Problem Solving and Creativity

Overview: The problem-solving cycle consists of a step-by-step approach that helps in effectively tackling problems.
- Steps include:
- Problem identification
- Problem definition and representation
- Constructing a strategy
- Monitoring and evaluation

Problem Identification
- Assess whether a problem truly exists.
Definition of Problem
- Understand what the problem is and how it is represented.
Constructing a Strategy
- Choose methods to address the problem (analysis vs synthesis).
- Analysis involves breaking down complex issues into manageable parts.
- Synthesis involves combining various elements to form a functional solution.
Generating Solutions
- Divergent Thinking: Producing multiple potential solutions.
- Convergent Thinking: Narrowing down options to find the best solution.
Organization of Information
- Understand how the different components of the problem interconnect.
Resource Allocation
- Determine the necessary time, effort, and money for solving the problem.
Monitoring and Evaluation
- Assess the effectiveness of the chosen solution.

Divergent Thinking:
- Produces multiple, varied solutions to a problem.
- Encourages exploration of many possibilities (e.g., brainstorming).
Convergent Thinking:
- Narrowing down options to find the best or most fitting solution.
- Focuses on finding a single correct answer.

Well-structured problems:
- Clear path to solution (e.g., math problems, specific puzzles).
Ill-structured problems:
- Lack clear definitions and parameters; often require subjective interpretation.
- Poorly defined dimensions, requiring interpretative work (e.g., finding an apartment).

Hobbits and Orcs Dilemma:
- Three hobbits and three orcs must cross a river without being outnumbered by the orcs. The task involves logistics of crossing.

Problem Space: All possible actions that can be taken.
- Consists of states (current situations) and operators (possible moves).

This concept involves using a known solution to a similar problem to solve a new problem.
Key findings from Gick & Holyoak's research illustrate that people can not only transfer learned solutions across different contexts but also struggle to see the parallels if they are not explicitly drawn.
Example: The analogy of a battle strategy to decipher a route through a maze.This highlights the importance of training individuals to recognize and articulate these analogies, as doing so can enhance their ability to tackle complex problems effectively.

Approaches to Problem Solving

Algorithms: Systematic procedures guaranteed to find a solution (structured).
Heuristics: Rules of thumb that are efficient but do not guarantee a correct solution.

Means-end Analysis:
- Break down problems into subgoals and prioritize actions to bridge the gap from the current state to the goal state.
Working Forward:
- Solve starting from the initial state toward the goal state.
Working Backward:
- Beginning at the goal and determining the necessary prior steps.
Generate and Test:
- Trial and error strategy for testing multiple solutions until successful.

Problems that have the same formal structure but differ in content, making them harder to detect in similarity.

Key States: Initial State, Intermediate States, Goal State.
Means-end Analysis: Focus on reducing the difference between initial state and goal state through strategic moves and subgoals.

Insight Problems: Characterized by a sudden realization leading to a solution.
Non-insight Problems: Typically involve systematic analysis and structured approaches without the element of sudden comprehension.

Sudden realization leads to a solution, often some time after reframing the approach.
Research indicates different neural activations (e.g., right hippocampus) during insight-based problem solving.

Mental Set: Fixed perspective that can hinder problem-solving efforts.
Functional Fixedness: Inability to see new uses for an object, such as shown in Duncker’s candle problem scenario.

A mental set refers to a tendency to approach a problem in a way that has worked in the past.
This can hinder problem-solving by limiting the ability to see new solutions or possibilities.
Example: In using a particular strategy for math operations, a student may continue to apply this strategy even when it is no longer effective.

A theoretical construct designed to simulate human problem-solving behavior.
Initiates strategies for solving problems by testing various approaches and adapting according to feedback.

Intermediate goals that help break down a complex problem into smaller, manageable parts.
Setting subgoals can provide motivation and a clearer direction towards achieving the overall goal.

Negative Transfer: Previous problem-solving experience complicates new problem-solving.
Positive Transfer: Previous experience aids in solving new problems.

Experts have organized knowledge and experience that allows for quick problem resolution.
They approach problems based on structural features rather than surface details, but are less flexible in adapting to new problems outside their expertise.

Techniques include: breaking mental sets, restating problems, providing incubation time, and challenging assumptions.

Stages: Preparation, Incubation, and Verification (as outlined by Basadur et al.).