W1 Problem Solving

Overview of Learning Outcomes

1.  Identify and explain Wessell’s four stages of problem solving and the role of insight and problem definition.

2.  Describe the role of mental representations and give examples of functional fixedness and strategies for reducing it.

3.  Explain heuristic and algorithmic strategies in problem solving, with examples.

4.  Define generate-test heuristic, difference-reduction heuristic, subgoal generation strategy, and incubation strategy, and their use in problem solving.

 What is Problem Solving?

• Defined as constructing and applying mental representations of issues to find solutions (Jonassen & Hung, 2011).

• A problem is defined as a discrepancy between the current state and a desired goal state, illustrated by various examples such as:

  • Caffeine withdrawal.

  • Solving anagrams like 'STBOUTOHRH'.

  • Global income inequality.

• A solution represents an action transforming the current state to the goal state.

• Simple reflex questions are not problem solving because they don’t involve the construction or application of mental representations

 Wessell's Four Stages of Problem Solving

1. Define the problem: Identify the goal state, current state, and actions available.

2. Devise a strategy: Select actions expected to move the current state towards the goal state.

3. Execute the strategy: Implement the chosen action(s).

4. Evaluate progress: Measure changes between goal state and current state.

Difficulty of Problems

• The greater the distance between goal state and current state, the more complex the problem.

• Example: Some anagrams are harder to solve than others because of the number of actions required.

• There’s a greater ease in problem-solving when fewer possible actions exist.

Solvability of Problems

• For a problem to be solvable, a sequence of actions must transform the current state into the goal state.

• Examples illustrate different problems' solvability.

Problem Definition

Well-defined Problems

• Characteristics include a clear current state, goal state, and available actions.

• Example: Solving a simple anagram or following a recipe.

Ill-defined Problems

• Lacks clear information on some aspects leading to ambiguity.

• Examples include vague directives such as "manage the economy" or "live a good life."

 Insight in Problem Solving

• Insight occurs suddenly during problem-solving, typically not through conscious stages.

• Examples of insight problems include lateral thinking puzzles and crosswords.

Problem Solving in Non-Human Animals

• Non-human animals exhibit problem-solving behaviours, although not all intelligent actions are problem-solving (e.g., Ajax the dog).

• Examples include Sultan the chimpanzee and New Caledonian crows using tools.

 Mental representation

• A mental representation is the way that our beliefs, knowledge, and memories are stored within our minds

• A mental representation of a problem in our knowledge about its different components  (starting state, goal state, available actions)

• They can be wrong and inaccurate; solving a problem often depends on finding the appropriate mental representation of that problem

 Functional Fixedness

• Defined as a mental block against using an object in a new way essential for solving a problem. (cognitive bias)

• It may hinder creative thinking and problem-solving ability.

Reducing Functional Fixedness

• Training in object usage and assigning nonsensical labels may help reduce fixedness.

• Listing alternative uses for objects can also encourage creative problem-solving.

Devising and Executing a Strategy

• A nuanced strategy is crucial for bridging the gap between current and goal states.

• Selection of strategy might appear straightforward but is complex with various possible actions.

 Heuristics vs. Algorithm strategies

• Algorithms: Step-by-step procedures that guarantee a solution; only applicable to specific problems.

• Heuristics: Shortcuts that are fast and easy but do not guarantee a solution; developed from experience.

Generate-Test Heuristic

• Involves generating solutions repeatedly to test if they work; effective when the solution space is small.

• Highlighted example involving anagrams demonstrates its application.

Difference Reduction Heuristic

• Action that yields the most reduction in the difference between current and goal state.

• Application can sometimes lead us to overlook necessary backtracking or sideways movement.

 Subgoal Generation

• Breaking a larger problem into smaller, manageable subgoals can enhance problem-solving efficacy.

 Means-End Analysis

• Identifies various ends and considers means to achieve each, a method guided by subgoals.

• The General Problem Solver of Newell & Simon (1972) is a theory of human problem solving that breaks problems down into subgoals uses the difference reduction heuristic to solve each subgoal

 Incubation

• Taking breaks can facilitate problem-solving breakthroughs, allowing the unconscious to work on issues away from focused attention.

Overview of Learning Outcomes

1.  Identify and explain Wessell’s four stages of problem solving and the role of insight and problem definition.

2.  Describe the role of mental representations and give examples of functional fixedness and strategies for reducing it.

3.  Explain heuristic and algorithmic strategies in problem solving, with examples.

4.  Define generate-test heuristic, difference-reduction heuristic, subgoal generation strategy, and incubation strategy, and their use in problem solving.

 What is Problem Solving?

• Defined as constructing and applying mental representations of issues to find solutions (Jonassen & Hung, 2011).

• A problem is defined as a discrepancy between the current state and a desired goal state, illustrated by various examples such as:

  • Caffeine withdrawal.

  • Solving anagrams like 'STBOUTOHRH'.

  • Global income inequality.

• A solution represents an action transforming the current state to the goal state.

• Simple reflex questions are not problem solving because they don’t involve the construction or application of mental representations

 Wessell's Four Stages of Problem Solving

1. Define the problem: Identify the goal state, current state, and actions available.

2. Devise a strategy: Select actions expected to move the current state towards the goal state.

3. Execute the strategy: Implement the chosen action(s).

4. Evaluate progress: Measure changes between goal state and current state.

Difficulty of Problems

• The greater the distance between goal state and current state, the more complex the problem.

• Example: Some anagrams are harder to solve than others because of the number of actions required.

• There’s a greater ease in problem-solving when fewer possible actions exist.

Solvability of Problems

• For a problem to be solvable, a sequence of actions must transform the current state into the goal state.

• Examples illustrate different problems' solvability.

Problem Definition

Well-defined Problems

• Characteristics include a clear current state, goal state, and available actions.

• Example: Solving a simple anagram or following a recipe.

Ill-defined Problems

• Lacks clear information on some aspects leading to ambiguity.

• Examples include vague directives such as "manage the economy" or "live a good life."

 Insight in Problem Solving

• Insight occurs suddenly during problem-solving, typically not through conscious stages.

• Examples of insight problems include lateral thinking puzzles and crosswords.

Problem Solving in Non-Human Animals

• Non-human animals exhibit problem-solving behaviours, although not all intelligent actions are problem-solving (e.g., Ajax the dog).

• Examples include Sultan the chimpanzee and New Caledonian crows using tools.

 Mental representation

• A mental representation is the way that our beliefs, knowledge, and memories are stored within our minds

• A mental representation of a problem in our knowledge about its different components  (starting state, goal state, available actions)

• They can be wrong and inaccurate; solving a problem often depends on finding the appropriate mental representation of that problem

 Functional Fixedness

• Defined as a mental block against using an object in a new way essential for solving a problem. (cognitive bias)

• It may hinder creative thinking and problem-solving ability.

Reducing Functional Fixedness

• Training in object usage and assigning nonsensical labels may help reduce fixedness.

• Listing alternative uses for objects can also encourage creative problem-solving.

Devising and Executing a Strategy

• A nuanced strategy is crucial for bridging the gap between current and goal states.

• Selection of strategy might appear straightforward but is complex with various possible actions.

 Heuristics vs. Algorithm strategies

• Algorithms: Step-by-step procedures that guarantee a solution; only applicable to specific problems.

• Heuristics: Shortcuts that are fast and easy but do not guarantee a solution; developed from experience.

Generate-Test Heuristic

• Involves generating solutions repeatedly to test if they work; effective when the solution space is small.

• Highlighted example involving anagrams demonstrates its application.

Difference Reduction Heuristic

• Action that yields the most reduction in the difference between current and goal state.

• Application can sometimes lead us to overlook necessary backtracking or sideways movement.

 Subgoal Generation

• Breaking a larger problem into smaller, manageable subgoals can enhance problem-solving efficacy.

 Means-End Analysis

• Identifies various ends and considers means to achieve each, a method guided by subgoals.

• The General Problem Solver of Newell & Simon (1972) is a theory of human problem solving that breaks problems down into subgoals uses the difference reduction heuristic to solve each subgoal

 Incubation

• Taking breaks can facilitate problem-solving breakthroughs, allowing the unconscious to work on issues away from focused attention.