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Problem-Solving Strategies and Obstacles

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

why is problem solving important in psychology

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

why is problem solving important in psychology

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

  • Discovery of the problem
  • Deciding to tackle the issue
  • Seeking to understand the problem more fully
  • Researching available options or solutions
  • Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

  • Perceptually recognizing the problem
  • Representing the problem in memory
  • Considering relevant information that applies to the problem
  • Identifying different aspects of the problem
  • Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

  • Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
  • Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
  • Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
  • Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

  • Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
  • Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
  • Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
  • Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

  • Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
  • Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
  • Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
  • Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
  • Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
  • Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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

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.

why is problem solving important in psychology

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

why is problem solving important in psychology

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.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

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.

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

   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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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

  • Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

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Further Reading

Baron, J. ( 2008 ). Thinking and deciding (4th ed). New York: Cambridge University Press.

Duncker, K. ( 1945 ). On problem solving. Psychological Monographs , 58(3) (Whole No. 270).

Holyoak, K. J. , & Morrison, R. G. ( 2005 ). The Cambridge handbook of thinking and reasoning . New York: Cambridge University Press.

Mayer, R. E. , & Wittrock, M. C. ( 2006 ). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ: Erlbaum.

Sternberg, R. J. , & Ben-Zeev, T. ( 2001 ). Complex cognition: The psychology of human thought . New York: Oxford University Press.

Weisberg, R. W. ( 2006 ). Creativity . New York: Wiley.

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The Process of Problem Solving

  • Editor's Choice
  • Experimental Psychology
  • Problem Solving

why is problem solving important in psychology

In a 2013 article published in the Journal of Cognitive Psychology , Ngar Yin Louis Lee (Chinese University of Hong Kong) and APS William James Fellow Philip N. Johnson-Laird (Princeton University) examined the ways people develop strategies to solve related problems. In a series of three experiments, the researchers asked participants to solve series of matchstick problems.

In matchstick problems, participants are presented with an array of joined squares. Each square in the array is comprised of separate pieces. Participants are asked to remove a certain number of pieces from the array while still maintaining a specific number of intact squares. Matchstick problems are considered to be fairly sophisticated, as there is generally more than one solution, several different tactics can be used to complete the task, and the types of tactics that are appropriate can change depending on the configuration of the array.

Louis Lee and Johnson-Laird began by examining what influences the tactics people use when they are first confronted with the matchstick problem. They found that initial problem-solving tactics were constrained by perceptual features of the array, with participants solving symmetrical problems and problems with salient solutions faster. Participants frequently used tactics that involved symmetry and salience even when other solutions that did not involve these features existed.

To examine how problem solving develops over time, the researchers had participants solve a series of matchstick problems while verbalizing their problem-solving thought process. The findings from this second experiment showed that people tend to go through two different stages when solving a series of problems.

People begin their problem-solving process in a generative manner during which they explore various tactics — some successful and some not. Then they use their experience to narrow down their choices of tactics, focusing on those that are the most successful. The point at which people begin to rely on this newfound tactical knowledge to create their strategic moves indicates a shift into a more evaluative stage of problem solving.

In the third and last experiment, participants completed a set of matchstick problems that could be solved using similar tactics and then solved several problems that required the use of novel tactics.  The researchers found that participants often had trouble leaving their set of successful tactics behind and shifting to new strategies.

From the three studies, the researchers concluded that when people tackle a problem, their initial moves may be constrained by perceptual components of the problem. As they try out different tactics, they hone in and settle on the ones that are most efficient; however, this deduced knowledge can in turn come to constrain players’ generation of moves — something that can make it difficult to switch to new tactics when required.

These findings help expand our understanding of the role of reasoning and deduction in problem solving and of the processes involved in the shift from less to more effective problem-solving strategies.

Reference Louis Lee, N. Y., Johnson-Laird, P. N. (2013). Strategic changes in problem solving. Journal of Cognitive Psychology, 25 , 165–173. doi: 10.1080/20445911.2012.719021

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Encyclopedia of the Sciences of Learning pp 2680–2683 Cite as

Problem Solving

  • David H. Jonassen 2 &
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Cognition ; Problem typology ; Problem-based learning ; Problems ; Reasoning

Problem solving is the process of constructing and applying mental representations of problems to finding solutions to those problems that are encountered in nearly every context.

Theoretical Background

Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in society (see Problem Typology ). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem. Finding...

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Newell, A., & Simon, H. (1972). Human problem solving . Englewood Cliffs: Prentice Hall.

Rumelhart, D. E., & Norman, D. A. (1988). Representation in memory. In R. C. Atkinson, R. J. Herrnstein, G. Lindzey, & R. D. Luce (Eds.), Steven’s handbook of experimental psychology (Learning and cognition 2nd ed., Vol. 2, pp. 511–587). New York: Wiley.

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Jonassen, D.H., Hung, W. (2012). Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_208

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In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

  • General Approaches to Problem Solving
  • Representational Accounts
  • Problem Space and Search
  • Working Memory and Problem Solving
  • Domain-Specific Problem Solving
  • The Rational Approach
  • Prospect Theory
  • Dual-Process Theory
  • Cognitive Heuristics and Biases

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Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

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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.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

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:

A square shaped outline contains three rows and three columns of dots with equal space between them.

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.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

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.

why is problem solving important in psychology

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] ).

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1:  blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

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 Copyright © 2014 by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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

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

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

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

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

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

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

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

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

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

Analyze, Evaluate, and Create

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

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

7.1. Different kinds of thought and knowledge

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

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

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

Factual and conceptual knowledge

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

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

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

Procedural knowledge

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

Metacognitive knowledge

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

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

The Dunning-Kruger Effect

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

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

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

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

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

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

Critical thinking

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

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

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

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

A Critical Thinker’s Toolkit 

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

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

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

Here are some common sources of biases:

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

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

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

why is problem solving important in psychology

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

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

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

why is problem solving important in psychology

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

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

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

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

bias : an inclination, tendency, leaning, or prejudice

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

7.2 Reasoning and Judgment

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

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

Deductive reasoning

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

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

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

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

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

therefore q

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

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

I won’t have pizza (not p)

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

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

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

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

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

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

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

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

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

You are not eleven feet tall

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

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

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

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

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

Inductive reasoning and judgment

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

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

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

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

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

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

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

Statement #1: Psychology is not my best subject

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

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

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

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

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

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

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

Statement #1: It is late at night.

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

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

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

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

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

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

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

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

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

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

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

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

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

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

Judgment: Breast cancer is the most common type.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

7.3 Problem Solving

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

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

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

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

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

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

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

Defining and Mentally Representing Problems in Order to Solve Them

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

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

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

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

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

Solving Problems with Algorithms and Heuristics

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

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

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

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

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

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

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

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

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

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

An Effective Problem-Solving Sequence

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

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

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

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

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

a mental representation of a category of things in the world

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

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

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

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

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

an inclination, tendency, leaning, or prejudice

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

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

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

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

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

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

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

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

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

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

noticing, comprehending and forming a mental conception of a problem

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

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

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

a sudden realization of a solution to a problem

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

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

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

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

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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.

Fig. 1

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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The Stages of the Problem Solving Cycle in Cognitive Psychology – Understanding, Planning, Execution, Evaluation, and Reflection

  • Post author By bicycle-u
  • Post date 08.12.2023

Problem solving is a fundamental aspect of human cognition. It involves the ability to identify and define a problem, generate potential solutions, evaluate those solutions, and select the most appropriate one. The problem solving cycle is a key concept in cognitive psychology that helps us understand how individuals approach and solve problems.

In the problem solving cycle , individuals first must recognize and define the problem they are facing. This involves identifying the specific issue or obstacle that needs to be overcome. Once the problem is clearly defined, individuals can then move on to the next stage of the cycle.

Next, individuals engage in the process of generating potential solutions . This may involve brainstorming ideas, seeking out information or advice, or experimenting with different approaches. The goal is to come up with as many possible solutions as possible, without judgment or evaluation.

Once a range of potential solutions has been generated, individuals then evaluate these solutions based on their feasibility and effectiveness . This involves assessing the advantages and disadvantages of each solution and considering the potential outcomes of implementing them. It may also involve consulting others or seeking additional information to inform the evaluation process.

Finally, individuals select the most appropriate solution from the evaluated options. This decision-making process takes into account various factors such as the individual’s goals, resources, and constraints. Once a solution has been selected, individuals can then implement and evaluate its effectiveness, closing the problem solving cycle.

The problem solving cycle is a dynamic and iterative process that can be applied to a wide range of problems and situations. It provides a framework for understanding how individuals approach and solve problems, and it can be useful in both personal and professional settings. By understanding the various stages of the problem solving cycle, individuals can become more effective problem solvers and make better decisions.

Understanding the Problem Solving Process

In cognitive psychology, the problem solving process is a key concept in understanding how individuals navigate and overcome challenges. Problem solving is a cyclical process that involves identifying a problem, developing a strategy to solve it, implementing the strategy, and then evaluating the results.

Identifying the problem: The first step in the problem solving cycle is identifying the problem at hand. This may involve defining the problem, gathering information and relevant data, and understanding the desired outcome.

Developing a strategy: Once the problem is identified, individuals must develop a strategy or plan of action to solve it. This may involve brainstorming ideas, evaluating potential solutions, and selecting the best approach.

Implementing the strategy: After a strategy is developed, it must be put into action. This may involve executing specific steps, utilizing resources, and adjusting the strategy as needed.

Evaluating the results: The final step in the problem solving cycle is evaluating the results of the implemented strategy. This may involve assessing the effectiveness of the solution, determining if the desired outcome was achieved, and making any necessary adjustments or improvements.

The Role of Cognitive Psychology

Cognitive psychology plays a crucial role in understanding the problem solving process. It focuses on how individuals perceive, think, and reason about problems, as well as the various strategies and mental processes involved in solving them.

Research in cognitive psychology has shown that problem solving is not purely a linear process, but rather a dynamic and iterative cycle. Individuals may iterate through the different stages of the problem solving cycle multiple times as they encounter new information or face unexpected challenges.

The study of problem solving in cognitive psychology has led to the development of various theories and models, such as the Gestalt theory, which emphasizes the importance of insight and reorganizing information, and the information processing model, which highlights the role of attention, memory, and decision-making in problem solving.

The Importance of Problem Solving Skills

Problem solving is a key concept in cognitive psychology. It is a process that involves identifying, analyzing, and coming up with solutions to problems. Problem solving skills are essential in various aspects of life, including personal and professional contexts.

Mastering problem solving skills enables individuals to tackle challenges and overcome obstacles effectively. It helps in critical thinking, decision making, and finding innovative solutions. Problem solving skills are also important in the field of psychology, as they are often used to understand and address complex psychological issues.

Enhancing Cognitive Abilities

Problem solving activities stimulate and enhance cognitive abilities. They require individuals to think critically, analyze information, and use logical reasoning. By engaging in problem solving, individuals improve their cognitive processes, such as memory, attention, and problem representation.

Building Resilience

Developing problem solving skills also helps in building resilience. It teaches individuals to approach challenges with a proactive mindset and seek solutions rather than giving up. This resilience can be applied in various aspects of life, including personal relationships, work, and education.

In conclusion, problem solving skills play a crucial role in cognitive psychology and various aspects of life. They enhance cognitive abilities, promote critical thinking, and build resilience. Developing and honing problem solving skills is essential for personal growth and success in today’s complex world.

The Four Stages of Problem Solving

Problem solving is a cognitive process that involves the use of mental processes to find a solution to a problem. It is a cycle that is often studied in cognitive psychology. The problem solving cycle consists of four stages, which are:

1. Understanding the Problem

In this stage, the individual must first understand and define the problem. This involves gathering information, analyzing the problem, and identifying the key elements that need to be addressed. It is important to have a clear understanding of the problem before moving on to the next stage.

2. Generating Potential Solutions

Once the problem is understood, the next stage involves generating potential solutions. This requires using both logical and creative thinking to come up with possible ways to solve the problem. It is important to consider different perspectives and explore a variety of options.

3. Evaluating and Selecting Solutions

After generating potential solutions, the individual must evaluate and select the most appropriate solution. This involves weighing the pros and cons of each potential solution and considering factors such as feasibility, effectiveness, and practicality. The goal is to select a solution that is likely to lead to the desired outcome.

4. Implementing and Evaluating the Solution

Once a solution has been selected, the final stage involves implementing the solution and evaluating its effectiveness. This may involve taking action, making changes, and monitoring the results. It is important to assess whether the solution has solved the problem and to make adjustments if needed.

In conclusion, problem solving is a cognitive process that involves four stages: understanding the problem, generating potential solutions, evaluating and selecting solutions, and implementing and evaluating the solution. By following this problem solving cycle, individuals can effectively approach and solve a wide range of problems.

Identifying the Problem

The first step in the problem solving cycle is identifying the problem. In cognitive psychology, this step involves recognizing that there is a problem to be solved and understanding what it entails.

When identifying a problem, it is important to clearly define and articulate what the issue is. This can involve breaking the problem down into smaller components or examining the factors that contribute to the problem.

Factors to consider when identifying a problem:

  • What is the desired outcome or goal?
  • What are the obstacles or challenges that need to be overcome?
  • What are the potential causes or explanations for the problem?

Identifying the problem involves gathering information and analyzing it to gain a better understanding of the situation. This can include conducting research, gathering data, or seeking input from others who may have expertise or experience in the area.

Once the problem has been clearly identified, it can then be approached using the problem solving cycle. By breaking down the problem into smaller steps and systematically working through each one, individuals can increase their chances of finding an effective solution.

Defining the Problem

Defining the problem is a crucial step in the problem-solving cycle. In the context of cognitive psychology, a problem can be defined as a situation or task that requires a solution. This could be a complex mathematical equation, a riddle, or a real-life challenge. The process of defining the problem involves clarifying the specific requirements or constraints of the situation and understanding what needs to be solved. By clearly defining the problem, it becomes easier to identify potential strategies and solutions.

When defining a problem, it is important to consider both the immediate and underlying issues. Often, the surface-level problem may not be the root cause, and addressing only the symptoms may not lead to a satisfactory solution. Therefore, it is essential to dig deeper and identify the underlying factors that contribute to the problem.

Clarifying the requirements

One aspect of defining the problem is clarifying the specific requirements or constraints that need to be considered. These requirements can include the desired outcome, the available resources, the time frame, and any limitations or restrictions. By understanding these requirements, it becomes easier to focus on finding a solution that meets the given criteria.

Understanding the problem space

Another important aspect of defining the problem is understanding the problem space. The problem space refers to the set of all possible solutions and strategies that can be explored to solve the problem. By understanding the problem space, individuals can develop a clearer understanding of the scope of the problem and the potential avenues for finding a solution.

Generating Solution Options

In cognitive psychology, problem solving is a key concept that explores how individuals go about finding solutions to problems. One important aspect of the problem solving cycle is generating solution options.

When faced with a problem, individuals engage in cognitive processes to come up with potential solutions. This often involves brainstorming, where individuals generate a list of possible options.

There are various strategies that individuals can use to generate solution options. One common approach is divergent thinking, which involves thinking creatively and generating a large number of potential solutions. This can be done by considering different perspectives, exploring alternative possibilities, and challenging assumptions.

Another strategy is convergent thinking, which involves evaluating and narrowing down the potential solutions. This can be done by considering the feasibility and practicality of each option, as well as weighing the potential risks and benefits.

It is important for individuals to consider a wide range of solution options, as this increases the likelihood of finding an effective solution. This can be achieved by using techniques such as mind mapping, where individuals visually organize their thoughts and ideas to generate new connections and possibilities.

By generating a variety of solution options, individuals can increase their chances of finding the most suitable and effective solution to a problem. This stage of the problem solving cycle is crucial in the overall problem solving process.

Evaluating and Selecting the Best Solution

Once you have gone through the problem solving cycle and generated potential solutions, the next step is to evaluate and select the best solution. This is an essential part of the problem solving process, as it involves critically analyzing each potential solution and determining which one is the most effective and feasible.

When evaluating potential solutions, it is important to consider various factors. One key factor is the effectiveness of each solution in actually solving the problem at hand. Will the solution address the root cause of the problem, or just temporarily alleviate the symptoms?

In addition to effectiveness, it is also important to consider the feasibility of each solution. Is the solution realistic and practical to implement? Does it require significant resources or time that may not be available? These are all important considerations to take into account when evaluating potential solutions.

Furthermore, it is important to consider the potential consequences of each solution. Will the solution create any new problems or unintended side effects? Will it have any negative impacts on other areas or stakeholders? These potential consequences must be carefully considered before making a final decision.

Finally, it is important to approach the evaluation process with an open and flexible mindset. It is not uncommon for new information or perspectives to emerge during the evaluation process, which may alter the assessment of potential solutions. Remaining open to new information and being willing to adapt the evaluation criteria is crucial in selecting the best solution.

By carefully evaluating each potential solution and considering factors such as effectiveness, feasibility, and potential consequences, you can effectively select the best solution to the problem at hand. This is an essential step in the problem solving cycle, as it moves you closer to a successful resolution.

Implementing the Solution

Once the problem-solving cycle has been completed in cognitive psychology, the next step is to implement the solution. This phase involves taking the proposed solution and putting it into action.

Before implementation, it is crucial to evaluate the solution thoroughly. This evaluation helps ensure that the proposed solution is practical and feasible.

Evaluating the Solution

The evaluation process involves considering possible obstacles and risks that could hinder the successful implementation of the solution. By identifying these potential challenges, steps can be taken to mitigate them.

In addition, evaluating the solution also involves conducting a cost-benefit analysis. This analysis takes into account the potential costs and benefits associated with implementing the solution. It helps determine whether the solution is worth pursuing.

Putting the Solution into Action

Once the solution has been thoroughly evaluated, it is time to put it into action. This requires careful planning and coordination.

During the implementation phase, it is important to closely monitor the progress and make any necessary adjustments. This ensures that the solution is effectively addressing the problem at hand.

Furthermore, clear communication is vital during implementation. All relevant stakeholders should be informed and involved in the process to ensure everyone is working towards a common goal.

By implementing the solution effectively, the problem-solving cycle in cognitive psychology can come to a successful conclusion.

Monitoring and Evaluating the Outcome

Monitoring and evaluating the outcome is a crucial step in the problem-solving process in cognitive psychology. After identifying and implementing a solution, it is important to assess whether the problem has been effectively solved and whether the desired outcome has been achieved.

Evaluating the Effectiveness of the Solution

One way to monitor and evaluate the outcome is to assess the effectiveness of the solution. This involves determining whether the chosen solution has successfully addressed the problem and whether it has led to the desired result. Cognitive psychologists often use various measures and metrics to evaluate the effectiveness of problem-solving strategies. These may include objective measures such as test scores or subjective measures such as self-report questionnaires.

By evaluating the effectiveness of the solution, cognitive psychologists can determine whether further adjustments or modifications are necessary. If the outcome is not satisfactory, they can go back to the problem-solving cycle and repeat the steps to find a more suitable solution.

Reflecting on the Process

In addition to evaluating the effectiveness of the solution, it is also important to reflect on the problem-solving process itself. This involves considering the strategies and techniques used, as well as identifying any obstacles or challenges encountered. By reflecting on the process, cognitive psychologists can gain valuable insights into how they approached the problem and how they can improve their problem-solving skills in the future.

Reflection can be done through self-reflection or by seeking feedback from others, such as colleagues or experts in the field. This feedback can provide alternative perspectives and help identify areas for improvement.

In conclusion, monitoring and evaluating the outcome is a critical aspect of the problem-solving cycle in cognitive psychology. By assessing the effectiveness of the solution and reflecting on the process, cognitive psychologists can continually improve their problem-solving skills and contribute to the development of this field.

The Role of Cognitive Processes in Problem Solving

In the field of cognitive psychology, problem solving is a fundamental aspect of human thinking. It involves the use of various cognitive processes to analyze a problem, develop possible solutions, and determine the best course of action.

One key cognitive process involved in problem solving is perception. This process allows individuals to perceive and understand the problem at hand, by gathering information from the environment and organizing it into meaningful patterns. Perception helps identify the relevant aspects of a problem and guides the problem-solving process.

Another important cognitive process in problem solving is reasoning. Reasoning involves logical thinking and the ability to draw conclusions based on available information. It helps individuals make sense of the problem and generate possible solutions. Reasoning also helps evaluate the potential outcomes of each solution and select the most appropriate one.

Memory plays a crucial role in problem solving as well. It allows individuals to recall relevant information from past experiences and apply it to the current problem. Memory aids in recognizing patterns, generating hypotheses, and retrieving information necessary for problem solving. Without memory, it would be challenging to solve problems efficiently.

Moreover, attention and concentration are essential cognitive processes in problem solving. They help individuals focus on the relevant aspects of a problem and block out distractions. Attention allows individuals to allocate cognitive resources effectively and process information in a systematic manner. Concentration enables individuals to stay engaged in problem solving and persevere until a solution is found.

The role of cognitive processes in problem solving is vital as they provide the framework for effective problem-solving strategies. Understanding how perception, reasoning, memory, attention, and concentration contribute to problem solving helps researchers and practitioners develop interventions and techniques to improve problem-solving skills.

In conclusion, cognitive processes are crucial in problem solving. Perception, reasoning, memory, attention, and concentration work together to help individuals analyze problems, generate solutions, and make informed decisions. By studying and understanding these cognitive processes, researchers can enhance problem-solving abilities, ultimately leading to more effective problem-solving strategies in various fields of study and practice.

How Cognitive Biases can Impact Problem Solving

Cognitive biases are inherent tendencies in human thinking that can lead to errors or deviations from rationality. These biases can have a significant impact on problem solving, as they can influence the way individuals perceive, interpret, and evaluate information.

Confirmation Bias

One common cognitive bias that can affect problem solving is confirmation bias. This bias leads individuals to favor information that confirms their existing beliefs or hypotheses while disregarding or downplaying information that contradicts them. In problem-solving scenarios, confirmation bias can prevent individuals from considering alternative solutions or exploring different perspectives, potentially leading to a less effective problem-solving process.

Availability Heuristic

The availability heuristic is another cognitive bias that can impact problem solving. This bias involves relying on easily accessible information or examples when making judgments or decisions. In problem-solving situations, this bias can lead individuals to overlook less accessible information or fail to consider all relevant factors. This can limit the effectiveness of problem solving by restricting the range of potential solutions or failing to consider alternative approaches.

  • Overcoming cognitive biases in problem solving

Recognizing and overcoming cognitive biases is crucial for effective problem solving. Strategies such as actively seeking out diverse perspectives, questioning assumptions, and considering alternative explanations can help mitigate the impact of cognitive biases. Additionally, fostering an environment that encourages open-mindedness, critical thinking, and intellectual humility can also support more effective problem-solving processes.

By understanding how cognitive biases can impact problem solving, psychologists and individuals alike can work towards improving their problem-solving skills and decision-making processes. By recognizing and addressing these biases, individuals can enhance their ability to approach problems with greater objectivity, flexibility, and creativity.

The Relationship Between Problem Solving and Decision Making

Problem solving and decision making are closely interconnected in cognitive psychology. When faced with a problem, individuals engage in a cognitive process known as problem solving, which involves identifying and evaluating possible solutions in order to reach a desired goal or outcome. Decision making, on the other hand, refers to the act of choosing one particular solution from the options generated during the problem-solving process.

The problem-solving cycle, a key concept in cognitive psychology, highlights the iterative nature of problem solving and decision making. This cycle consists of several steps, including problem identification, problem analysis, solution generation, solution evaluation, and solution implementation. During the problem identification phase, individuals recognize and define the problem they are facing. Problem analysis involves gathering information and analyzing the underlying causes and factors contributing to the problem. Once a thorough analysis is conducted, individuals can generate potential solutions through creative thinking and brainstorming.

After generating potential solutions, individuals must evaluate the effectiveness and feasibility of each option. This involves considering the potential consequences and weighing the pros and cons of each alternative. By carefully assessing each solution, individuals can make an informed decision and choose the most suitable course of action. Finally, the chosen solution is implemented, and individuals monitor the outcomes to determine whether the problem has been effectively resolved.

It is important to note that problem solving and decision making are not linear processes, but rather they involve feedback loops and revisions as new information becomes available or as the initial solution proves to be ineffective. Successful problem solving and decision making require flexibility, critical thinking, and adaptability to changing circumstances.

In summary, problem solving and decision making are intertwined cognitive processes within the problem-solving cycle. Problem solving involves identifying and evaluating possible solutions, while decision making involves choosing the most appropriate solution. By understanding the relationship between problem solving and decision making, individuals can enhance their problem-solving skills and make more effective decisions in various aspects of life and work.

The Effect of Expertise on Problem Solving

In the cognitive psychology field, the problem solving cycle is a key concept that involves several stages: understanding the problem, devising a plan, executing the plan, and evaluating the solution. An important factor that can influence problem solving abilities is expertise.

Experts, who have extensive knowledge and experience in a specific domain, often exhibit superior problem solving skills compared to novices. This is because experts have a large mental database of problem-solving strategies and a deep understanding of the underlying concepts. They can quickly recognize patterns and make accurate decisions based on their knowledge.

Research has shown that experts are able to solve problems more efficiently and effectively than novices. They are able to quickly identify the relevant information and ignore irrelevant details, which allows them to focus on the core of the problem. Experts also have a better ability to generate and evaluate multiple potential solutions, leading to more creative problem solving.

Furthermore, experts are more likely to use metacognitive strategies, such as self-monitoring and self-regulation, during the problem solving process. They are able to reflect on their own thinking and adjust their strategies as needed. This metacognitive awareness helps experts to overcome obstacles and adapt their problem solving approach as necessary.

However, it is important to note that expertise is domain-specific. An individual may be an expert in one area but not in another. For example, a chess grandmaster may struggle with solving complex math problems. Therefore, expertise does not guarantee proficiency in all problem-solving domains.

In conclusion, expertise plays a significant role in problem solving. Experts have a deeper understanding of the problem domain, possess a larger repertoire of strategies, and exhibit metacognitive awareness. These factors contribute to their more efficient and effective problem solving abilities compared to novices.

Developing Problem Solving Skills through Practice

In the field of psychology, problem solving is considered an essential cognitive skill that helps individuals navigate through various challenges and obstacles. The problem solving cycle, a key concept in cognitive psychology, emphasizes the importance of practice in developing and honing problem solving skills.

Practice plays a crucial role in problem solving as it helps individuals familiarize themselves with different problem-solving techniques and strategies. By engaging in regular practice, individuals can strengthen their analytical thinking, creative problem solving, and decision-making abilities.

Through practice, individuals learn to approach problems systematically, breaking down complex tasks into smaller, more manageable steps. This systematic approach allows individuals to identify the root causes of a problem, generate potential solutions, and evaluate the effectiveness of each solution.

In addition to improving analytical thinking, practice also helps individuals develop their creative problem solving skills. By repeatedly facing various problems, individuals become more comfortable with thinking outside the box and exploring unconventional solutions. This creative thinking enables individuals to come up with innovative and effective solutions to complex problems.

Moreover, practice enhances individuals’ decision-making abilities. As individuals engage in problem solving practice, they become more skilled at assessing different options, weighing the pros and cons, and making informed decisions. This ability to make sound decisions is crucial in both personal and professional contexts.

In conclusion, developing problem solving skills requires consistent practice. By engaging in regular problem solving practice, individuals can improve their analytical thinking, creative problem solving, and decision-making abilities. The problem solving cycle emphasizes the importance of practice in developing these skills, and individuals who actively engage in practice are more likely to become adept problem solvers.

Teaching Problem Solving Skills in Education

Problem solving skills are an essential component of education, as they enable students to analyze and tackle complex issues across various subject areas. By teaching problem solving skills, educators help students develop critical thinking abilities and cognitive strategies that can be applied in real-life situations.

The Problem Solving Cycle

One effective approach to teaching problem solving skills is through the use of the problem solving cycle. The problem solving cycle is a key concept in cognitive psychology, which involves a systematic approach to identifying, analyzing, and resolving problems.

First, students are introduced to a problem or a question that requires analysis and solution. They are encouraged to define the problem clearly and understand its scope. This initial step helps students develop problem awareness and identify potential barriers or constraints that may affect the problem-solving process.

Next, students engage in information gathering and analysis. They gather relevant data, facts, and evidence, and apply critical thinking skills to evaluate and interpret the information. This step helps students develop analytical skills and generate possible solutions.

Once students have gathered and analyzed the information, they move on to the generation of potential solutions. This involves brainstorming and exploring different approaches to the problem, encouraging creativity and flexibility in thinking. Students are encouraged to think outside the box and consider multiple perspectives.

After generating potential solutions, students evaluate each option based on effectiveness, feasibility, and potential consequences. They consider the advantages and disadvantages of each solution, weighing the pros and cons. This step helps students develop decision-making skills and enhances their ability to critically evaluate potential solutions.

Finally, students select the most appropriate solution and implement it. They develop an action plan, outlining the steps needed to solve the problem. This requires effective communication skills, as students may need to collaborate and communicate their ideas with others.

Benefits of Teaching Problem Solving Skills

Teaching problem solving skills in education offers numerous benefits to students. Firstly, it enhances their cognitive abilities, allowing them to think critically and logically. This helps students become more independent learners and problem solvers.

Additionally, teaching problem solving skills improves students’ creativity and innovation. By encouraging them to think outside the box and explore different solutions, educators foster a mindset of curiosity and exploration.

Moreover, problem solving skills are transferable to various contexts, both within and outside of the classroom. Students can apply these skills to academic subjects, as well as to real-life situations, such as social issues, personal challenges, and future career paths.

In conclusion, teaching problem solving skills in education is crucial for students’ cognitive development and future success. By implementing the problem solving cycle and fostering critical thinking abilities, educators empower students with the skills necessary to navigate complex challenges and become lifelong learners.

Real-World Applications of the Problem Solving Cycle

The problem solving cycle is a fundamental concept in cognitive psychology that has numerous applications in real-world situations. This cycle involves a series of steps that individuals go through in order to identify, analyze, and solve problems.

1. Business

In the business world, problem solving is essential for success. From identifying market trends and determining customer needs to finding solutions to production issues or administrative challenges, the problem solving cycle is used to tackle a variety of business-related problems.

2. Education

The problem solving cycle is also highly applicable in education. Teachers often use this approach to help students develop critical thinking skills and solve complex problems. By following this cycle, students learn to break down problems, gather relevant information, analyze various options, and come up with effective solutions.

3. Medicine

Medical professionals frequently employ the problem solving cycle when diagnosing and treating patients. By systematically gathering patient history, evaluating symptoms, conducting tests, and analyzing data, doctors are able to identify the underlying problem and develop appropriate treatment plans.

4. Engineering

In the field of engineering, the problem solving cycle is crucial for designing and implementing solutions. Engineers use this approach to identify and address technical challenges, improve existing systems, and develop innovative technologies. By following this cycle, engineers can efficiently solve complex problems and ensure the success of their projects.

5. Everyday Life

Lastly, the problem solving cycle is applicable to everyday life. Whether it’s figuring out the best route to work, resolving conflicts in relationships, or making important decisions, individuals use this cycle to identify issues, explore possible solutions, and make informed choices.

The problem solving cycle is a versatile concept that finds widespread applications in various domains. From business and education to medicine and engineering, this approach facilitates effective problem solving and decision making. By following the steps of the cycle, individuals and organizations can overcome challenges and achieve their goals.

The Future of Problem Solving Research

In the field of cognitive psychology, research on problem solving is an ongoing and dynamic area of study. As technology continues to advance and our understanding of the cognitive processes involved in problem solving deepens, the future of problem solving research looks promising.

Advancements in Technology

Advancements in technology have already had a significant impact on problem solving research. The use of computer simulations and virtual environments has allowed researchers to create realistic problem-solving scenarios and collect data in a controlled environment. This technology has also allowed for the development of intelligent tutoring systems that can provide personalized feedback and guidance to individuals as they work through various problem-solving tasks.

In the future, we can expect even more sophisticated technologies to be developed, which will enhance our ability to study problem solving. For example, virtual reality technology may allow researchers to create immersive problem-solving environments that closely mimic real-life situations. This could provide researchers with valuable insights into how individuals approach and solve complex problems in a realistic setting.

Integration of Cognitive Processes

As our understanding of cognitive processes continues to grow, future research on problem solving will likely focus on the integration of various cognitive processes. Problem solving is a complex task that involves numerous cognitive processes, such as attention, memory, decision-making, and reasoning. Understanding how these processes interact and influence problem-solving performance will be crucial in developing effective strategies for problem solving.

Researchers may also explore the role of emotions in problem solving. Emotions can have a significant impact on cognitive processes and decision-making. Understanding how emotions influence problem-solving performance may provide valuable insights into how individuals can improve their problem-solving abilities.

Collaborative Problem Solving

Collaborative problem solving, or problem solving in a group setting, is another area that holds great potential for future research. Many real-world problems require collaboration and teamwork to solve effectively. Research on collaborative problem solving can provide valuable insights into how individuals interact and communicate with each other during problem-solving tasks, and how team dynamics impact problem-solving performance.

Furthermore, advancements in communication technology have made it easier than ever for individuals to collaborate remotely. Studying how individuals solve problems in virtual teams or online communities can provide valuable insights into the dynamics of collaborative problem solving in today’s interconnected world.

Continued Development of the Problem Solving Cycle

The problem solving cycle, which involves the stages of problem identification, solution generation, solution implementation, and solution evaluation, will continue to be a key concept in problem solving research. Researchers will seek to understand how individuals move through these stages, the strategies they employ at each stage, and how their problem-solving performance can be optimized.

By understanding the cognitive processes involved in each stage of the problem solving cycle, researchers can develop interventions and strategies to help individuals become more effective problem solvers.

In conclusion, the future of problem solving research in cognitive psychology looks promising. Advancements in technology, a deeper understanding of cognitive processes, the study of collaborative problem solving, and the continued development of the problem solving cycle will all contribute to our understanding of problem solving and help individuals become more effective in solving complex problems.

Questions and answers:

What is the problem-solving cycle.

The problem-solving cycle is a key concept in cognitive psychology that refers to the sequence of steps or processes involved in solving a problem.

What are the stages of the problem-solving cycle?

The problem-solving cycle typically consists of four stages: problem identification, problem definition, strategy selection, and solution implementation.

How does problem identification occur in the problem-solving cycle?

Problem identification involves recognizing that there is a problem or a discrepancy between a desired state and the current state.

What is problem definition in the problem-solving cycle?

Problem definition involves clearly specifying or defining the problem in a way that allows for a focused approach to finding a solution.

What is strategy selection in the problem-solving cycle?

Strategy selection involves choosing an appropriate approach or method to solve the problem, such as using a specific algorithm or heuristic.

What is the problem-solving cycle in cognitive psychology?

The problem-solving cycle is a concept in cognitive psychology that outlines the steps individuals go through when tackling a problem. It involves identifying the problem, gathering information, generating possible solutions, evaluating the solutions, and implementing the best one.

How does the problem-solving cycle help in problem-solving?

The problem-solving cycle provides a structured approach to problem-solving by breaking it down into manageable steps. By following this cycle, individuals can better understand the problem, explore various solutions, evaluate their effectiveness, and ultimately make an informed decision on how to solve the problem.

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What is problem solving and why is it important

why is problem solving important in psychology

By Wayne Stottler , Kepner-Tregoe

  • Problem Solving & Decision Making Over time, developing and refining problem solving skills provides the ability to solve increasingly complex problems Learn More

For over 60 years, Kepner-Tregoe has been helping companies across industries and geographies to develop and mature their problem-solving capabilities through KT’s industry leading approach to training and the implementation of best practice processes. Considering that problem solving is a part of almost every person’s daily life (both at home and in the workplace), it is surprising how often we are asked to explain what problem solving is and why it is important.

Problem solving is at the core of human evolution. It is the methods we use to understand what is happening in our environment, identify things we want to change and then figure out the things that need to be done to create the desired outcome. Problem solving is the source of all new inventions, social and cultural evolution, and the basis for market based economies. It is the basis for continuous improvement, communication and learning.

If this problem-solving thing is so important to daily life, what is it?

Problem-solving is the process of observing what is going on in your environment; identifying things that could be changed or improved; diagnosing why the current state is the way it is and the factors and forces that influence it; developing approaches and alternatives to influence change; making decisions about which alternative to select; taking action to implement the changes; and observing impact of those actions in the environment.

Each step in the problem-solving process employs skills and methods that contribute to the overall effectiveness of influencing change and determine the level of problem complexity that can be addressed. Humans learn how to solve simple problems from a very early age (learning to eat, make coordinated movements and communicate) – and as a person goes through life problem-solving skills are refined, matured and become more sophisticated (enabling them to solve more difficult problems).

Problem-solving is important both to individuals and organizations because it enables us to exert control over our environment.

Fixing things that are broken

Some things wear out and break over time, others are flawed from day-1. Personal and business environments are full of things, activities, interactions and processes that are broken or not operating in the way they are desired to work. Problem-solving gives us a mechanism for identifying these things, figuring out why they are broken and determining a course of action to fix them.

Addressing risk

Humans have learned to identify trends and developed an awareness of cause-and-effect relationships in their environment. These skills not only enable us to fix things when they break but also anticipate what may happen in the future (based on past-experience and current events). Problem-solving can be applied to the anticipated future events and used to enable action in the present to influence the likelihood of the event occurring and/or alter the impact if the event does occur.

Improving performance

Individuals and organizations do not exist in isolation in the environment. There is a complex and ever-changing web of relationships that exist and as a result, the actions of one person will often have either a direct impact on others or an indirect impact by changing the environment dynamics. These interdependencies enable humans to work together to solve more complex problems but they also create a force that requires everyone to continuously improve performance to adapt to improvements by others. Problem-solving helps us understand relationships and implement the changes and improvements needed to compete and survive in a continually changing environment.

Seizing opportunity

Problem solving isn’t just about responding to (and fixing) the environment that exists today. It is also about innovating, creating new things and changing the environment to be more desirable. Problem-solving enables us to identify and exploit opportunities in the environment and exert (some level of) control over the future.

Problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations. Developing and refining these skills through training, practice and learning can provide the ability to solve problems more effectively and over time address problems with a greater degree of complexity and difficulty. View KT’s Problem Solving workshop known to be the gold standard for over 60 years.

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why is problem solving important in school psychology

Why is Problem-Solving Important in School Psychology?

Nov 17, 2014

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Why is Problem-Solving Important in School Psychology?. Rachel Brown-Chidsey, Ph.D., NCSP University of Southern Maine. Module Overview. Definition of Problem Solving Purpose of Problem Solving Benefits of Problem Solving Case Example Summary Review Questions.

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Why is Problem-Solving Important in School Psychology? Rachel Brown-Chidsey, Ph.D., NCSP University of Southern Maine

Module Overview • Definition of Problem Solving • Purpose of Problem Solving • Benefits of Problem Solving • Case Example • Summary • Review Questions Futures Task Force on Academic Outcomes

Definition of Problem Solving • Problem-solving school psychology practices are based on the following definition of a problem: • Problem = the distance between what is expected and what is occurring • Problem-solving is the work of reducing the distance between what is expected and what is occurring Futures Task Force on Academic Outcomes

Problem-Solving Steps (Deno, 1995) • Problem identification: Someone thinks there’s a problem • Problem definition: The size of the problem is described in measurable ways and a hypothesis about the cause is developed • Exploring solutions: A possible solution is tried • Monitoring progress: Weekly student progress is measured to see if the solution works • Problem (re)solution: The student meets the learning goal or a new solution is tried Futures Task Force on Academic Outcomes

Purpose of Problem Solving • Problem solving activities are designed to achieve three main goals: • Clearly state what is expected of students • Identify how close a student is to meeting the goal(s) • Identify instructional methods best suited to help students meet goal(s) Futures Task Force on Academic Outcomes

Establishing Expectations • Having clear expectations for what students should be able to do at each grade level clarifies the learning objectives for students, teachers and parents • Clear expectations provide a more equitable and accessible curriculum because they avoid the presence of a “hidden curriculum”: • Hidden curriculum refers to knowledge and skills students should have already learned or are expected to learn despite it not being stated specifically • Example: expecting all students to say “please” and “thank you” during classroom interactions Futures Task Force on Academic Outcomes

Expectations and Standards • Recent initiatives in all 50 U.S. states have resulted in state-level learning standards • These standards provide grade level expectations for all students • Standards can only be achieved if effective instruction is used Futures Task Force on Academic Outcomes

Measuring Progress • Student attainment of standards can only be known if sensitive measures of knowledge and skills are used • Problem solving school psychology practices rely on assessment measures that can reliably indicate how close a student is to a learning goal • State exams are not sufficient measures of student progress Futures Task Force on Academic Outcomes

Problem Solving Measures • Two major types of problem solving assessments are used: • Benchmark: these are baseline measures of a student’s knowledge and skills in the curriculum being taught • Usually done 3 times/year • Progress Monitoring: These are regular measures of a student’s progress toward learning goal(s) • Usually done weekly Futures Task Force on Academic Outcomes

Why is Regular Assessment Necessary for Problem-Solving? • “If you don’t know where you are going, any road will get you there”(George Harrison) • Only by measuring how close a student is to the learning expectations can teachers know how much instruction is needed • Only by measuring student progress regularly can teachers know if the instruction is working Futures Task Force on Academic Outcomes

How is Problem Solving Different from Traditional Assessment? • Traditional assessment focuses on finding out whether a student has a disability • This is a deficit focused model • Problem solving assessment focuses on finding out what kind of instruction a student needs to be successful in school and life • This is a success focused model Futures Task Force on Academic Outcomes

Benefits of Problem Solving • Focuses on student’s skills and strengths instead of weaknesses and deficits • Points directly to the type of instruction needed • Provides a baseline measure of student knowledge and skills which makes monitoring progress easy Futures Task Force on Academic Outcomes

Summary • Problem solving school psychology practices are beneficial to students because they • Focus on student success and not deficits • Link directly to instruction for students • Include measurable indicators of student progress • Prevent over-identification of learning disabilities Futures Task Force on Academic Outcomes

Resources • Brown-Chidsey, R. (Ed.). (2005). Assessment for intervention: A problem-solving approach. New York: Guilford Press. Deno, S. (1995). The school psychologist as problem solver. In J. Grimes & A. Thoms (Eds.), Best practices in school psychology III (pp. 471-484). Silver Spring, MD: National Association of School Psychologists. • National Association of School Psychologists. (2007). NASP position statement on identification of students with specific learning disabilities. Retrieved 20 September 2007 from http://www.nasponline.org/about_nasp/positionpapers/SLDPosition_2007.pdf Futures Task Force on Academic Outcomes

Review Questions • The following slides include review questions about the information contained in this module • Click to advance to the next slide • After reading the slide and questions, click again to see the correct answer Futures Task Force on Academic Outcomes

A) What is the definition of a problem? • A discrepancy of 15 points or more • The difference between what is expected and what is occurring • Identified only through the use of published norm-referenced testing • None of the above Futures Task Force on Academic Outcomes

A) Answer: #2 The difference between what is expected and what is occurring Futures Task Force on Academic Outcomes

B) What are the 5 stages of problem solving? • Identification, definition, exploring solutions, monitoring solutions, solution • Definition, monitoring solutions, identification, referral • Benchmarking, progress monitoring, exploring solutions, defining, identification • None of the above Futures Task Force on Academic Outcomes

B) Answer: #1 Identification, definition, exploring solutions, monitoring solutions, solution Futures Task Force on Academic Outcomes

C) What are 2 advantages of problem solving practices? • The opportunity to use advanced and extended testing procedures • It is success focused and leads to instructional change • It provides data on how long a problem has been observed • None of the above Futures Task Force on Academic Outcomes

C) Answer: # 2 It is success focused and leads to instructional change Futures Task Force on Academic Outcomes

D) True or False? • Problem solving school psychology is compatible with the 2007 NASP position statement on the identification of students with specific learning disabilities Futures Task Force on Academic Outcomes

D) Answer: True Problem solving school psychology is very compatible with the 2007 NASP position statement on the identification of students with specific learning disabilities Futures Task Force on Academic Outcomes

E) Problem solving school psychology is: • A deficit-focused method • A discrepancy-based method • A success-based method • None of the above Futures Task Force on Academic Outcomes

E) Answer: #3 A success-based method Futures Task Force on Academic Outcomes

For More Information… • To learn more about problem solving, view the module entitled “Problem Solving Process.” Futures Task Force on Academic Outcomes

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Gregg Henriques Ph.D.

What Is the Problem of Psychology and Why Is It Important?

The problem of psychology is that there's no clearly agreed upon subject matter..

Posted January 3, 2023 | Reviewed by Abigail Fagan

  • Other sciences, like physics and biology, have clearly identified "things in the world" that they are trying to describe and explain.
  • Psychologists do not agree on whether psychology is about behavior or mind or about all animals or only humans.
  • This means that the coherence of our scientific understanding breaks down for psychology.
  • The problem of psychology highlights this fact and points to it being an important problem with our current systems of knowledge.

One of my goals this year is to make people more aware of something I call the “problem of psychology.” It is a clearly defined problem and when you learn to see it, it helps you realize that there are deep and profound problems with the way modern academic systems frame our knowledge about the world.

Given that it is now 2023, it is perhaps fitting to frame our initial understanding by asking the AI chatbot ChatGPT: “What is the problem of psychology?” Here is the answer it gave:

It's not accurate to say that psychology has a single, overarching problem that it is trying to solve. Rather, psychology is a broad field that encompasses a wide range of topics and aims to understand the many facets of human behavior, thought, and experience. Some specific areas that psychologists might study include perception, cognition , emotion , development, personality , social behavior, and mental health. Within these broad areas, psychologists may be interested in understanding how people process information, how they form and maintain relationships, how they cope with stress and adversity, and how they learn and adapt to new situations. The goals of psychology are varied, but they generally involve gaining a better understanding of how people function and using that knowledge to improve people's lives.

This is a good summary of the current state of psychology. At the same time, if you know how to read the chatbot’s answer, it reveals the problem I am referring to. So, what, exactly, is “the” problem I am pointing to and why is it so important? The problem of psychology is the fact that there is no consensual agreement—even in broad outlines—among psychologists regarding the thing(s) in the world that psychological science is about.

For a remarkable contrast, consider the science of biology. All biologists agree that biology is the science of life. Life, defined here as the set of all living things and their structures and behaviors, is a clear and obvious set of things in the world. We can look to the physical sciences and see the same pattern. For example, physics is the science of the behavior of energy and matter across scales, from particles to galaxies to the shape of the whole universe. The behavioral patterns of matter and energy are obvious things in the world that the physical sciences are about.

The point is that the various natural sciences, from physics to chemistry to biology and all the sciences in between, are about well-defined things in the world. We can introduce a technical term to be clear about this, and say that each of these sciences has a clear “ontological referent” for its subject matter. For example, the behavior of energy and matter across scales of space and time is the ontological referent for physics. We can also identify the nervous system as the ontological referent for neuroscience, and the behavior of living organisms as the ontological referent for biology. In each case, the domain of science aligns with a clear ontological referent.

This alignment between the domain of science and the ontological referent breaks down when we get to psychology. That is, there is no agreement among psychologists about the thing in the world that the science of psychology is about. Consider, for example, that some psychologists say psychology is about behavior, while others say it is about the mind or mental processes. For some psychologists, virtually all animals exhibit mental processes or behaviors of interest. And there is a specific branch of the field called comparative psychology that examines mental processes throughout the animal kingdom. And yet other psychologists claim, similar to ChatGPT, that psychology is only concerned with human behavior, thoughts, or conscious experiences. Of course, behavior and mind and animals and humans are very different categories in the world. And hopefully that makes clear and drives home the point that psychologists cannot agree on what psychology is about. The science has no clear ontological referent. And this is the problem of psychology.

It can be stated in the form of a question:

Why do the physical and biological sciences have a clear ontological referent and why does that coherence completely break down when we get to psychology?

In my opinion, this problem should be well-known as one of the great problems in science and philosophy . It used to be the case that many people struggled with this issue. Indeed, to historians of psychology, this problem is known as “the crisis of psychology.” However, even though it is well-documented, over time, the field of psychology lost interest in the problem. They decided that it was something that could not be solved and so they then decided it was not really a problem. My just-released book, A New Synthesis for Solving the Problem of Psychology: Addressing the Enlightenment Gap , explains in depth why the mainstream view is wrong. It is a very important problem, not just for psychology, but for science and philosophy as well.

My goal for this year is to help other people see why this is such a pressing problem, and why solving it will lead to a transformation in our scientific understanding of the world and our place in it. So, with this blog, I encourage you to increase your awareness of the problem and to wonder why it is the case that scientists have not been able to frame the thing in the world that psychological science is about. In addition, if you know any students in psychology or any professors of psychology, be sure to ask them about the problem and see if they have an answer that makes sense.

Henriques, G. (2022). A new synthesis for solving the problem of psychology: Addressing the Enlightenment Gap . Palgrave-Macmillan.

Gregg Henriques Ph.D.

Gregg Henriques, Ph.D. , is a professor of psychology at James Madison University.

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COMMENTS

  1. The Problem-Solving Process

    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.

  2. Problem-Solving Strategies and Obstacles

    Problem-solving helps you figure out how to achieve these desires. The problem-solving process involves: Discovery of the problem Deciding to tackle the issue Seeking to understand the problem more fully Researching available options or solutions Taking action to resolve the issue

  3. 7.3 Problem-Solving

    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.

  4. Problem Solving

    Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

  5. The Process of Problem Solving

    In a series of three experiments, the researchers asked participants to solve series of matchstick problems. In matchstick problems, participants are presented with an array of joined squares. Each square in the array is comprised of separate pieces. Participants are asked to remove a certain number of pieces from the array while still ...

  6. Problem-Solving Strategies: Definition and 5 Techniques to Try

    Working backward Means-end analysis Recap 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...

  7. PDF The Psychology of Problem Solving

    The Psychology of Problem Solving organizes in one volume much of what psychologists know about problem solving and the factors that contribute to its success or failure.

  8. Problem Solving

    Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to ...

  9. Problem Solving and Decision Making

    Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal.

  10. Problem Solving

    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 ( [link]) is a 4×4 grid.

  11. Solving Problems the Cognitive-Behavioral Way

    Problem solving is another part of behavioral therapy. Problem-solving is one technique used on the behavioral side of cognitive-behavioral therapy. The problem-solving technique is an iterative ...

  12. Motivation to learn and problem solving

    The motivation to deal with problem-solving tasks can come from the learners themselves or be triggered by task design. In this context, Muenks et al. ( 2016) differentiated between self-initiated effort, which is due to learners' own motivation and task-elicited effort, which is due to the subjective difficulty of the task.

  13. 7 Module 7: Thinking, Reasoning, and Problem-Solving

    Module 7: Thinking, Reasoning, and Problem-Solving. This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure ...

  14. Problem Solving: Definition, Skills, & Strategies

    Problem-solving is an important skill to develop because life will always throw you curveballs. Being able to respond to these problems with flexibility and calmness will generate much better results than if you respond to the problem with resistance or avoidance.

  15. Are You Problem-Solving, or Just Worrying?

    The short answer is: yes. While it may be totally normal to feel a surge of anxiety when you first identify a threat or problem, it's not so helpful to keep that anxiety going when you're ...

  16. Problem solving through values: A challenge for thinking and capability

    Abstract. 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 ...

  17. Using Psychology to Address Social Problems

    Judith Glassgold, Psy.D. is a licensed psychologist and an expert in applying psychology to problems of public policy, focused on mental health. She is a consultant to national civil rights ...

  18. The science behind creativity

    Specifically, creativity often involves coordination between the cognitive control network, which is involved in executive functions such as planning and problem-solving, and the default mode network, which is most active during mind-wandering or daydreaming (Beaty, R. E., et al., Cerebral Cortex, Vol. 31, No. 10, 2021).

  19. The Problem Solving Cycle: A Key Concept in Cognitive Psychology

    The problem solving cycle is a key concept in cognitive psychology that helps us understand how individuals approach and solve problems. In the problem solving cycle, individuals first must recognize and define the problem they are facing. This involves identifying the specific issue or obstacle that needs to be overcome.

  20. What is problem solving and why is it important

    Problem-solving enables us to identify and exploit opportunities in the environment and exert (some level of) control over the future. Problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations.

  21. 3 Strategies for Solving Problems in Polarized Times

    Key points. Let's critically examine our goals, communication, and strategies to ensure they address problematic issues. Carefully identifying shared goals can diminish polarization and lead to ...

  22. Why is Problem-Solving Important in School Psychology?

    Why is Problem-Solving Important in School Psychology? Rachel Brown-Chidsey, Ph.D., NCSP University of Southern Maine. Module Overview • Definition of Problem Solving • Purpose of Problem Solving • Benefits of Problem Solving • Case Example • Summary • Review Questions Futures Task Force on Academic Outcomes. Definition of Problem Solving • Problem-solving school psychology ...

  23. What Is the Problem of Psychology and Why Is It Important?

    Theory of Knowledge Philosophy What Is the Problem of Psychology and Why Is It Important? The problem of psychology is that there's no clearly agreed upon subject matter. Posted January...