefficient.
Instead of using an algorithm, we often use shortcuts in our thinking. For example, you might have looked at that set of letters, and then kind of randomly guessed a few words that seemed plausible to see if they worked. This strategy—trial and error—involves attempting different solutions to see if one might work. This strategy can work and even be more efficient than an algorithm, but of course it’s not guaranteed.
This article comes directly from content in the video series Introduction to Psychology . Watch it now, on Wondrium .
Another problem-solving strategy that is also designed to be faster than an algorithm is a heuristic. Heuristics are basically educated guesses, based on general knowledge of the world, which can help us solve problems faster. For example, heuristics can narrow down what we try when attempting to unscramble the letters that spell psychology. We probably skip any combinations that never appear in any words we can think of; for example, we can skip two YYs in back to back combination, and any words that start YP or YG.
But heuristics can also lead us astray. If one asks which city is further west, Reno, Nevada or Los Angeles, California, which would be our guess? Most people would say Los Angeles. This is an educated guess, which relies on what we know: LA is in California and touches water on the West Coast, whereas Reno is in Nevada, which is to the east of California. But this guess is in fact wrong: Reno is actually further west than Los Angeles.
Problem-solving Through Insight
That brings us to the final problem-solving approach that we can use—insight, meaning a sudden realization of the solution to a problem. For example, we might have started solving the psychology anagram with trial and error, and been aware of some heuristics, but if we found the solution, it was probably by insight. We felt like the answer just came to us.
Here’s another example of a problem in which insight is needed: An influential Arab sheikh decides to hold a competition to see which one of his two sons will inherit his substantial fortune. He tells them to race their camels to a distant city, but the one whose camel arrives last will inherit the fortune.
The two sons set out, determined to win the inheritance, and wander the desert for days, each attempting to outlast the other. Finally, they come across a wise man and ask him for advice. After the wise man speaks to the two sons, they immediately jump on the camels and race at full gallop to the target city. What two words do you think the wise man said? He said, “Switch camels”.
Again one might have guessed this or not, but the key point here is that there’s no strategy for looking at all the options we can use to get this right. It’s not feasible to try all different two-word combinations in the English language.
Out-of-the-box Thinking
What we need in this case, and what the sons needed, was ‘out-of-the-box’ thinking, something that allows us to question the assumption that they have to ride their own camels.
Such insights arrive in a way that is largely, or even entirely, unconscious. That’s why it can sometimes be helpful to set a problem aside, for an incubation period, after which the solution may emerge without additional conscious thought.
Needless to say, these problem-solving strategies can all be useful in daily life. However, choosing the correct one, while being fully aware of its limitations, is a challenge.
Common Questions about the Different Problem-solving Strategies
There is a very distinct advantage of an algorithm in problem-solving : it will always work to get you a correct answer. But it also has a downside; it’s time-consuming, and it may be very inefficient.
A problem-solving strategy that is also designed to be faster than an algorithm is a heuristic . Heuristics are basically educated guesses, based on general knowledge of the world, which can help us solve problems faster.
A problem-solving approach that we can use is insight, meaning a sudden realization of the solution to a problem.
Keep Reading Facebooks’s New Algorithm Raises New Privacy Concerns What Happens in Your Brain When You are Being “Creative?” Einstein’s Field Equations: A Long Road of Trial and Error
- Professor Catherine A. Sanderson
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5 Effective Problem-Solving Strategies
Got a problem you’re trying to solve? Strategies like trial and error, gut instincts, and “working backward” can help. We look at some examples and how to use them.
We all face problems daily. Some are simple, like deciding what to eat for dinner. Others are more complex, like resolving a conflict with a loved one or figuring out how to overcome barriers to your goals.
No matter what problem you’re facing, these five problem-solving strategies can help you develop an effective solution.
What are problem-solving strategies?
To effectively solve a problem, you need a problem-solving strategy .
If you’ve had to make a hard decision before then you know that simply ruminating on the problem isn’t likely to get you anywhere. You need an effective strategy — or a plan of action — to find a solution.
In general, effective problem-solving strategies include the following steps:
- Define the problem.
- Come up with alternative solutions.
- Decide on a solution.
- Implement the solution.
Problem-solving strategies don’t guarantee a solution, but they do help guide you through the process of finding a resolution.
Using problem-solving strategies also has other benefits . For example, having a strategy you can turn to can help you overcome anxiety and distress when you’re first faced with a problem or difficult decision.
The key is to find a problem-solving strategy that works for your specific situation, as well as your personality. One strategy may work well for one type of problem but not another. In addition, some people may prefer certain strategies over others; for example, creative people may prefer to depend on their insights than use algorithms.
It’s important to be equipped with several problem-solving strategies so you use the one that’s most effective for your current situation.
1. Trial and error
One of the most common problem-solving strategies is trial and error. In other words, you try different solutions until you find one that works.
For example, say the problem is that your Wi-Fi isn’t working. You might try different things until it starts working again, like restarting your modem or your devices until you find or resolve the problem. When one solution isn’t successful, you try another until you find what works.
Trial and error can also work for interpersonal problems . For example, if your child always stays up past their bedtime, you might try different solutions — a visual clock to remind them of the time, a reward system, or gentle punishments — to find a solution that works.
2. Heuristics
Sometimes, it’s more effective to solve a problem based on a formula than to try different solutions blindly.
Heuristics are problem-solving strategies or frameworks people use to quickly find an approximate solution. It may not be the optimal solution, but it’s faster than finding the perfect resolution, and it’s “good enough.”
Algorithms or equations are examples of heuristics.
An algorithm is a step-by-step problem-solving strategy based on a formula guaranteed to give you positive results. For example, you might use an algorithm to determine how much food is needed to feed people at a large party.
However, many life problems have no formulaic solution; for example, you may not be able to come up with an algorithm to solve the problem of making amends with your spouse after a fight.
3. Gut instincts (insight problem-solving)
While algorithm-based problem-solving is formulaic, insight problem-solving is the opposite.
When we use insight as a problem-solving strategy we depend on our “gut instincts” or what we know and feel about a situation to come up with a solution. People might describe insight-based solutions to problems as an “aha moment.”
For example, you might face the problem of whether or not to stay in a relationship. The solution to this problem may come as a sudden insight that you need to leave. In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness.
4. Working backward
Working backward is a problem-solving approach often taught to help students solve problems in mathematics. However, it’s useful for real-world problems as well.
Working backward is when you start with the solution and “work backward” to figure out how you got to the solution. For example, if you know you need to be at a party by 8 p.m., you might work backward to problem-solve when you must leave the house, when you need to start getting ready, and so on.
5. Means-end analysis
Means-end analysis is a problem-solving strategy that, to put it simply, helps you get from “point A” to “point B” by examining and coming up with solutions to obstacles.
When using means-end analysis you define the current state or situation (where you are now) and the intended goal. Then, you come up with solutions to get from where you are now to where you need to be.
For example, a student might be faced with the problem of how to successfully get through finals season . They haven’t started studying, but their end goal is to pass all of their finals. Using means-end analysis, the student can examine the obstacles that stand between their current state and their end goal (passing their finals).
They could see, for example, that one obstacle is that they get distracted from studying by their friends. They could devise a solution to this obstacle by putting their phone on “do not disturb” mode while studying.
Let’s recap
Whether they’re simple or complex, we’re faced with problems every day. To successfully solve these problems we need an effective strategy. There are many different problem-solving strategies to choose from.
Although problem-solving strategies don’t guarantee a solution, they can help you feel less anxious about problems and make it more likely that you come up with an answer.
Last medically reviewed on October 31, 2022
8 sources collapsed
- Chu Y, et al. (2011). Human performance on insight problem-solving: A review. docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1094&context=jps
- Dumper K, et al. (n.d.) Chapter 7.3: Problem-solving in introductory psychology. opentext.wsu.edu/psych105/chapter/7-4-problem-solving/
- Foulds LR. (2017). The heuristic problem-solving approach. tandfonline.com/doi/abs/10.1057/jors.1983.205
- Gick ML. (1986). Problem-solving strategies. tandfonline.com/doi/abs/10.1080/00461520.1986.9653026
- Montgomery ME. (2015). Problem solving using means-end analysis. sites.psu.edu/psych256sp15/2015/04/19/problem-solving-using-means-end-analysis/
- Posamentier A, et al. (2015). Problem-solving strategies in mathematics. Chapter 3: Working backwards. worldscientific.com/doi/10.1142/9789814651646_0003
- Sarathy V. (2018). Real world problem-solving. frontiersin.org/articles/10.3389/fnhum.2018.00261/full
- Woods D. (2000). An evidence-based strategy for problem solving. researchgate.net/publication/245332888_An_Evidence-Based_Strategy_for_Problem_Solving
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Psychological Steps Involved in Problem Solving
A mental process or a phenomenon dedicated towards solving problems by discovering and analyzing the problem is referred to as problem-solving. It is a process dedicated to finding not just any solution, but the best solution to resolve any problems. There is no such thing as one best way to solve every kind of problem, since there are unique problems depending upon the situation there are unique solutions too.
There are number of rigid psychological steps involved in problem solving, which is also referred as problem-solving cycle. The steps are in sequential order, and solving any problem requires following them one after another. But, we tend to avoid following this rigid set of steps, which is why it often requires us to go through the same steps over and over again until a satisfactory solution is reached.
Here are the steps involved in problem solving, approved by expert psychologists.
1. Identifying the Problem
Identifying the problem seems like the obvious first stem, but it’s not exactly as simple as it sounds. People might identify the wrong source of a problem, which will render the steps thus carried on useless.
For instance , let’s say you’re having trouble with your studies. identifying the root of your failure is your first priority. The problem here could be that you haven’t been allocating enough time for your studies, or you haven’t tried the right techniques. But, if you make an assumption that the problem here is the subject being too hard, you won’t be able to solve the problem.
2. Defining/Understanding the Problem
It’s vital to properly define the problem once it’s been identified. Only by defining the problem, further steps can be taken to solve it. While at it, you also need to take into consideration different perspectives to understand any problem; this will also help you look for solutions with different perspectives.
Now, following up with the previous example . Let’s say you have identified the problem as not being able to allocate enough time for your studies. You need to sort out the reason behind it. Have you just been procrastinating? Have you been too busy with work? You need to understand the whole problem and reasons behind it, which is the second step in problem solving.
3. Forming a Strategy
Developing a strategy is the next step to finding a solution. Each different situation will require formulating different strategies, also depending on individual’s unique preferences.
Now, you have identified and studied your problem. You can’t just simply jump into trying to solve it. You can’t just quit work and start studying. You need to draw up a strategy to manage your time properly. Allocate less time for not-so-important works, and add them to your study time. Your strategy should be well thought, so that in theory at least, you are able to manage enough time to study properly and not fail in the exams.
4. Organizing Information
- What do you know about the problem?
- What do you not know about the problem?
Accuracy of the solution for your problem will depend on the amount of information available.
The hypothetical strategy you formulate isn’t the all of it either. You need to now contemplate on the information available on the subject matter. Use the aforementioned questions to find out more about the problem. Proper organization of the information will force you to revise your strategy and refine it for best results.
5. Allocating Resources
Time, money and other resources aren’t unlimited. Deciding how high the priority is to solve your problem will help you determine the resources you’ll be using in your course to find the solution. If the problem is important, you can allocate more resources to solving it. However, if the problem isn’t as important, it’s not worth the time and money you might spend on it if not for proper planning.
6. Monitoring Progress
Problem solving isn’t an overnight feat. You can’t just have a body like that of Brad Pitt after a single session in the gym. It takes time and patience. Likewise, you need to work towards solving any problem every day until you finally achieve the results. Looking back at the previous example , if everything’s according to plan, you will be allocating more and more time for your studies until finally you are confident that you’re improving. One way to make sure that you’re on a right path to solving a problem is by keeping track of the progress. To solve the problem illustrated in the first example, you can take self-tests every week or two and track your progress.
7. Evaluating the Results
- Take time to identify the possible sources of the problem. It’s better to spend a substantial amount of time on something right, than on something completely opposite.
- Ask yourself questions like What, Why, How to figure out the causes of the problem. Only then can you move forward on solving it.
- Carefully outline the methods to tackle the problem. There might be different solutions to a problem, record them all.
- Gather all information about the problem and the approaches. More, the merrier.
- From the outlined methods, choose the ones that are viable to approach. Try discarding the ones that have unseen consequences.
- Track your progress as you go.
- Evaluate the outcome of the progress.
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