Problem Solving in Psychology

PROBLEM SOLVING PSY 311

WHAT IS A PROBLEM?

  • Definition: An obstacle between a present state and a goal state.

    • Types of problems:

    • Insight Problems: Characterized by sudden realization of solution.

      • Example:

      • Pine, Crab, Sauce

    • Non-Insight Problems: Require steady work towards a solution.

      • Example:

      • Algebra: Given the expression ( rac{1}{3}x^2 + 7x - 16 = 6)

INSIGHT IN PROBLEM-SOLVING

  • Referenced Study: Metcalfe and Wiebe (1987)

    • Types of problems examined:

    • Insight Problems:

      • Examples: Triangle problem, Chain problem

      • Warmth Judgments: Taken every 15 seconds on a scale from 1 to 7.

    • Triangle Problem:

    • Task: Make the triangle face downwards with up to 3 dot movements.

EXAMPLES OF INSIGHT PROBLEMS

  • Chain Problem:

    • Scenario: A woman has 4 pieces of chain, each made up of 3 links.

    • Goal: Join these pieces into a single closed loop.

    • Costs:

    • Open a link: 2 cents

    • Close a link: 3 cents

    • Budget: 15 cents

ORGANIZATION OF PROBLEMS

  • Type: Mostly well-defined problems found in intelligence tests.

  • Major Types of Problems:

    • Arrangement:

    • Inducing Structure:

    • Transformation:

ARRANGEMENT PROBLEMS

  • Definition: Requires rearrangement of elements of the problem.

    • Example: Anagrams:

    • THO → TOMIV

    • LOVEN → YKSE

    • AWEHL

SKILLS IN ARRANGEMENT PROBLEMS

  • Fluency in generating possibilities: Ability to generate possible solutions and discard unpromising ones.

  • Retrieval of solution patterns: Ability to match possible solutions with known patterns in long-term memory (LTM).

  • Knowledge that constrains search: Understanding which patterns are feasible within the context of the problem.

  • Example of Anagrams:

    • Given Letters: ZUQRAT

    • Possible Solutions: QUARTZ, TAUMER

    • Concept:

    • ZUQRAT has a smaller problem space than TAUMER despite both having 720 potential arrangements (calculated as 6! = 720).

    • Reason: The arrangement constraints of English yield fewer promising combinations for ZUQRAT (e.g., "Q" precedes "U").

"AREA" OF THE PROBLEM

  • Problem Space: All possible steps or states of the problem as defined by the problem.

  • Search Space: Possible steps or states of the problem that the solver examines.

MATCHSTICK PROBLEM EXAMPLE

  • Task: Move one matchstick to create a true arithmetic statement.

    • Constraint: The stick cannot be discarded.

OBSTACLES TO PROBLEM-SOLVING

  • Functional Fixedness: The limitation of using an object only for its familiar functions.

    • Example:

    • Candle Problem: Misuse of boxes as supports inhibits innovative solutions.

    • Two-String Problem: The typical use of pliers obstructs creative thinking.

      • Solution: Simply brushing the strings to get them in motion can facilitate problem-solving.

INDUCING STRUCTURE

  • Definition: Finding a pattern among a fixed set of relations.

    • Examples:

    • Series Extrapolation:

      • Sequence: 1, 2, 8, 3, 4, 6, 5, 6, ext{ ? }

    • Raven Progressive Matrices: Tasks that require visual pattern recognition.

    • Analogy Problems:

      • Example:

      • Sugar : Sweet :: Lemon : (Options: Yellow, Sour, Fruit, Squeeze)

DUNCKER’S RADIATION PROBLEM

  • Importance of analogies in problem-solving:

    • Only 10% of individuals could solve the radiation problem outright.

    • When exposed to the Fortress Story, 30% succeeded in solving.

  • Surface Features vs. Structural Features:

    • The superficial details can mislead, but abstract structural features must be utilized in problem-solving.

    • Hints may be necessary to reveal connections.

    • When explicitly directed to contemplate the story, success rates rose to 75%.

TRANSFORMATION PROBLEMS

  • Definition: Problems where the solver transitions from an initial state to a goal state through defined operations.

  • Operators: Rules that outline permissible moves.

    • Example Problems:

    • Tower of Hanoi

    • Orc and Hobbits Problem

    • Luchin’s Water-Jug Problem

MEANS-END ANALYSIS

  • Strategy: Reduce the difference between the initial and goal states through subgoals.

  • Visual: Initial steps in solving the Tower of Hanoi problem can be broken down into manageable subgoals.

MENTAL SET

  • Definition: The tendency to approach problems in a particular way based on prior experiences.

    • Example: Inexperienced users may have a habitual approach when using computers.

MUTILATED-CHECKERBOARD PROBLEM

  • Importance of problem presentation:

    • The description greatly influences how solvable the problem appears to be.

    • Providing relevant information aids in reaching the solution successfully.

FOUR CONDITIONS OF THE MUTILATED-CHECKERBOARD PROBLEM

  • Visual Representation:

    • Variations show either blank squares or colored squares (black & pink) and different relationships with bread and butter.

PROBLEM SOLVING STRATEGIES

  • Algorithms: Precise rules that, if followed, guarantee a solution to a problem.

  • Heuristics: Short-cut strategies that often work but are not guaranteed to be successful.

  • Example of Algorithm in a Maze:

    • Start by touching one wall and follow it until reaching the maze's end; effective for simple mazes but may not succeed in all cases.

  • Anagram Analysis:

    • Example: TCRA — 720 total combinations found systematically.

    • Example: For ZUQRAT, only 6 are promising due to letter patterns in English.

FINAL NOTES ON PROBLEM-SOLVING

  • Most discussed problems are well-defined; future discussions will address ill-defined problems and creativity in problem-solving.