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Psychology

7.3 Problem Solving

Psychology7.3 Problem Solving
  1. Preface
  2. 1 Introduction to Psychology
    1. Introduction
    2. 1.1 What Is Psychology?
    3. 1.2 History of Psychology
    4. 1.3 Contemporary Psychology
    5. 1.4 Careers in Psychology
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  3. 2 Psychological Research
    1. Introduction
    2. 2.1 Why Is Research Important?
    3. 2.2 Approaches to Research
    4. 2.3 Analyzing Findings
    5. 2.4 Ethics
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  4. 3 Biopsychology
    1. Introduction
    2. 3.1 Human Genetics
    3. 3.2 Cells of the Nervous System
    4. 3.3 Parts of the Nervous System
    5. 3.4 The Brain and Spinal Cord
    6. 3.5 The Endocrine System
    7. Key Terms
    8. Summary
    9. Review Questions
    10. Critical Thinking Questions
    11. Personal Application Questions
  5. 4 States of Consciousness
    1. Introduction
    2. 4.1 What Is Consciousness?
    3. 4.2 Sleep and Why We Sleep
    4. 4.3 Stages of Sleep
    5. 4.4 Sleep Problems and Disorders
    6. 4.5 Substance Use and Abuse
    7. 4.6 Other States of Consciousness
    8. Key Terms
    9. Summary
    10. Review Questions
    11. Critical Thinking Questions
    12. Personal Application Questions
  6. 5 Sensation and Perception
    1. Introduction
    2. 5.1 Sensation versus Perception
    3. 5.2 Waves and Wavelengths
    4. 5.3 Vision
    5. 5.4 Hearing
    6. 5.5 The Other Senses
    7. 5.6 Gestalt Principles of Perception
    8. Key Terms
    9. Summary
    10. Review Questions
    11. Critical Thinking Questions
    12. Personal Application Questions
  7. 6 Learning
    1. Introduction
    2. 6.1 What Is Learning?
    3. 6.2 Classical Conditioning
    4. 6.3 Operant Conditioning
    5. 6.4 Observational Learning (Modeling)
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  8. 7 Thinking and Intelligence
    1. Introduction
    2. 7.1 What Is Cognition?
    3. 7.2 Language
    4. 7.3 Problem Solving
    5. 7.4 What Are Intelligence and Creativity?
    6. 7.5 Measures of Intelligence
    7. 7.6 The Source of Intelligence
    8. Key Terms
    9. Summary
    10. Review Questions
    11. Critical Thinking Questions
    12. Personal Application Questions
  9. 8 Memory
    1. Introduction
    2. 8.1 How Memory Functions
    3. 8.2 Parts of the Brain Involved with Memory
    4. 8.3 Problems with Memory
    5. 8.4 Ways to Enhance Memory
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  10. 9 Lifespan Development
    1. Introduction
    2. 9.1 What Is Lifespan Development?
    3. 9.2 Lifespan Theories
    4. 9.3 Stages of Development
    5. 9.4 Death and Dying
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  11. 10 Emotion and Motivation
    1. Introduction
    2. 10.1 Motivation
    3. 10.2 Hunger and Eating
    4. 10.3 Sexual Behavior
    5. 10.4 Emotion
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  12. 11 Personality
    1. Introduction
    2. 11.1 What Is Personality?
    3. 11.2 Freud and the Psychodynamic Perspective
    4. 11.3 Neo-Freudians: Adler, Erikson, Jung, and Horney
    5. 11.4 Learning Approaches
    6. 11.5 Humanistic Approaches
    7. 11.6 Biological Approaches
    8. 11.7 Trait Theorists
    9. 11.8 Cultural Understandings of Personality
    10. 11.9 Personality Assessment
    11. Key Terms
    12. Summary
    13. Review Questions
    14. Critical Thinking Questions
    15. Personal Application Questions
  13. 12 Social Psychology
    1. Introduction
    2. 12.1 What Is Social Psychology?
    3. 12.2 Self-presentation
    4. 12.3 Attitudes and Persuasion
    5. 12.4 Conformity, Compliance, and Obedience
    6. 12.5 Prejudice and Discrimination
    7. 12.6 Aggression
    8. 12.7 Prosocial Behavior
    9. Key Terms
    10. Summary
    11. Review Questions
    12. Critical Thinking Questions
    13. Personal Application Questions
  14. 13 Industrial-Organizational Psychology
    1. Introduction
    2. 13.1 What Is Industrial and Organizational Psychology?
    3. 13.2 Industrial Psychology: Selecting and Evaluating Employees
    4. 13.3 Organizational Psychology: The Social Dimension of Work
    5. 13.4 Human Factors Psychology and Workplace Design
    6. Key Terms
    7. Summary
    8. Review Questions
    9. Critical Thinking Questions
    10. Personal Application Questions
  15. 14 Stress, Lifestyle, and Health
    1. Introduction
    2. 14.1 What Is Stress?
    3. 14.2 Stressors
    4. 14.3 Stress and Illness
    5. 14.4 Regulation of Stress
    6. 14.5 The Pursuit of Happiness
    7. Key Terms
    8. Summary
    9. Review Questions
    10. Critical Thinking Questions
    11. Personal Application Questions
  16. 15 Psychological Disorders
    1. Introduction
    2. 15.1 What Are Psychological Disorders?
    3. 15.2 Diagnosing and Classifying Psychological Disorders
    4. 15.3 Perspectives on Psychological Disorders
    5. 15.4 Anxiety Disorders
    6. 15.5 Obsessive-Compulsive and Related Disorders
    7. 15.6 Posttraumatic Stress Disorder
    8. 15.7 Mood Disorders
    9. 15.8 Schizophrenia
    10. 15.9 Dissociative Disorders
    11. 15.10 Personality Disorders
    12. 15.11 Disorders in Childhood
    13. Key Terms
    14. Summary
    15. Review Questions
    16. Critical Thinking Questions
    17. Personal Application Questions
  17. 16 Therapy and Treatment
    1. Introduction
    2. 16.1 Mental Health Treatment: Past and Present
    3. 16.2 Types of Treatment
    4. 16.3 Treatment Modalities
    5. 16.4 Substance-Related and Addictive Disorders: A Special Case
    6. 16.5 The Sociocultural Model and Therapy Utilization
    7. Key Terms
    8. Summary
    9. Review Questions
    10. Critical Thinking Questions
    11. Personal Application Questions
  18. References
  19. Index

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 (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.

Method Description Example
Trial and error Continue trying different solutions until problem is solved Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm Step-by-step problem-solving formula Instruction manual for installing new software on your computer
Heuristic General problem-solving framework Working backwards; breaking a task into steps
Table 7.2 Problem-Solving Strategies

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.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.
Figure 7.8 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 7.9) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.
Figure 7.9 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 7.10). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”
Figure 7.10 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 Table 7.3.

Bias Description
Anchoring Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation Focuses on information that confirms existing beliefs
Hindsight Belief that the event just experienced was predictable
Representative Unintentional stereotyping of someone or something
Availability Decision is based upon either an available precedent or an example that may be faulty
Table 7.3 Summary of Decision Biases

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).

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1:  blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.
Figure 7.11
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