Chapter 7: Cognition – Problem Solving, Reasoning, Decision Making, and Intelligence

Chapter 7: Cognition

Outline

• Thinking

• Problem Solving

• Reasoning and Decision Making

• Intelligence

Problem Solving

Problem States

Problem solving is a fundamental cognitive process involving the identification and resolution of obstacles to achieve a desired goal. Problems are defined by their initial and goal states, and the difference between these states creates the need for problem solving.

• Initial State: The situation at the beginning of the problem.

• Goal State: The desired end situation.

• Problem: Exists when the initial state does not match the goal state.

• Rules/Constraints: Limitations on what actions are possible.

• Obstacles: Factors that must be overcome to reach the goal.

Steps in Problem Solving

Effective problem solving typically involves several steps, each requiring different cognitive strategies.

1. Identify the Problem (and States):

   • Define the goal clearly (e.g., Solve $27 \times 21$).

   • Many problems are vague or ill-defined (e.g., "I want to get an A in this class," "I want world peace").

2. Develop/Use Strategy:

   • Subgoals (Means-Ends Analysis): Break the problem into smaller, intermediate goals. Example: To solve $27 \times 21$, break it into $27 \times 1$ and $27 \times 20$.

   • Working Backwards: Start from the goal state and work in reverse to the initial state. Useful for complex problems.

   • Algorithm: A step-by-step strategy that guarantees a solution. Example: Trying every possible letter combination to solve a puzzle. Disadvantage: Often slow and not always practical for complex problems.

   • Heuristic: A shortcut or rule of thumb that suggests a solution but does not guarantee correctness. Example: Using common letter combinations like "ing" in word puzzles. Disadvantage: May not always lead to the correct solution.

3. Evaluate Solution:

   • Assess whether the solution is correct. This can be subjective, especially for open-ended problems (e.g., writing the "perfect" essay).

4. Rethink Problem/Solution:

   • Reflect on the efficiency and effectiveness of the solution. Consider alternative strategies or mindsets if necessary.

Classic Problem Solving Example: Duncker's Candle Problem

The Duncker's candle problem is a well-known test of creative problem solving and overcoming functional fixedness.

• Task: Use the provided objects (candle, box of tacks, matches) to attach the candle to the wall and light it, without burning the wall or dripping wax on the table.

• Solution: Use the box as a candle holder, tack it to the wall, and place the candle inside.

• Functional Fixedness: The tendency to see objects as only serving their typical function (e.g., seeing the box only as a container for tacks).

Other Problem Solving Challenges

• Matchstick Problem: Arrange six matches to form four equilateral triangles, each side one match in length. Additional info: This requires thinking in three dimensions (forming a tetrahedron).

• 9-Dot Problem: Draw through all nine dots with only four straight lines without lifting your pencil. Additional info: This requires "thinking outside the box" and breaking mental constraints.

Obstacles to Problem Solving

• Fixation: Relying on a single strategy or approach, even when it is ineffective.

• Functional Fixedness: Seeing objects as only serving their usual function, which can hinder creative solutions.

• Overcoming Functional Fixedness: Using objects in novel ways (e.g., using a shoe as a paperweight, a shovel as a hammer).

Reasoning and Decision Making

Types of Reasoning

Reasoning is the process of transforming information to reach conclusions. There are two main types:

• Inductive Reasoning: Drawing general conclusions from specific observations. Example: "I ate a peanut, now my face is swollen. Therefore, I am allergic to peanuts." Used in the scientific method: Interpret data to hypothesize how a process works. Science can support or disprove hypotheses, but cannot prove them correct.

• Deductive Reasoning: Drawing specific conclusions from general premises. Example: "All college students like pizza. Tim is a college student. Therefore, Tim likes pizza." Validity: Does the conclusion logically follow from the premises? Soundness: Are the premises true?

Decision Making

Decision making involves evaluating alternatives and choosing among them, often under conditions of uncertainty.

• Use of Reasoning: Compare alternatives to make choices (e.g., picking a register line, choosing a major).

• Example: Register 1 has 1 person with a full cart; Register 2 has 3 people with 2-5 items each. Decision involves weighing speed and convenience.

Biases and Heuristics in Decision Making

• Loss Aversion: The tendency to prefer avoiding losses over acquiring equivalent gains. Example: Unwillingness to change majors when close to graduation.

• Confirmation Bias: The tendency to seek information that supports one's beliefs and ignore contradictory evidence. Example: Political debates where supporters believe their candidate won regardless of evidence.

• Hindsight Bias: The tendency to believe, after an event has occurred, that one predicted or expected the outcome all along. Example: After a sports tournament, people overestimate their original prediction of the winner.

• Availability Heuristic: Judging the likelihood of events based on how easily examples come to mind. Example: Fear of flying due to news coverage of plane crashes, despite driving being statistically riskier.

• Representativeness Heuristic: Judging the probability of an event based on how much it matches a prototype or stereotype. Example: Assuming a random sequence of coin tosses should "look" random.

Intelligence

Definition and Measurement

Intelligence is the ability to acquire and apply knowledge and skills. It is often considered a general ability ("g"), but definitions vary across cultures.

• IQ (Intelligence Quotient): A measure of intelligence based on standardized tests.

• Formula: $IQ = 100 \times \frac{\text{mental age}}{\text{actual age}}$

• Mental Age: Level of mental development as measured by test performance.

• Actual Age: Chronological age of the individual.

• Example Calculations:

  • Mental age = 7, Actual age = 6: $IQ = 117$

  • Mental age = 7, Actual age = 7: $IQ = 100$

  • Mental age = 7, Actual age = 8: $IQ = 88$

• After age 15, IQ is calculated by comparing scores to the population distribution.

IQ Score Distribution

IQ scores are distributed across the population, with most people scoring near the average and fewer people at the extremes.

IQ Range	Percentage of Population
Below 70	~2%
70-130	~96%
Above 130	~2%

Nature vs. Nurture in Intelligence

• Nature: Biological factors, such as genetics, contribute to intelligence. Twin studies suggest 50-75% of intelligence is heritable.

• Nurture: Environmental factors, such as education, nutrition, and upbringing, also influence intelligence. Improvements in these areas can increase IQ.

• Flynn Effect: The observed rise in average IQ scores over time, suggesting environmental factors play a significant role. Example: In 1997, the average person would have scored 120 on the 1932 IQ test.

Individual Differences in IQ

• Cultural Bias: IQ tests may disadvantage individuals from certain backgrounds (e.g., low SES, non-white, rural).

• Giftedness: Very high intelligence (IQ above 130). Educational policies may not always support gifted students.

• Intellectual Disability: Very low intelligence (IQ below 70). Formerly referred to as "mental retardation." Individuals may have variable skills and abilities.

Theories of Multiple Intelligences

• Sternberg's Triarchic Theory:

  • Analytical Intelligence: Judge, evaluate, compare, contrast.

  • Creative Intelligence: Create, design, invent, imagine.

  • Practical Intelligence: Apply and implement ideas.

• Gardner's Multiple Intelligences:

  • Verbal

  • Mathematical

  • Spatial

  • Body-kinesthetic

  • Musical

  • Interpersonal

  • Intrapersonal

  • Naturalist

  • Existentialist

Review Questions (Selected)

• Which of the following is NOT a step in problem solving? Answer: Algorithm (it is a strategy, not a step).

• A strategy that provides a shortcut to the solution but does not guarantee the correct answer is a(n) heuristic.

• Sally uses her phone to take a picture of her license when her copier fails, demonstrating overcoming functional fixedness.

• "All tall people play basketball. Jim is a tall person. Conclusion: Jim plays basketball." Answer: Valid but not sound (premise may not be true).

• Loss aversion: Hank is unwilling to gamble his paycheck even though the expected value is higher.

• Sarah concludes apples fall due to gravity after repeated observation: Inductive reasoning.

• Frank fears flying due to news of crashes, but not driving: Availability heuristic.

• Fran ignores opposing arguments after a debate: Confirmation bias.

• IQ scores have increased over time: Flynn effect, supporting an environmental component of IQ.