Problem Solving

Problem solving: overcoming some obstacles in order to answer a question or achieve a goal
Four phases
- Understanding
- Generating hypotheses
- Testing hypotheses
- Checking results

Strategies
- Used in the generating hypotheses stage
- Algorithm
Algorithm: a mechanical repetitive procedure for solving a problem
- Guarantee a correct solution to the problem
- Heuristics
Heuristics: strategies for solving a problem or for guiding an investigation
- Narrow the range of options we have to consider when trying to solve a problem

Types of Problems
- Inducing Structure
- Try and discover relations among parts of the problem
- Transformation
- Involve carrying out a sequence of transformations in order to reach a specific goal
- Problems of arrangement
- Involve arranging the parts of the problem in such a way that it satisfies some criterion
- Often solved with a burst of insight
Insight: the sudden discovery of the correct solution following incorrect attempts based primarily on trial and error
- Insight Problems
- Problem solution suddenly enters our mind
- Immediately realize the solution to the problem is correct
- Occurs suddenly
- Novel approach to the problem has been taken
- Novel interpretation of the problem has been made
- Non-insight problem
- Solve gradually
- Using reasoning skills and a routine set of procedures
- Metcalf & Wiebe (1987)
- Insight problems
- Algebra problems
- “Warmth” ratings
- Results
- Algebra problems
- Warmth ratings gradually grew until solution
- Insight problems
- No increase in warmth ratings until the person solved the problem in a flash of insight

Barriers to Problem Solving
- Involve assumptions affecting problem solving
Fixation: an impediment to problem solving
- Perceptual fixation
- Involves perceptual (visual/spatial) assumptions about the problem domain that blocks ability to reach a solution
- Mental Set
- Get stuck on a set of rules to solve the problem
- Use them even when the set of rules will prevent the solution or there is an easier solution
- Functional Fixation
- Getting stuck on a particular use for an object