what are the factors affecting problem solving in psychology

7.3 Problem-Solving

Learning objectives.

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

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

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

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

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

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

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

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

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

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

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

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

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

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

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

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

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

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

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

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

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

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

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

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

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

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

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

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

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

heuristic:  mental shortcut that saves time when solving a problem

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

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

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

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

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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 REVIEWED: 26 June 2019 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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Problem-Solving

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Problem solving refers to the process of identifying a gap between a desired goal state and a present state, and proposing and performing a set of operations or solutions in order to move toward the goal state. Generally, the solution to the problem is not immediately known and the process can involve multiple solutions and attempts to reach the intended goal. Problem solving involves a set of cognitive processes associated with problem definition, information gathering, analyzing, planning, and execution. An individual’s capacity to problem solve is influenced by a number of factors including cognitive ability, disposition, knowledge, and background.

Introduction

Problem solving involves a set of complex cognitive processes that require thinking and reasoning. A problem occurs when there is a goal that needs to be reached and there is not a clear path to achieving the goal (Mayer 2013 ). Problems can range in terms of type, complexity, strategy use, domain, and other...

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7.3 Problem Solving

Learning objectives.

• 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 ( Table 7.2 ). 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.

Everyday Connection

Solving puzzles.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.8 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

Here is another popular type of puzzle ( Figure 7.9 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Take a look at the “Puzzling Scales” logic puzzle below ( Figure 7.10 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

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 Table 7.3 .

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 Figure 7.10 ? You need nine. Were you able to solve the problems in Figure 7.8 and Figure 7.9 ? Here are the answers ( Figure 7.11 ).

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What Is Cognitive Psychology?

The Science of How We Think

Topics in Cognitive Psychology

• Current Research
• Cognitive Approach in Practice

Careers in Cognitive Psychology

How cognitive psychology differs from other branches of psychology, frequently asked questions.

Cognitive psychology is the study of internal mental processes—all of the workings inside your brain, including perception, thinking, memory, attention, language, problem-solving, and learning. Learning about how people think and process information helps researchers and psychologists understand the human brain and assist people with psychological difficulties.

This article discusses what cognitive psychology is—its history, current trends, practical applications, and career paths.

Findings from cognitive psychology help us understand how people think, including how they acquire and store memories. By knowing more about how these processes work, psychologists can develop new ways of helping people with cognitive problems.

Cognitive psychologists explore a wide variety of topics related to thinking processes. Some of these include: 

• Attention --our ability to process information in the environment while tuning out irrelevant details
• Choice-based behavior --actions driven by a choice among other possibilities
• Decision-making
• Information processing
• Language acquisition --how we learn to read, write, and express ourselves
• Problem-solving
• Speech perception -how we process what others are saying
• Visual perception --how we see the physical world around us

History of Cognitive Psychology

Although it is a relatively young branch of psychology , it has quickly grown to become one of the most popular subfields. Cognitive psychology grew into prominence between the 1950s and 1970s.

Prior to this time, behaviorism was the dominant perspective in psychology. This theory holds that we learn all our behaviors from interacting with our environment. It focuses strictly on observable behavior, not thought and emotion. Then, researchers became more interested in the internal processes that affect behavior instead of just the behavior itself. 

This shift is often referred to as the cognitive revolution in psychology. During this time, a great deal of research on topics including memory, attention, and language acquisition began to emerge. 

In 1967, the psychologist Ulric Neisser introduced the term cognitive psychology, which he defined as the study of the processes behind the perception, transformation, storage, and recovery of information.

Cognitive psychology became more prominent after the 1950s as a result of the cognitive revolution.

Current Research in Cognitive Psychology

The field of cognitive psychology is both broad and diverse. It touches on many aspects of daily life. There are numerous practical applications for this research, such as providing help coping with memory disorders, making better decisions , recovering from brain injury, treating learning disorders, and structuring educational curricula to enhance learning.

Current research on cognitive psychology helps play a role in how professionals approach the treatment of mental illness, traumatic brain injury, and degenerative brain diseases.

Thanks to the work of cognitive psychologists, we can better pinpoint ways to measure human intellectual abilities, develop new strategies to combat memory problems, and decode the workings of the human brain—all of which ultimately have a powerful impact on how we treat cognitive disorders.

The field of cognitive psychology is a rapidly growing area that continues to add to our understanding of the many influences that mental processes have on our health and daily lives.

From understanding how cognitive processes change as a child develops to looking at how the brain transforms sensory inputs into perceptions, cognitive psychology has helped us gain a deeper and richer understanding of the many mental events that contribute to our daily existence and overall well-being.

The Cognitive Approach in Practice

In addition to adding to our understanding of how the human mind works, the field of cognitive psychology has also had an impact on approaches to mental health. Before the 1970s, many mental health treatments were focused more on psychoanalytic , behavioral , and humanistic approaches.

The so-called "cognitive revolution" put a greater emphasis on understanding the way people process information and how thinking patterns might contribute to psychological distress. Thanks to research in this area, new approaches to treatment were developed to help treat depression, anxiety, phobias, and other psychological disorders .

Cognitive behavioral therapy and rational emotive behavior therapy are two methods in which clients and therapists focus on the underlying cognitions, or thoughts, that contribute to psychological distress.

What Is Cognitive Behavioral Therapy?

Cognitive behavioral therapy (CBT) is an approach that helps clients identify irrational beliefs and other cognitive distortions that are in conflict with reality and then aid them in replacing such thoughts with more realistic, healthy beliefs.

If you are experiencing symptoms of a psychological disorder that would benefit from the use of cognitive approaches, you might see a psychologist who has specific training in these cognitive treatment methods.

These professionals frequently go by titles other than cognitive psychologists, such as psychiatrists, clinical psychologists , or counseling psychologists , but many of the strategies they use are rooted in the cognitive tradition.

Many cognitive psychologists specialize in research with universities or government agencies. Others take a clinical focus and work directly with people who are experiencing challenges related to mental processes. They work in hospitals, mental health clinics, and private practices.

Research psychologists in this area often concentrate on a particular topic, such as memory. Others work directly on health concerns related to cognition, such as degenerative brain disorders and brain injuries.

Treatments rooted in cognitive research focus on helping people replace negative thought patterns with more positive, realistic ones. With the help of cognitive psychologists, people are often able to find ways to cope and even overcome such difficulties.

Reasons to Consult a Cognitive Psychologist

• Alzheimer's disease, dementia, or memory loss
• Brain trauma treatment
• Cognitive therapy for a mental health condition
• Interventions for learning disabilities
• Perceptual or sensory issues
• Therapy for a speech or language disorder

Whereas behavioral and some other realms of psychology focus on actions--which are external and observable--cognitive psychology is instead concerned with the thought processes behind the behavior. Cognitive psychologists see the mind as if it were a computer, taking in and processing information, and seek to understand the various factors involved.

A Word From Verywell

Cognitive psychology plays an important role in understanding the processes of memory, attention, and learning. It can also provide insights into cognitive conditions that may affect how people function.

Being diagnosed with a brain or cognitive health problem can be daunting, but it is important to remember that you are not alone. Together with a healthcare provider, you can come up with an effective treatment plan to help address brain health and cognitive problems.

Your treatment may involve consulting with a cognitive psychologist who has a background in the specific area of concern that you are facing, or you may be referred to another mental health professional that has training and experience with your particular condition.

Ulric Neisser is considered the founder of cognitive psychology. He was the first to introduce the term and to define the field of cognitive psychology. His primary interests were in the areas of perception and memory, but he suggested that all aspects of human thought and behavior were relevant to the study of cognition.

A cognitive map refers to a mental representation of an environment. Such maps can be formed through observation as well as through trial and error. These cognitive maps allow people to orient themselves in their environment.

While they share some similarities, there are some important differences between cognitive neuroscience and cognitive psychology. While cognitive psychology focuses on thinking processes, cognitive neuroscience is focused on finding connections between thinking and specific brain activity. Cognitive neuroscience also looks at the underlying biology that influences how information is processed.

Cognitive psychology is a form of experimental psychology. Cognitive psychologists use experimental methods to study the internal mental processes that play a role in behavior.

Sternberg RJ, Sternberg K. Cognitive Psychology . Wadsworth/Cengage Learning. 

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Cutting JE. Ulric Neisser (1928-2012) . Am Psychol . 2012;67(6):492. doi:10.1037/a0029351

Ruggiero GM, Spada MM, Caselli G, Sassaroli S. A historical and theoretical review of cognitive behavioral therapies: from structural self-knowledge to functional processes .  J Ration Emot Cogn Behav Ther . 2018;36(4):378-403. doi:10.1007/s10942-018-0292-8

Parvin P. Ulric Neisser, cognitive psychology pioneer, dies . Emory News Center.

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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."

Chapter 9: Facilitating Complex Thinking

Problem-solving.

Somewhat less open-ended than creative thinking is problem solving , the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). Problem solving is needed, for example, when a physician analyzes a chest X-ray: a photograph of the chest is far from clear and requires skill, experience, and resourcefulness to decide which foggy-looking blobs to ignore, and which to interpret as real physical structures (and therefore real medical concerns). Problem solving is also needed when a grocery store manager has to decide how to improve the sales of a product: should she put it on sale at a lower price, or increase publicity for it, or both? Will these actions actually increase sales enough to pay for their costs?

Example 1: Problem Solving in the Classroom

Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The responses of students to such problems, as well as the strategies for assisting them, show the key features of problem solving. Consider this example, and students’ responses to it. We have numbered and named the paragraphs to make it easier to comment about them individually:

Scene #1: A problem to be solved

A teacher gave these instructions: “Can you connect all of the dots below using only four straight lines?” She drew the following display on the chalkboard:

The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. But two volunteers tried doing it at the board, but were unsuccessful. Several others worked at it at their seats, but also without success.

Scene #2: Coaxing students to re-frame the problem

When no one seemed to be getting it, the teacher asked, “Think about how you’ve set up the problem in your mind—about what you believe the problem is about. For instance, have you made any assumptions about how long the lines ought to be? Don’t stay stuck on one approach if it’s not working!”

Scene #3: Alicia abandons a fixed response

After the teacher said this, Alicia indeed continued to think about how she saw the problem. “The lines need to be no longer than the distance across the square,” she said to herself. So she tried several more solutions, but none of them worked either.

The teacher walked by Alicia’s desk and saw what Alicia was doing. She repeated her earlier comment: “Have you assumed anything about how long the lines ought to be?”

Alicia stared at the teacher blankly, but then smiled and said, “Hmm! You didn’t actually say that the lines could be no longer than the matrix! Why not make them longer?” So she experimented again using oversized lines and soon discovered a solution:

Scene #4: Willem’s and Rachel’s alternative strategies

Meanwhile, Willem worked on the problem. As it happened, Willem loved puzzles of all kinds, and had ample experience with them. He had not, however, seen this particular problem. “It must be a trick,” he said to himself, because he knew from experience that problems posed in this way often were not what they first appeared to be. He mused to himself: “Think outside the box, they always tell you. . .” And that was just the hint he needed: he drew lines outside the box by making them longer than the matrix and soon came up with this solution:

When Rachel went to work, she took one look at the problem and knew the answer immediately: she had seen this problem before, though she could not remember where. She had also seen other drawing-related puzzles, and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. After staring at the dots briefly, she drew a solution faster than Alicia or even Willem. Her solution looked exactly like Willem’s.

This story illustrates two common features of problem solving: the effect of degree of structure or constraint on problem solving, and the effect of mental obstacles to solving problems. The next sections discuss each of these features, and then looks at common techniques for solving problems.

The effect of constraints: well-structured versus ill-structured problems

Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. A well-structured problem provides much of the information needed and can in principle be solved using relatively few clearly understood rules. Classic examples are the word problems often taught in math lessons or classes: everything you need to know is contained within the stated problem and the solution procedures are relatively clear and precise. An ill-structured problem has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and a multiple solutions are likely (Voss, 2006). Extreme examples are problems like “How can the world achieve lasting peace?” or “How can teachers insure that students learn?”

By these definitions, the nine-dot problem is relatively well-structured—though not completely. Most of the information needed for a solution is provided in Scene #1: there are nine dots shown and instructions given to draw four lines. But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Students had to “think outside the box,” as Willem said—in this case, literally.

When a problem is well-structured, so are its solution procedures likely to be as well. A well-defined procedure for solving a particular kind of problem is often called an algorithm ; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. In that situation it pretty much guarantees a correct solution. They do not work well, however, with ill-structured problems, where they are ambiguities and questions about how to proceed or even about precisely what the problem is about. In those cases it is more effective to use heuristics , which are general strategies—“rules of thumb,” so to speak—that do not always work, but often do, or that provide at least partial solutions. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalogue for titles that look relevant. There is no guarantee that this strategy will yield the books most needed for the paper, but the strategy works enough of the time to make it worth trying.

In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: “Draw one line, then draw another, and another, and another.” Unfortunately this simple procedure did not produce a solution, so they had to find other strategies for a solution. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). Of these, Willem’s response resembled a heuristic the most: he knew from experience that a good general strategy that often worked for such problems was to suspect a deception or trick in how the problem was originally stated. So he set out to question what the teacher had meant by the word line , and came up with an acceptable solution as a result.

Common obstacles to solving problems

The example also illustrates two common problems that sometimes happen during problem solving. One of these is functional fixedness : a tendency to regard the functions of objects and ideas as fixed (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. For another, consider this problem: “The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?” If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is not relevant to the solution, and only serves to distract from the truly crucial information, the fact that the lilies double their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

Strategies to assist problem solving

Just as there are cognitive obstacles to problem solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). One helpful strategy is problem analysis —identifying the parts of the problem and working on each part separately. Analysis is especially useful when a problem is ill-structured. Consider this problem, for example: “Devise a plan to improve bicycle transportation in the city.” Solving this problem is easier if you identify its parts or component subproblems, such as (1) installing bicycle lanes on busy streets, (2) educating cyclists and motorists to ride safely, (3) fixing potholes on streets used by cyclists, and (4) revising traffic laws that interfere with cycling. Each separate subproblem is more manageable than the original, general problem. The solution of each subproblem contributes the solution of the whole, though of course is not equivalent to a whole solution.

Another helpful strategy is working backward from a final solution to the originally stated problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. The water lily problem described above is a good example: starting with the day when all the lake is covered (Day 100), ask what day would it therefore be half covered (by the terms of the problem, it would have to be the day before, or Day 99). Working backward in this case encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution.

A third helpful strategy is analogical thinking —using knowledge or experiences with similar features or structures to help solve the problem at hand (Bassok, 2003). In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Even solving simpler, more basic problems is helped by considering analogies. A first grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. If the child cannot yet read the word screen , for example, he can note that part of this word looks similar to words he may already know, such as seen or green , and from this observation derive a clue about how to read the word screen . Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider.

Bassok, J. (2003). Analogical transfer in problem solving. In Davidson, J. & Sternberg, R. (Eds.). The psychology of problem solving. New York: Cambridge University Press.

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

Leiserson, C., Rivest, R., Cormen, T., & Stein, C. (2001). Introduction to algorithms. Cambridge, MA: MIT Press.

Luchins, A. & Luchins, E. (1994). The water-jar experiment and Einstellung effects. Gestalt Theory: An International Interdisciplinary Journal, 16 (2), 101–121.

Mayer, R. & Wittrock, M. (2006). Problem-solving transfer. In D. Berliner & R. Calfee (Eds.), Handbook of Educational Psychology, pp. 47–62. Mahwah, NJ: Erlbaum.

Thagard, R. (2005). Mind: Introduction to Cognitive Science, 2nd edition. Cambridge, MA: MIT Press.

Voss, J. (2006). Toulmin’s model and the solving of ill-structured problems. Argumentation, 19 (3), 321–329.

• Educational Psychology. Authored by : Kelvin Seifert and Rosemary Sutton. Located at : https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=153 . License : CC BY: Attribution

What are the Factors that Affect Problem-Solving Activities? Part 1

• Categories : Resource management
• Tags : Project management

Identification of the Problem

The most important of factors that affect problem-solving activities is realization of the problem. A problem is decided by the purpose. For instance, manufacturing managers evaluated based on the percentage of time they have operated the production lines do not have a problem with operating the production line without orders from their sales division. On the other hand, the sales division will have a major problem with this action if there are no orders and excessive inventory piles up as a result of this action.

Identification or realization of the problem, keeping the big picture in mind, is the first and most important step toward problem solving. They key to doing so lies in understanding the purpose of the action. The basic steps toward this direction include:

• Defining the problem.
• Identifying the potential causes for the problems.
• Listing out the various solutions.
• Selecting the best alternative.
• Planning implementation.
• Monitoring and verifying the implementation.

Image Credit: flickr.com/Martino Franchi

Personality Types

In 1987, M. McCaulley undertook one of the earliest research projects to link individual differences in personality to problem-solving approaches. He used Carl Jung’s theory of individual preferences to correlate the four mental processes of sensing, intuiting, thinking, and feeling to decision-making preferences. Sensing individuals considers facts, details, and reality when making decisions to solve problems. Intuitive individuals try to understand the meaningfulness of the facts, the relationships among the facts, and the possibilities of future events that can be imagined from these facts to make decisions, and usually develop new, original solutions. Thinking individuals tend to use logic and objective analysis during problem solving, and Feeling individuals tend to veer toward subjective considerations of values and feelings in the problem-solving process. Sensing and Intuitive people approach problems through their perceptions, and they prefer flexibility and adaptability. Thinking- and Feeling-oriented people usually make judgments and tend to prefer the problem-solving process to demonstrate closure.

Individuals preferring introversion take time to think and clarify their ideas before acting, while those preferring extroversion talk through their ideas to clarify them before acting. Introverts remain concerned with their own understanding of important concepts and ideas, whereas extroverts seek feedback from the environment.

Temperament

The ability of a person to solve problems depends on both personality type and temperament. People motivated toward a goal , or those who are high achievers, take that extra effort and initiative to find the root cause of problems and solve it. Others go by the routine procedure and do the minimum required.

High-risk takers who usually find themselves in more problems generally tend to be more adept in solving problems, also.

A far bigger personality dimension, however, lies in the positive treatment of the problem, or considering it as an opportunity to learn new things. A negatively charged problem impedes solution.

Thinking Patterns

Another of the major factors that affect problem-solving activities includes the thought processes or thinking patterns of the concerned individual.

The major thought process dimensions include:

• Strategic thinking or a bigger long-term focus instead of short-term departmental focus.
• Emotional thinking or judging whether a solution is right or wrong based on emotional commitment.
• Realistic thinking or the approach of starting from what can be done and fixing the essential problem first.
• Empirical thinking or judging whether the situation is right or wrong based on past experiences.

Problem solvers need to choose the appropriate thinking pattern based on the situation.

Besides such dimensions, the ability to think systematically through a rational process, such as systems things, thought and effect process, and contingent thinking, and the ability to forge hypothesis improves the thinking processes.

Skills and Technical Competency

The ability to solve a problem depends greatly on the person’s competency relative to the problem in hand. For instance, a team leader skilled in computer networking might be able to manage a network failure, create ad hoc procedures until the systems are restored, or effectively direct the recovery by functional experts. A team leader with no clue on networking would remain totally at sea and at the mercy of the functional experts.

At times problem-solving requires creativity and innovation, which again depends on the personality and temperament of the person, and the culture of the organization.

Hierarchies

Hierarchical organizations that tend to give importance to designations and fixed job descriptions , insist on adherence to procedures, and do not encourage ad hoc measures, stifle creativity and innovation and have a profound impact on problem-solving activities.

The ability to solve problems often depends on the administrative mazes and bureaucratic hurdles. For instance, a computer expert working in human resources might be the best person to recover a crashed system. This person, however, might not have the necessary permissions or authorization to access the main server, and the work remains disrupted until the authorized repair personnel arrive from far away.

External Environment

The external environment of an organization remains the root cause of many problems in a project, and the solution depends on the external environment itself. For instance, availability of skilled manpower depends on the labor market, running of machinery depends on the provision of energy by the utility provider, and starting operations depends on compliance with the procedures to securing the necessary permits. The best approach to problem solving is having a good understanding of the state of the external environment to reconcile the business operations with the external environment.

A business cannot control or alter the external environment. It can only harness it to its advantage. In this realization lies the key to solving most problems.

• Huitt, William, G. “Problem Solving and Decision Making: Consideration of Individual Differences Using the Myers-Briggs Type Indicator.” Retrieved from https://teach.valdosta.edu/whuitt/papers/prbsmbti.html on 21 October 2010.
• Shibata, Hidetoshi. “Problem Solving: Definition, terminology, and patterns.”Retrieved from https://www.mediafrontier.com/Article/PS/PS.htm on 21 October 2010.
• McNamara, Carter. “ Basic Guidelines to Problem Solving and Decision Making.”. Retrieved from https://www.managementhelp.org/prsn _prd/prb_bsc.htm on 21 October 2010.

• Open access
• Published: 25 May 2023

Factors influencing the complex problem-solving skills in reflective learning: results from partial least square structural equation modeling and fuzzy set qualitative comparative analysis

• Ying Wang 1   na1 ,
• Ze-Ling Xu 1   na1 ,
• Jia-Yao Lou 1   na1 &
• Ke-Da Chen 1  

BMC Medical Education volume  23 , Article number:  382 ( 2023 ) Cite this article

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Metrics details

The Organization for Economic Cooperation and Development emphasizes the importance of complex problem-solving (CPS) skills in the 21st century. CPS skills have been linked to academic performance, career development, and job competency training. Reflective learning, which includes journal writing, peer reflection, selfreflection, and group discussion, has been explored to improve critical thinking and problem-solving abilities. The development of various thinking modes and abilities, such as algorithmic thinking, creativity, and empathic concern, all affect problem-solving skills. However, there is a lack of an overall theory to relate variables to each other, which means that different theories need to be integrated to focus on how CPS skills can be effectively trained and improved.

Data from 136 medical students were analyzed using partial least square structural equation modeling (PLSSEM) and fuzzy set qualitative comparative analysis (fsQCA). A hypothesized model examining the associations between the CPS skills and influence factors was constructed.

The evaluation of the structural model showed that some variables had significant influences on CPS skills, while others did not. After deleting the insignificant pathways, a structural model was built, which showed that mediating effects of empathic concern and critical thinking were observed, while personal distress only had a direct effect on CPS skills. The results of necessity showed that only cooperativity and creativity are necessary conditions for critical thinking. The fsQCA analysis provided clues for each different pathway to the result, with all consistency values being higher than 0.8, and most coverage values being between 0.240 and 0.839. The fsQCA confirmed the validity of the model and provided configurations that enhanced the CPS skills.

Conclusions

This study provides evidence that reflective learning based on multi-dimensional empathy theory and 21 stcentury skills theory can improve CPS skills in medical students. These results have practical implications for learning and suggest that educators should consider incorporating reflective learning strategies that focus on empathy and 21 stcentury skills to enhance CPS skills in their curricula.

Peer Review reports

Introduction

When putting forward the theoretical framework of skills and competencies in the 21st century, the Organization for Economic Cooperation and Development takes complex problem-solving (CPS) skills as an important component and brings them into the evaluation system of the Program for International Student Assessment [ 1 ]. Previous research results have proved that there is a significant positive correlation between CPS skills and academic performance [ 2 ], that is, the stronger the problem-solving skill, the better the academic performance. Similarly, it is also considered to have a great influence on career selection [ 3 ], career development [ 4 ], and job competency training [ 5 ]. Therefore, the improvement of the above-mentioned comprehensive qualities, such as learning ability and post competence, and the cultivation of CPS skills, has been emphasized by a variety of teaching strategies, such as problem-based learning (PBL) [ 6 ], context-based learning (CBL) [ 7 ], situational simulation [ 8 ], and reflective learning [ 9 ].

As an important process of metacognition, reflective learning is closely related to CPS skills. Gadbury-Amyot et al. claimed that the use of reflection and writing as educational strategies to promote critical thinking and problem-solving is one of the best ways for students to express their thought processes [ 10 ]. Exploration to improve CPS skills based on reflective learning and training can be seen in medicine, computer science, mathematics, and other industries. According to Bernack, establishing problem-solving training courses could feasibly enhance the abilities of pre-service teachers [ 11 ]. Kellogg suggested that reflection and writing, as educational strategies to promote critical thinking and problem-solving skill, is one of the best ways to improve students’ expression ability and logical thinking [ 12 ]. “Reflective learning” is a common way of exploring problems and solutions in the deliberative environment, a process of learning through experience, and is a necessary learning tool in professional education [ 13 ]. Reflective learning includes journal writing, peer reflection, self-reflection, and group discussion under the guidance of teachers [ 14 ]. Illeris suggested that the result of reflective learning spans cognitive, psychodynamic, and social-societal dimensions [ 15 ]. Through its influence on students’ behavior, thoughts, and emotions, it realizes the training and improvement of students’ various abilities. It has gradually developed into a more efficient and autonomous learning model and has become an indispensable educational and learning tool for many professionals [ 16 ]. Many experts suggest that the implementation of reflective learning can improve students’ critical thinking [ 17 ], insight [ 18 ], empathic concern [ 19 ], computational thinking [ 20 ], and other skills, and this improvement of a variety of thinking modes and abilities will eventually lead to improvement of their CPS skills [ 21 ]. Our research on the factors affecting the CPS skills is based on reflective learning.

The purpose of human problem solving is to promote the understanding of human thinking through a detailed investigation of the way people solve difficult problems, such as logic or chess. Unlike computer simulations, human problem solving is influenced by psychological factors that cannot be ignored [ 22 ]. Therefore, problem solving is dynamic and needs to consider the influence of speculation, social background, and culture, while CPS skills emphasize the process of successful interaction between the problem solver and the dynamic task environment [ 23 ]. CPS skills are collections of self-regulating psychological processes necessary in the face of complex and dynamic non-routine situations across different domains [ 24 ], and comprises a combination of skills, abilities, motivation, and other psychological structures [ 25 , 26 ]. The factors that impact CPS skills are complex and include cognitive and non-cognitive factors. Research shows that the development of a variety of thinking modes and abilities, such as algorithmic thinking, cooperativity, creativity, critical thinking, personal distress, fantasy, perspective-taking, and empathic concern, all affect the problem-solving skill in varying degrees [ 27 , 28 ]. Among them, empathetic concern and critical thinking have been proven to affect problem-solving skill by many studies. After comprehensively exploring the emerging research on the impact of the factors on the CPS skills, we found that previous studies mainly focused on a single causality in the improvement of problem-solving skill, while there is a lack of overall theory to relate variables to each other, which means that we need to integrate different theories to advance existing research and focuson how CPS skills can be effectively trained and improved.

Theoretical background

The literature analysis of CPS skills reveals the current research status. Based on the relevant theories of skills needed in the 21st century [ 1 ], individuals use analytical, reasoning, and cooperative skills to identify and solve problems consistent with their areas of interest [ 29 ]. Kocak proposes that problem-solving skills are shaped by algorithmic thinking, creativity, cooperativity, critical thinking, digital literacy, and effective communication, and develops a model with critical thinking as a mediating factor [ 21 ]. Developing solutions for complex problems is a complicated process, and individuals require critical thinking skills [ 21 , 30 ] to do so. Critical thinking often occurs at the same time as CPS skills and is one of the core objectives of general education in all subjects of higher education [ 29 ]. Critical thinking, closely related to reflective learning [ 17 ], which has been emphasized in many studies, especially in the implementation of learning strategies including reflective learning. In problem-based learning and case-based learning, instructors encourage learners to use critical reflection to engage with subject matter and to develop their own practice in closing any knowledge gaps that may exist [ 31 ]. Additionally, digital literacy involves the ability to assess the accuracy and value of online resources [ 32 ]. In this study, reflective learning was the primary learning strategy [ 33 ]; therefore, digital literacy skills were not observed in detail. Drawing on the above analysis, we developed a theoretical model that identifies algorithmic thinking, creativity, and cooperativity as antecedents, and critical thinking as an intermediary variable that influences CPS skills.

Another major area related to affecting CPS skills is empathic concern. The research suggests that students with a higher level of cognitive empathy show more positive attitudes and deal with problems more effectively [ 34 ]. In essence, empathetic concern fosters values, beliefs, attitudes, and assumptions, and affect the CPS skills from the perspective of execution [ 35 , 36 ]. Some studies suggest that reflective learning improves empathy [ 37 ]. Based on Davis’s Interpersonal Reactivity Index [ 38 ], empathy was divided into four dimensions mentioned: Empathic concern, fantasy, perspective-taking, and personal distress. Nevertheless, some scholars disagree that personal distress belongs to the category of empathy. Personal distress is defined as an over-arousal caused by the lack of boundaries between oneself and others [ 39 , 40 ]. Some studies show that personal distress leads to egoism and overwhelms altruistic activities mediated by empathetic concern [ 41 ]. And there is a statistically significant correlation between personal distress and empathetic concern [ 42 ]. Therefore, we still adhere to the view that the two cannot be regarded as mutually exclusive emotions, bringing personal distress into the scope of our research and exploring its role in CPS skills. Empathetic concern has been proved to associate with prosocial behavior [ 43 ]. In the relationship between empathic concern and prosocial concern, empathic concern elicits an approach orientation toward the target [ 44 ] and is used as a mediator variable in some models. For example, some studies consider empathic concern and personal distress are both mediators of perspective-taking to helping behavior [ 45 ]. Based on the above analysis, we built our theoretical model and assume that personal distress, perspective-taking, and fantasy as antecedents and empathetic concern as intermediary variables that affect the CPS skills.

Above all, the empathic concern and the critical thinking are two remarkable characteristics of the CPS skills, which can play a common role in the CPS skills [ 46 ], however, there is a lack of overall theory to connect them, which means that different theories need to be integrated to promote research. The comprehensive study of the combination of the two aspects can better understand how to improve CPS skills, which cannot be provided by any theory alone. Moreover, the results on the factors affecting the CPS skills also show some inconsistencies. For example, Batson believes that personal distress in empathy inhibits the development of problem-solving skills [ 41 ], whereas Mora disagrees [ 47 ]. A possible reasonable explanation for these contradictory results is that the previous studies on the factors influencing problem-solving skill mainly adopted traditional symmetric methods (such as regression and SEM), which did not fully capture the complexity of the factors that influence problem-solving skills, and the factors affecting the CPS skills are often based on multiple causalities rather than a single causal relationship. Simply evaluating symmetric relationships might lead to divergent results, thus masking the complexity of the problem-solving skill. Considering the complex nature of CPS skills under the condition of reflective learning, it is necessary to check the symmetric and asymmetric relationships between structures to fully understand the strategies and methods to improve CPS skills, therefore, PLS-SEM [ 48 ] and fsQCA [ 49 ] were used in our study comprehensively.

Research model and hypothesis development

Designing the pls-sem research model.

Critical thinking in the field of cognition and empathic concern in the field of emotion are representatives of two different thinking modes affecting the CPS skills. PLS-SEM assumes that fantasy, perspective-taking, personal distress, algorithmic thinking, creativity, and cooperativity have a direct impact on the CPS skills. Empathetic concern and critical thinking play an intermediary role between these relationships and the CPS skills (Fig.  1 A).

Partial least square structural equation modeling (PLS-SEM) conceptual model and fuzzy set qualitative comparative analysis (fsQCA) conceptual model: ( A ) The PLS-SEM conceptual model. ( B ) The fsQCA conceptual model

Personal distress and CPS skills

The definition of personal distress in this study pertains to the discomfort and anxiety that respondents experience when observing negative experiences of others, including fear, apprehension, and discomfort. Personal distress is an aspect of emotional empathy [ 38 ]. Some studies show that personal distress and empathy are complex and dynamic emotional experiences [ 50 ]. Personal distress, as an indicator of self-other differentiation and emotional regulation, is a kind of negative emotion. Excessive personal distress can lead to emotional regulation and interpersonal difficulties [ 51 ]. These studies advocate reducing personal distress to relieve stress [ 52 ]. The healthcare sector prioritizes a patient-centered healthcare model, which mandates that we respond to patients’ emotional distress with this principle in mind. However, in practice, health professionals tend to regard emotional health problems as “routine”; therefore, it is necessary to put patients’ emotional and identity issues in the dominant position of the marginal biomedical model used by health professionals [ 53 ]. However, empathic pain is crucial to Hoffman’s moral development framework. He believed that pain can cause significant effects that might lead to action [ 54 ]. Moitra’s research also supports the positive effect of personal distress on problem-solving skill [ 47 ]. Reflection encourages individuals to confront their own embarrassing and uncomfortable past experiences, learn from their errors, and enhance their CPS skills [ 55 ].

Fantasy and CPS skills

Fantasy acts on all aspects of reflective learning. First, to some extent, our brains process information and decisions in an irrational way, and reflection contributes to the cultivation of irrational thinking [ 56 ]. The improvement of subjects’ irrational thinking, including fantasy, can be promoted through reflective learning. Research indicates that individuals with higher fantasy and perspective-taking skills tend to have stronger social understanding [ 57 ]. Second, the development of imagination and fantasy is an important part of cultivating empathic concern [ 58 ]. This is because people understand the world through fantasy, and fantasy gives people hope that the world will become a better place [ 59 ]. For example, Melissa McInnis Brown’s research showed that children who play using fantasies are better at sharing emotions than their peers [ 60 ]. Many studies have proven the role of fantasy in problem-solving. For example, David Weibel pointed out that one can effectively use imagination in an environment, such as in artistic expression or problem-solving [ 61 ]. Fantasy is an imaginative way to find creative solutions that can help people predict the realization of creative structures [ 61 ]. From a sociological point of view, scholars usually regard fantasy as an important factor in cultivating children’s prosocial behaviour [ 57 , 62 ]. Empathic concern requires a person or the whole team to have an overall and largely unconscious “feeling” in terms of emotions, body language, previous experiences, and interpersonal relationships; therefore, this requires significant support from the fantasy system [ 63 ].

Perspective-taking and CPS skills

The effectiveness of group problem solving heavily depends on group member interactions and group composition. For perspective-taking, it provides the possibility for effective communication, which mainly affects the effective presentation of information, effective understanding of that information, conflict resolution, and cooperative interaction [ 64 , 65 ]. In management, perspective-taking has become an important factor in teamwork to solve problems [ 66 ]. During perspective-taking, the problem-solving process can be facilitated by promoting empathic concern, which is evident in the subjects’ cognitive dimension. For example, Falk found that perspective-taking leads to more creative solutions, and team members are more cooperative and facilitate more effective communication [ 64 ]. Bethune and Brown suggested that reflection affects the professional identity of patients by encouraging personal insights and providing different perspectives on patient interaction [ 67 ]. Reflection requires us to think about the past and sum up experiences and lessons from it. Thinking about problems from the standpoint of others can circumvent the limitations of our perspective of looking at problems only through ourselves and can promote the solution of complex problems.

Based on the points discussed above, we propose the following assumptions:

Personal distress is positively related to the CPS skills.

Fantasy is positively related to the CPS skills.

Perspective-taking is positively related to the CPS skills.

Algorithmic thinking and CPS skills

Algorithm thinking draws lessons from the algorithms of computers and artificial intelligence, which enables people to think and deal with things in parallel, process things in data, carry on data and logical reasoning to things, and finally achieve the goal of completing plans and tasks. As one of the core skills in the 21st century, algorithmic thinking abstractly and logically determines the elements used to solve problems through analysis [ 28 ]. One of the major applications of algorithmic thinking is jigsaw puzzle-based learning, which aims to make subjects think about how to build and solve problems, and improve their critical analysis and problem-solving skills [ 68 ]. Hasan Gürbüz leveraged straightforward visual and language templates to help individuals develop models and analyze information about events through games, resulting in improved problem-solving skills [ 69 ]. This mode of thinking, based on logic and steps, is very important for the development of critical thinking and computational thinking [ 28 ]. Many studies have shown that there is a positive correlation between algorithmic thinking and critical thinking [ 70 ]. In reflective learning, algorithmic thinking plays a significant role in computing, as evidenced in this study by recording a short video that necessitates organizing large amounts of data to develop suitable algorithms for analysis [ 71 ].

Creativity and CPS skills

Creativity affects our lives and is vital to the progress of society [ 72 ]. The definition of creativity highlights the integration of novel (original, unexpected) and appropriate (useful, adaptive concerning task constraint) ideas [ 73 ]. Since the 20th century, a large number of scholars in various fields have paid attention to creativity and CPS skills. Creativity is a valuable skill while designing solutions to new challenges that arise in developing societies [ 74 ]. For instance, Garrett noted that creativity plays a crucial role in problem-solving [ 75 ]. In many studies, creativity and critical thinking are interdependent, and creative tasks can improve people’s creativity [ 76 ]. In reflective learning, we utilize divergent thinking that frequently enhances our creativity.

Cooperativity and CPS skills

Many critics believe that cooperativity plays an important role in the cultivation of critical thinking [ 77 ]. Cooperativity receives considerable attention in the learning process due to its association with effective communication. For example, service-learning attaches great importance to cooperation, democratic citizenship, and moral responsibility in the learning process [ 78 ], and preschool educational institutions need to improve the experience through the collaborative exchange, to create favorable conditions for educators to re-examine educational activities, and determine the direction of new relationships through observation [ 79 ]. In reflective learning, subjects become aware of their contradictions and gain valid information, and critically assess peer opinions through active communication, which advances their ideas for program and CPS skills improvement.

Algorithmic thinking is positively related to the CPS skills.

Creativity is positively related to the CPS skills.

Cooperativity is positively related to the CPS skills.

Mediators and CPS skills

This study assumes that empathetic concern and critical thinking act as mediators between the CPS skills and their antecedents.

In Gibbs’s theory, the emotional dimension is a very important aspect of reflective learning [ 80 ]. Madeline Kelly’s research showed that reflection has a positive effect on the improvement of cognitive empathy [ 81 ]; however, there are few studies on the effect of reflective learning on empathy. Cognitive empathy includes fantasy and perspective-taking, while the emotional empathy includes personal distress and empathic concern [ 82 ]. Research shows that the concept of emotional empathy is state empathy, with the focus on altruism [ 83 , 84 ]. Emotional empathy plays an important role in patient-nurse communication [ 85 ]. Failure to deal with or understand emotions will make it difficult for nurses to think rationally and critically about issues that are important to nursing practice [ 86 ]. Therefore, we cannot ignore the influence of empathic concern on the CPS skills in reflective learning. We assumed that the ability of empathic concern can increase altruism and help to improve CPS skills. However, personal distress is usually considered to lead to egoism, which is not conducive to the formation of altruism [ 41 ]. In-depth investigation is necessary to understand its effect on CPS skills. As an important factor in prosocial behavior, the empathic concern serving as a mediator between cognitive behavior and prosocial behavior [ 87 ]. Based on the theories of O’Brien and Gülseven, we constructed a CPS skills model with empathic concern as the mediating variable [ 88 , 89 ].

Effective reflection is characterized by purposeful, focused, and questioning [ 90 ]. In the process of reflection, this mode of thinking requires us to think critically and center on the results. Reflective learning, also known as critical reflection [ 17 ], emphasizes the use of critical thinking. Many critics affirm the results of critical reflection [ 91 , 92 , 93 ]. Parrish and Crookes found that among nursing graduates, reflection helped them to solve problems through thoughtful reasoning and to develop strategies for self-monitoring of their professional competence [ 94 ]. Critical thinking is typically rational thinking, and through combining theory with practice, exploring the similarities and differences between theoretical knowledge and practical experience, and considering a variety of different viewpoints and opinions, the effect of reflective learning can be enhanced. Therefore, speculative reflection is designed to help us identify our shortcomings and think about how to correct and improve them. Critical thinking is widely recognized as an important skill in mediating CPS skills [ 10 ]. Based on the research of Kocak and Tee, we also view critical thinking as an intermediary variable, playing a mediating role in algorithmic thinking, creativity, and cooperativity within CPS skills [ 21 , 95 ].

Personal distress indirectly affects the CPS skills through empathic concern.

Fantasy indirectly affects the CPS skills through empathic concern.

Perspective-taking indirectly affects the CPS skills through empathic concern.

Empathic concern is positively related to the CPS skills.

Algorithmic thinking indirectly affects the CPS skills through critical thinking.

Creativity indirectly affects the CPS skills through critical thinking.

Cooperativity indirectly affects the CPS skills through critical thinking.

Critical thinking is positively related to the CPS skills.

Designing the fsQCA configuration model

In this study, a Venn diagram is used to design the fsQCA configuration model (Fig.  1 B), which was used to explore the causal model for improving CPS skills. In the diagram, arrow A represents a combination of perspective-taking, fantasy, and personal distress, and adds configurations that affect the CPS skills through, or including, empathetic concern. Arrow B represents a combination of algorithmic thinking, creativity, and cooperativity, and adds configurations that affect the CPS skills through, or including, critical thinking. Arrow C represents the combination of all the variables and represents the complex interaction of these factors to predict the resulting conditions.

Participants

Participants were 136 freshmen and medical majors from a university in southeastern China (‾Xage = 18.47, female = 82.35%, male = 17.65%). The inclusion criterion comprised students who had conducted reflective learning. The exclusion criteria comprised: (1) Students who did not make reflective videos, or (2) students suspected of plagiarizing reflective learning achievements. A total of 163 cases were included in the empirical study of reflective learning, and 136 effective samples were recovered, with an effective recovery rate of 83.44%.

Design and procedure

After receiving appropriate online training, classroom teachers implemented a reflective learning curriculum design among medical students in the autumn of 2021 (Fig.  2 ). Based on the Biochemistry and Molecular Biology Courses, the two rounds of teaching plan lasted a total of 14 weeks was design. In the first round of reflective learning, subjects were asked to read relevant literature, watch relevant video materials, etc., and carry out online learning. They were then asked to record learning videos on their own, and then upload the videos, followed by a double-blind mutual evaluation of learning videos between online students. In the second round of reflective learning, students adjusted their reflective learning according to the feedback from the previous round of mutual evaluation, implemented a second round of deeper material learning exploration, improved their reflective video, and summarized the main points of reflective learning. Teachers evaluated the reflective videos and learning points offline, and students learned and summarized according to the evaluation results. After the end of the entire process, we issued a competency assessment questionnaire to measure learners’ competency levels and the data was collected.

Reflective learning process

To measure the constructs under study, existing scales were used (see Table  1 for items associated with each construct and scale reliabilities).

A questionnaire was developed based on the existing mature scale, and the items were slightly adjusted according to the model. The relationship between the retained items and the dimensions was not complementary. Improvement of CPS skills is described as a structure composed of six antecedent variables and two mediating variables with different ways of thinking. The Davis Interpersonal Reactivity Index (IRI) was used for personal distress, fantasy, perspective-taking, and empathic concern [ 38 ], and the Computational Thinking Scale (CTS) was used for critical thinking, algorithmic thinking, creativity, problem solving, and cooperativity [ 74 , 96 , 97 ]. We structured it as personal distress (three items), fantasy (three items), and perspective-taking (two items) as ante-dependent variables, and the mediating effect of empathic concern (three items) on CPS skills (three items) was directly and through empathic concern (3 items). Similarly, algorithmic thinking (3 items), creativity (three items), and cooperativity (three items) acted as ante-variables, both directly and through the mediating effect of critical thinking (three items). All items were evaluated using a Likert 5-point scale, 5 = strongly agree, 4 = agree, 3 = neither agree nor disagree, 2 = disagree, 1 = strongly disagree, and the scores of items in reverse scoring were reversed. Entries for reverse scoring are marked with * in Table  1 . The questionnaire was translated into Chinese and distributed after discussion with experts.

Data analysis

We use multiple methods to analyze the data. First, PLS-SEM was carried out on the data through Smart-PLS 3.0 software to adapt the complex model analysis and explore the impact of various factors [ 48 ].

We measured the characteristics of the structure using internal consistency reliability, convergence validity, and discrimination validity. Internal consistency reliability was measured using the alpha and combinatorial reliability of Cronbach. And we checked the collinearity of the internal model and evaluated the deviation of the method using a variance inflation factor (VIF). According to the research objectives, we tested two models with different paths with significant correlations. The direct predictive effects of fantasy, personal distress, perspective-taking, creativity, cooperativity, and algorithmic thinking, as well as the mediating effects of empathic concern and critical thinking, on CPS skills were tested. A nonparametric, bias-corrected bootstrap with 5,000 subsamples and a 95% confidence interval was used. The structural model was evaluated by R² and by the significance of the estimated value of pathway relationships. The significance of pathway coefficients was evaluated using the bootstrap subsamples, and the structural model was evaluated using 5000 bootstrap subsamples [ 98 ]. R² values of 0.25, 0.50, or 0.75 are considered weak, moderate, and significant, respectively.

Although PLS-SEM can handle both external (measurement) and internal (structural) models [ 98 ], it is limited by symmetry. Therefore, we used fsQCA 3.1 software [ 49 ] to analyze asymmetry and obtain a sufficient causal combination configuration to study the complex relationship between variables more comprehensively and in detail. According to the fsQCA user guide, data calibration, truth table construction, and causal condition analysis are necessary steps in the process of data analysis [ 49 ]. In the first step, we converted the ordinary data into fuzzy sets by setting the original values from the Likert scale, which corresponded to full membership, cross-over anchors, and full non-membership based on Kallmuenzer’s analysis [ 99 ]. The second step is to construct the truth table and generate different combinations of causal conditions that are sufficient to affect the CPS skills by specifying a consistent cutoff value as the natural breakpoint in the consistency and the case number threshold as 1. The third, we analyzed the necessity of all the variables (critical thinking, creativity, algorithmic thinking, cooperativity, empathetic concern, perspective-taking, personal distress and fantasy) to the CPS skills, and the antecedent variables for mediate variables (critical thinking and empathic concern), and the necessity of mediating variables to the outcome variables. It is generally believed that a condition or combination of conditions is “necessary” or “almost always necessary” when the consistency score is higher than 0.9 [ 49 ]. Finally, we use standard analysis to obtain “intermediate solutions” (i.e., partial logical remainders are incorporated into the solution) to identify causal patterns that affect CPS skills.

The result of PLS-SEM

Evaluation of the reflection measurement model.

Except for the perspective-taking, the Cronbach’s alpha in the other dimensions was generally more than 0.7, reaching the standard recommended by Cohen (Table  1 ) [ 100 ]. After examining the external loads in the external model, we observed that most of the loads were more than 0.7, while the PD1 project was still less than 0.7. After checking the Cronbach’s alpha and average variance extracted (AVE), we confirmed that this factor had no negative effect on our research [ 98 ], and was thus retained the project. The sample size of the model is small (less than 300), and the items considered by perspective-taking are 2 (less than 3), so Cronbach’s alpha is easily less than 0.6. The alpha of perspective-taking is more than 0.5, which is still in a slightly plausible range. Therefore, we kept the item of perspective-taking. Secondly, the square root of AVE was greater than 0.5, which accords with the convergence validity [ 101 ]. In addition, we used the Fornell-Larker criteria to evaluate the discriminant validity (Table  2 ).

Evaluation of formative measurement models

The results showed that the VIF of all constructs was lower than the threshold of 3.3 (see Additional file. 1 ) [ 98 ]. In order to further analyze, this study evaluated the quality by blindfolding program (Q 2 ) and standardized root mean square residual (SRMR). The results showed that SRMR = 0.079, not exceeding 0.09 [ 102 ]. The blindfold program showed that Q 2 was greater than 0, which verified the predictive correlation of the research model [ 103 ].

Structural model evaluation

Evaluation of the structural model showed that the R² value was reasonable for exploratory research. Meanwhile, the direct pathway effect of fantasy, algorithmic thinking, creativity, and cooperativity on CPS skills was not significant ( p  > 0.05), and the pathway effect of personal distress on empathic concern was also not significant ( p  > 0.05). The other variables showed significant influences on CPS skills ( p  < 0.05) (Table  3 ). After deleting the insignificant pathways, we built a structural model between the CPS skills and the influencing factors (critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, and personal distress) (Fig.  3 ). Compared with the hypothetical model, mediating effects of empathic concern and critical thinking were observed; however, personal distress only had a direct effect on CPS skills, which was consistent with the previous view that empathic concern and personal distress should be discussed [ 51 ].

Path model and partial least square structural equation modeling (PLS-SEM) estimates

The result of fsQCA

The results of necessity showed that only cooperativity and creativity are necessary conditions for critical thinking (see Additional file. 2 , Additional file. 3 , and Additional file. 4 ).

FsQCA assessed the complex causal combination that led to improved CPS skills (Tables  4 , 5 , 6 and 7 ). The solution provided clues for each different pathway to the result, with all consistency values being higher than 0.8, and most coverage values being between 0.240 and 0.839 [ 104 ].

As shown in Table  4 , there are six approaches to the final model of complex conditions that lead to high CPS skills, among which the top three in terms of coverage are: (1) To achieve high CPS skills through high critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, personal distress, and perspective-taking (consistency = 0.974, coverage = 0.354). (2) Under conditions of high critical thinking, cooperativity, algorithmic thinking, and creativity, combined with high empathic concern, personal distress, and fantasy, the CPS skills can be improved (consistency = 0.950, coverage = 0.352). (3) A high level of critical thinking, cooperativity, algorithmic thinking, creativity, personal distress, perspective-taking, and fantasy (consistency = 0.950, coverage = 0.340) can promote the improvement of CPS skills.

To examine the mediating effect of empathic concern and critical thinking on the CPS skill, we analyzed the complex causality of fantasy, personal distress, perspective-taking, and empathic concern. The results showed in Table  5 indicated that the complex causal statement of fantasy, personal distress, perspective-taking, and empathic concern is one way, i.e., high perspective-taking and fantasy improves empathic concern skill (consistency = 0.821; coverage = 0.612), which supports the H7b and H7c assumptions in the SEM model. By contrast, the results of analyzing the complex causal relationship of creativity, cooperativity, and algorithmic thinking for critical thinking showed that there is a pathway for the complex causal statement of creativity, cooperativity, algorithmic thinking, and critical thinking (consistency = 0.867, coverage = 0.760), which will lead to improved critical thinking ability. This supported the hypotheses of H8a, H8b, and H8c in the SEM model.

The results of further analysis of the complex causal relationship between empathic concern and critical thinking for improved CPS skills (Table  7 ) showed that high empathic concern and critical thinking (consistency = 0.890, coverage = 0.550) will lead to improved CPS skills. This supported the H7d and H8d assumptions in the SEM model.

Discussion and conclusion

Theoretical implication.

To improve its ability to deal with complex practical problems, education has been committed to providing teaching measures that can stimulate subjects’ rational and irrational thinking. Healthcare professionals who utilize reflective learning must apply empathetic concern and critical thinking to confront challenges with high-quality solutions. Although previous studies confirmed the positive effects of empathic concern [ 19 ], and critical thinking [ 17 ] on CPS skills through symmetrical analysis, few studies have tested empathic concern and critical thinking at the same time. There is a dearth of studies that specifically investigate the factors that affect CPS skills in the context of reflective learning. And the previous studies on the factors influencing CPS skills mainly adopted traditional symmetric methods (such as regression and SEM), which did not fully capture the complexity behind the factors of influencing CPS skills. For instance, Hwang discovered that collaboration plays a crucial role in problem-solving, whereas communication may not be essential. In contrast, Kocak holds a contrasting perspective [ 21 , 105 ]. The factors affecting the CPS skills are often based on multiple causalities rather than a single causal relationship. Therefore, based on the theory of multi-dimensional empathy [ 38 ] and 21st-century skills [ 21 ], we analyzed the data of 136 medical students undergoing reflective learning using PLS-SEM and fsQCA, and constructed a hypothetical model to examine the relationships between the CPS skills and influence factors (critical thinking, cooperativity, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, personal distress).

The PLS-SEM results (Table  3 ) showed that a variety of attributes can affect the CPS skills, among which critical thinking and empathic concern play an intermediary role between most antecedents and CPS skills. The fsQCA results partly verified the mediating effect of critical thinking and empathetic concern (Tables  5 and 6 ). In the PLS-SEM results (Table  3 ), personal distress was identified to directly affect the CPS skills; and the effect of personal distress on empathic concern was not shown in the fsQCA solution (Table  5 ), which proved that personal distress directly affects the CPS skills without the intermediary of empathetic concern. This result is similar to that of Jeon [ 106 ]; however, he believed that there is a negative correlation between personal distress and problem solving, which might be related to the different learning patterns (reflective learning) used in this study. Personal distress is a necessary process in reflective learning because the motivation of prosocial behavior eases our uncomfortable state of mind by reducing the disgusting and awakening cues sent out by others [ 107 ]. Reflection urges us to face these emotions and draw lessons from them. Hoffman noted that excessive personal distress can turn others-oriented motivation into self-directed motivation, thus reducing the occurrence of prosocial behavior [ 54 ], which emphasizes the differential treatment of personal distress in different learning modes. In addition, perspective-taking was identified to affect the CPS skills directly (Table  3 ; C1 in Table  4 ) and indirectly (Table  3 ; C1 in Table  5 ). Therefore, some of the results obtained from fSQCA validated the conclusions of PLS-SEM to some extent (Table  8 ).

The fsQCA results provided more configuration solutions of complex causality, which extended the results of PLS-SEM and further revealed the complexity of affecting the CPS skills. For example, the fsQCA results in Table  7 not only proved the mediating effect of empathetic concern and critical thinking, but also suggest that they work together to affect the CPS skills. This demonstrates that CPS skills are impacted by both rational and irrational thinking, and positive emotions play a critical role in fostering CPS skills [ 108 ]. In Table  4 cooperativity, creativity, algorithmic thinking, critical thinking, and personal distress all appear in forward solutions with high coverage (C1, C2, C3 in Table  4 ). This suggested that personal distress, cooperativity, creativity, algorithmic thinking, and critical thinking can be regarded as the core conditions to affect the CPS skills, and these conditions make an important contribution in the context of reflective learning. Researches by Chen [ 77 ], Garrett [ 75 ], Geisinger [ 70 ] and Ellis [ 17 ] respectively believed that collaboration, creativity, algorithmic thinking and critical thinking play an important role in CPS skills, and Sze [ 109 ] believed that personal distress could have a positive impact on prosocial behavior and altruism. The studies above provide are similar to our perspective.

Critical thinking is not only one of the basic skills in the 21st Century but also a key ability in reflective learning [ 110 , 111 ]. The process of questioning and reorganizing critical thinking is key to reflective learning. The complex structure of the problem-solving process requires critical thinking skills to find different solutions [ 30 , 112 , 113 , 114 ]. Table  4 higher coverage solutions (C1, C2, C3, NC1, NC2, NC3 in Table  4 ) and Table  7 higher coverage solutions (C1, NC1 in Table  7 ) showed that critical thinking ability training is helpful to improve a subject’s CPS skills. By contrast, a lack of critical thinking training is not conducive to improving CPS skills (NC1, NC2, NC3 in Table  4 ; NC1 in Table  7 ). Critical thinking is widely considered to be a competency closely linked to CPS skills [ 29 ], and our study approves this perspective. Moreover, cooperativity, creativity, and algorithmic thinking also appear in the forward solutions with high coverage (C1, C2, C3 in Table  4 ), combined with the mediating effect of critical thinking on cooperativity, creativity, algorithmic thinking, and the CPS skills. It is logical that the antecedents of critical thinking, such as cooperativity, creativity and algorithmic thinking, also play a positive role in the CPS skills. The result is similar to the findings of Özgenel [ 115 ], who believed that critical thinking and creative thinking affected problem-solving skill through decision-making style. These results suggested that we should pay attention to the cultivation of a critical thinking ability, especially through the cultivation of cooperativity, creativity, and algorithmic thinking, which positively and significantly improve a subject’s ability to solve complex problems.

Empathetic concern relationship with the complex configuration between its antecedent variables provides new ideas and insights to improve our ability to solve complex problems. Empathic concern, as a key factor of prosocial behavior [ 43 ], is also of positive significance to CPS skills in this study. The higher coverage solutions (C1, C2, C3 in Table  4 ; NC1, NC2, NC3 in Table  4 ; C1 in Table  7 ; NC1 in Table  7 ) showed that training in empathic concern is beneficial to improve a subject’s CPS skills, while a lack of empathic concern training is not conducive to improving CPS skills (NC1, NC2 in Table  4 ; NC1 in Table  7 ). By contrast, fantasy (C2, C3 in Table  4 ) and perspective-taking (C1, C3 in Table  4 ) appeared among the forward solutions with higher coverage in Table  4 . Combined with the mediating effect among empathic concern, fantasy, perspective-taking, and the CPS skills, it is not difficult for us to understand that the empathic concern antecedent variable: fantasy, and perspective-taking, also have positive significance for the CPS skills. This result aligns with the research findings of Hashmi [ 57 ] and Davenport [ 66 ]. Moreover, in the absence of empathetic concern, the pathway support of the combination of fantasy, perspective-taking, and personal distress for CPS skills also verified this positive significance from the other side (C3 in Table  4 ). However, personal distress (C1, C2, C3 in Table  4 ) appears independently in the forward solution, with high coverage in Table  4 , which verifies the direct effect of personal distress on the CPS skills, which was consistent with the results of PLSSEM. These further confirmed the theory of Dorner and Funke, who suggested that complex and dynamic non-routine situations across different domains require a collection of self-regulating psychological processes and a creative combination of knowledge and strategies, and is influenced by motivation and emotion, especially in a high-stakes environment[24]. In addition, according to the observation of the reverse solution of Table  4 , the combination of negative perspectivetaking and negative personal distress will be conducive to the low-level CPS skills (NC1, NC2, NC3, NC5 in Table  4 ). Interestingly, fantasy appeared not only in the forward solution with high coverage (C2, C3 in Table  4 ), but also in the inverse solution with high coverage (NC2, NC3 in Table  4 ), which seemed to suggest that the contribution of fantasy to improving CPS skills is neutral, which requires further research.

Consistent with the principle of causal asymmetry, fsQCA suggested that solutions generated by the same attributes in different areas might have the opposite impact on CPS skills, depending on how they combine or interact with other attributes. The lack or negation of some positive factors will lead to improved CPS skills, while the existence of some negative factors might also lead to similar results, depending on how they are configured with the other factors. For example, solution 4 in Table  4 shows that in the absence of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy, a combination of empathetic concern, personal distress, and perspective-taking could also have a positive effect on the improvement of CPS skills. There is a paucity of literature exploring the effects of empathetic concern, personal distress, and perspective-taking on CPS skills under conditions of low levels of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy. These insights provide new ideas for exploring improvements in CPS skills. Although PLS-SEM can verify the predetermined relationship between previous factors and the results of interest, it cannot provide these insights.

In addition, considering the complex nature of problem-solving skill under the condition of reflective learning, it is necessary to check the linear and nonlinear relationships between structures to fully understand the strategies and methods to improve CPS skills. In this study, as an ideal approach, PLS-SEM was used to identify the linear (symmetric) causal relationship between the improvement of CPS skills and influence factors. The fSQCA was used to identify the nonlinear (asymmetric), heterogeneous, and dynamic interactions between antecedents and behavioral results. The fSQCA improved identifying sufficient causal conditions for outcomes. The comprehensive application of PLS-SEM and fsQCA helped capture complex multiple causalities in the improvement of CPS skills, which makes theoretical contributions in terms of analytical techniques.

Practical implications

Aquino believes that the implementation of reflective learning strategies is conducive to the improvement of CPS skills [ 116 ], which is of practical significance for the design of learning strategies and training tools, including reflective learning. The PLS-SEM results showed that perspective-taking, as an important condition for affected CPS skills, not only plays a role through the intermediary effect of empathetic concern, but also directly affects the CPS skills. The researchers and learners can train subjects to think for others in the form of team communication and exchange of views. For the sake of others, it is necessary to think about CPS skills solutions from multiple angles and more comprehensively, by thinking about problems from the standpoint and perspective of others. Therefore, it is necessary to adopt evidence-based strategies for training to improve the CPS skills.

While the fsQCA results confirmed the PLS-SEM results, in turn its complex configuration helps researchers and learners to make more informed decisions about learning methods to improve CPS skills. The derived pathways indicated that there is more than one causal configuration that can improve CPS skills, and how to improve depends on a combination of attributes. For example, our results showed that the high level of critical thinking and its antecedent attributes, combined with the high level of empathic concern, personal distress, and perspective-taking, will lead to improvement of the CPS skills. The lack of critical thinking, cooperativity, algorithmic thinking, creativity, and fantasy, which to some extent emphasizes the utility of empathic concern, personal distress, and perspective-taking (Table  4 solution 4), make it necessary to pay attention to training medical students in empathic concern, personal distress, and perspective-taking using reflective learning. Aligned with our own research, it was acknowledged reflective learning as a potent method to enhance empathy [ 37 ]. Medical reflection should focus on cultivating the ability to speculate on materials and self-views, and at the same time, understand decision-making from the situation of others and feel the emotions of others to trigger empathy. Improvement of CPS skills should not only emphasize the reduction of personal distress, but also should look at the role of personal distress critically. At the same time, it also reminds us that we should fully consider the training situation of the subjects in the design of learning strategies. Critical thinking and its antecedents are regarded as the key solutions in fsQCA, which suggests that we can focus on the reflective learning mode when we train subjects for critical thinking, creativity, cooperativity, and algorithmic thinking. We should also consciously use this kind of thinking to solve problems in the process of reflective learning. In the design of other learning strategies, training in critical thinking ability and its antecedent variables, cooperativity, creativity, and algorithmic thinking, can effectively help subjects to improve their CPS skills.

Based on our understanding of how empathic concern and critical thinking work together to improve the CPS skills, we suggest that real and complex problems in life be taken as examples in the choice of reflective teaching strategies, to involve a series of related skills and characteristics, and fully exercise the two modes of thinking. This is because, in reflective learning, subjects internalize the thinking skills taught by others into their own thinking skills, cultivating the ability to monitor and reflect on the whole problem-solving process, and helping subjects to extract useful strategies, experiences, and patterns into their cognitive structure, thereby improving their CPS skills and accumulating more experience for possible intuitive thinking. This is more suitable for problems based on real-life, which is in line with the medical learning problem-based learning and case-based learning models.

In this study, a hypothetical model of the relationship between the CPS skills and influencing factors (critical thinking, cooperation, creativity, algorithmic thinking, empathic concern, fantasy, perspective-taking, and personal distress) was constructed and validated. The model confirmed the mediating effect of critical thinking and empathic concern on the CPS skills, the direct effect of personal distress, and the direct and indirect effect of perspective-taking on the CPS skills. Besides, fsQCA results provided a variety of configurations that enhanced the improvement of CPS skills. The findings not only enriched the theoretical system of affecting CPS skills, but also provided practical guidance for the development of learning strategies and assessment tools aimed at improving CPS skills.

Limitations and future research

Although this study enriches the theoretical and practical knowledge concerning the relationship between CPS skills and critical thinking, empathic concern, and other variables, it also has some limitations. First, the subjects were beginners in terms of reflective learning under the guidance of teachers, and lack experience in reflective learning, which might affect the accuracy and applicability of variables to some extent. In future research, we will improve these shortcomings, practice reflective learning practices in more subjects, and validate the model in a broader learning strategy, which would be very meaningful. Second, based on the model of this study, it is necessary to enrich the paths and develop a variety of learning and training tools to improve the CPS skills in the future research. The development of assessment tools for factors related to the measurement of CPS skills will facilitate targeted training and realize personalized learning practice guidance.

Data Availability

The data sets used and / or analyzed in this study have not been made public. If there is a reasonable need, they can be obtained from and provided by the corresponding author of this article.

Abbreviations

Complex problem-solving

Organisation for Economic Co-operation and Development

Partial least square structural equation modeling

• Fuzzy set qualitative comparative analysis

Average variance extracted

Variance inflation factor

Interpersonal Reactivity Index

Computational Thinking Scale

Structural equation modeling.

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Acknowledgements

The authors would like to thank the teachers and students who participated (including the teachers and students of Shulan International Medical College, Zhejiang Shuren University, China), and SmartPLS 3.0 and fsQCA 3.1 for their assistance in analysis of data of this process.

This study was funded by the Provincial Industry-University Cooperation Collaborative Education Project (NO.318 [2022] of the Zhejiang Development Reform Society), the Scientific and technological Innovation activity Plan and New Seedling Talent Plan for College students in Zhejiang Province in 2023, the First-class curriculum project of Zhejiang Province of China (NO.195 [2022] of the Zhejiang Education Office Letter, NO.352 [2022] of the Zhejiang Education Office Letter), the First batch of ideological and political demonstration courses of Zhejiang Province of China (NO.47 [2021] of the Zhejiang Education Letter), and the High-level pre-level program of Zhejiang Shuren University in 2019.

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Ying Wang, Ze-Ling Xu, Jia-Yao Lou & Ke-Da Chen

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ZLX and JYL conceived the project with the input of YW and KDC. YW, ZLX, and JYL collected and analyzed the relevant data for this study. YW and ZLX are the main authors of this study. All the authors read and approved the manuscript.

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Wang, Y., Xu, ZL., Lou, JY. et al. Factors influencing the complex problem-solving skills in reflective learning: results from partial least square structural equation modeling and fuzzy set qualitative comparative analysis. BMC Med Educ 23 , 382 (2023). https://doi.org/10.1186/s12909-023-04326-w

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Thinking and Intelligence

Problem Solving

OpenStaxCollege

[latexpage]

Learning Objectives

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

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

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

PROBLEM-SOLVING STRATEGIES

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

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

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

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

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

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

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

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

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

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

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

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

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Review Questions

A specific formula for solving a problem is called ________.

• an algorithm
• a heuristic
• a mental set
• trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

• anchoring bias
• confirmation bias
• representative bias
• availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

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

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

The Factors Surrounding Memory and Focus

Memory is a complicated “blank hard drive” driven by many factors..

Posted July 25, 2020 | Reviewed by Kaja Perina

We tend to think of ourselves as being born with a magnificent and intricate piece of organic hardware we call the brain, along with a massive but blank hard drive that we refer to as memory. What we become is an accumulation and culmination of our continuous learning and life experiences, which are added one by one to memory.

Defining memory

Memory is a complicated “blank hard drive” driven by genetics , life experiences, learned processes, and environmental factors such as diet , medication , sleep, and lifestyle choices.

Working memory is a cognitive system responsible for temporarily holding information available for processing at a moment’s notice. It is our short-term storage drive that must be accessed and actively used. It is part of our executive functioning , which is the cognitive processes that are necessary for the cognitive control of behavior.

Our working memory is critical for activities such as reading, writing, problem-solving, planning, and coherent verbal communication. These skills are called upon regularly in daily life, and their impairment could lead to severe disruption in an individual’s day-to-day functioning.

Long-term memory refers to the storage of information over an extended period. If you can remember something that happened more than just a few moments ago, whether it occurred just hours ago or decades earlier, then it is long-term memory. Long-term memories are often outside of the conscious mind but can be pulled into our working memory when needed. Some of this information is relatively easy to recall, while other memories are much harder to access.

• Declarative memory (explicit memory): Consists of facts and events that can be consciously recalled or "declared.” Declarative memory comprises episodic memory and semantic memory.
• Episodic memory: Memory of specific events, such as your memory of your last birthday party.
• Semantic memory: Memory of information that is presented as a fact, for example, the current President or the capital of the United States.
• Procedural memory: Memory of how to do things that are deeply embedded and are performed without being aware, for example, your memory of how to swim or change a light bulb.
• Muscle memory: Form of procedural memory that involves consolidating a specific motor task into memory through repetition, which has been used synonymously with motor learning.
• Visuospatial memory: The ability to represent, analyze, and mentally manipulate objects.

Focus, attention, and distractibility

The term distractibility refers to the ability to focus on an activity for a concise period. People who are distracted are quick to lose focus as their attention is easily shifted. They become distracted by outside stimuli or even by their internal thoughts. Inattention can be a consequence of distractibility.

Why does this happen? Oftentimes when we hear the terms, “inattentiveness and distractibility” we think of attention-deficient hyperactivity disorder ( ADHD ), a common behavioral disorder that is often diagnosed in children and teenagers .

We live in a sensory overloaded society, and many of us lose focus and attention because we are simply too overwhelmed by our environment and internal thoughts.

Our brains are constantly being bombarded with an array of sensory information from our environment. But there is a limit to how much information, on a moment-by-moment basis, the brain can process effectively.

Attention: The brain’s effort to prioritize the volume of incoming sensory information from the environment . A mechanism by which only the most relevant and important information is focused on, and the rest — the noise — is “ignored.”

It is important to be able to identify factors that steal our focus and to develop skills to improve our concentration , as these can have a positive impact on our memory. In other words, sharpening our focus and attention can improve our memory.

There are many factors that can adversely affect our focus and limit our ability to concentrate, which are all associated with memory impairment:

• Sleep hygiene
• Dehydration
• Physical inactivity
• Sedating antihistamines
• Painkillers
• Anticholinergics

Do you ever feel like you are sleepwalking through life, as if you are going through the motions but are unaware of your thoughts or actions? Individuals with “ brain fog ” often report feeling tired, difficulty focusing, forgetfulness, or hazy thought processes. With brain fog, even simple tasks can become a challenge. Brain fog can create havoc on your concentration, attention, and memory, which can affect your work performance and cause a rift in your social life . The following are factors known to contribute to brain fog:

• Depression /Mental health conditions
• Medical conditions (Lupus, Multiple Sclerosis, Thyroid disorders, Chronic Fatigue Syndrome)
• Medication side effects
• Vitamin deficiencies
• Food sensitivities/diet
• Heavy metal exposure

Is your capacity for memory genetic?

Babies know how to suck without being taught how to do it. This is a kind of procedural memory, and it is clearly genetic. The central, and much more controversial, question is whether episodic and semantic memory can be inherited.

Recently, researchers have identified more than 100 genes related to memory in humans, which have helped build important correlations between gene data and brain activity during memory processing, providing a new window into human memory.

The human genome is comprised of approximately 20,000 genes. all of which may present genetic variants, or alleles. The different nucleotide sequences of these alleles can alter the messages they encode. Just as some people have green eyes while others have brown or blue eyes, or as some are taller than others, individual variations due to genetic influences are neurological and psychological. Psychological traits include those related to cognitive functions such as memory, focus, stress response, social behavior, habits, and mood.

Memories are stored in the brain in the form of neural networks in the cerebral cortex, the brain’s outer layer. The brain deposits specific proteins along the neurons’ synapses that make it more likely for the neurons to communicate in the future. While the proteins are normally deposited as a result of learning, it is possible that some of them could be coded for by an individual's genetics.

So many different factors can influence gene expression. Diet (including your parents' and grandparents' diet), medications, the number of neurotransmitters, chemicals, and even stress can modify our genes, determining which genes are expressed and which genes are turned off, a process known as epigenetics . This can contribute to cognitive aging and may explain why certain people develop neurodegenerative disease and memory loss earlier than do others.

Poor memory can also be caused by a variety of things, not just genetics. The most common sources of poor memory tend to be from very preventable conditions:

• Lack of sleep
• Traumatic brain injuries
• Poor diet/nutritional deficiencies
• Mental health and substance abuse disorders

Kristen Fuller, M.D., is a physician and a clinical mental health writer for Center For Discovery.

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Psychology solving problems

Vol. 53 No. 3 Print version: page 8

A refrain I hear from psychologists is the importance of our field helping the public to better understand and use psychology. This is such a strong sentiment that it emerged as a major priority in APA’s strategic plan. As the association has pursued this goal, we have learned a lot about how we can be more effective at achieving it.

The key is connecting relevant science to the issues the public cares about and sharing this knowledge in digestible ways.

Here are three examples of what has been successful:

Consistently incorporating the human element. Complex problems are frequently framed in ways that omit the human element—human cognition, emotion, and behavior. This not only renders psychology irrelevant in the minds of the public, but it also weakens potential solutions to these challenges. Throughout the pandemic, we have seen the effectiveness of public health strategies wane without consideration of human factors issues, such as what motivates people to engage in healthy behaviors and take risks. Psychology can help leaders and policymakers solve complex problems, but we must ensure that the human element is included from the outset.

Word choice matters. The language we use to describe our work has a direct bearing on its success. For example, how we describe APA’s efforts to address racism impacts whether people see the work as central or extraneous to our mission. Word choice affects how people understand this work—across the country and the political spectrum. When addressing systemic racism is conveyed as not only a social justice issue, but as critical for building more equitable and effective organizations, people are more likely to see the relevance.

Using the lens of others. Effectively explaining complex concepts to solve real-world problems requires viewing them through the lens of others, not just our own. For example, in APA’s conversations with business leaders about fostering psychologically healthy workplaces, we emphasize the positive effects not only on employee well-being, but on the company’s efficiency, productivity, and bottom line.

While some of these strategies may seem obvious, putting them into consistent practice is hard. We must remind ourselves that how we communicate is not only key to advancing APA’s strategic vision, but an effective way to elevate psychology and the impact we want to have.

Arthur C. Evans Jr., PhD , is the chief executive officer of APA. Follow him on Twitter: @ArthurCEvans.

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