Problem Solving

Question 1

What is Problem Solving?

Answer 1

Eysenck & Keane (2020)
- Purposeful (goal-directed)
- Involves cognitive processes
- Only exists when someone lacks the relevant knowledge to produce an immediate solution

Question 2

What is the Two-string problem (Maier, 1931)

Answer 2

• Task is to tie one string to the other
• Cannot reach one string while holding the other
• Room contains objects such as poles, pliers, and extension cords

Question 3

Insight problems vs Non-insight problems

Answer 3

Insight problems
- Solution requires a one-off insight
- E.g., two-string problem

Non-insight problems
- Require incremental and sequential problem solving
- E.g., tower of Hanoi, algebra

Question 4

What is the Matchstick problem?

Answer 4

Knoblich et al. (2001)
You have to arrange six matches to form four equilateral triangles
- The goal is to correct the arithmetic statement by moving a single matchstick from one position in the statement to another

The matchstick problem of Knoblich et al. (2001) is difficult because in our experience of maths we are more used to changing numbers than operators

Question 5

THEORY: Representational Change Theory Ohlsson (1992)

Answer 5

• Insight problems permit several mental representations
• Current representation is used to search memory for relevant information
• A block occurs when the problem representation is appropriate

The block can be passed by changing the representation
This can occur in 3 ways:
- Elaboration: new information (e.g., hint)
- Constraint relaxation: extend ideas of what actions are possible
- Re-encoding (e.g., pliers can act as a weight

Insight often follows the formation of a correct representation

Question 6

The Mutilated Chessboard problem

Answer 6

Given an 8 x 8 mutilated board, could we cover all the board with 31 pieces of 2 x 1 tile?

An intact board can be covered by 32 tiles. Can the remaining 62 squares on the board be filled by 31 tiles?

Kaplan & Simon (1990)
Participants thought aloud whilst solving the problem
Most mentally covered the board
Each domino covers one white and one black square (re-encoding)
The board has lost two white squares (re-encoding/elaboration)
So, 31 dominos cannot cover the board
The General Problem Solver (Newell & Simon, 1972)

• A computer program created in 1972 intended to work as a universal problem solver machine
• Problems represented in ‘problem space’
• Problem-solving involves a range of different knowledge states between initial state and goal state

Question 7

Tower of Hanoi problem (Lucas, 1883)

Answer 7

• the number of moves of disk number k is 2^(k-1), and the total number of moves required to solve the puzzle with N disks is 2^N - 1.

The initial state is the state the agent begins in. A goal state is a state where the agent may end the search. An agent may take different actions that will lead the agent to new states.

Newell & Simon (1972)

• In complex problems, operators are chosen using heuristics
• Means-ends analysis
• Hill climbing
• These approaches were based on participants thinking aloud during problem solving

Question 8

Candle Problem (Duncker, 1945)

Answer 8

The candle problem is a test of creative problem solving developed by psychologist Karl Duncker in 1945. The test challenges “functional fixedness”, a cognitive bias that makes it difficult to use familiar objects in abnormal ways. The subjects were asked to attach a candle to the wall and are given a box of tacks, candle, and matches.

Negative transfer – functional fixedness
Functional fixedness- a cognitive bias that impacts an individual’s ability to be creative. Functional fixedness is commonly used to describe why an individual develops an inability to use an object in more ways that it is traditionally intended to be used
- Impairs their creativity

Functional fixedness – a box is for holding tacks, not candles
Improved performance if the tack box is empty at the start of the task

Analogical problem solving
Finding a problem (source) that is like the problem you need to solve (target) and mapping the solution of that source problem onto the target problem.

Question 9

Knoblich et al. (2001) eye-tracking study

Answer 9

Eye Movements in Matchstick Arithmetic

• We used matchstick arithmetic problems because each problem consists of a small number of distinct elements, arranged in a horizontal sequence