Problem-solving and reasoning

Question 1

What is a problem?

Answer 1

An obstacle between a present state and a goal.
If it’s not immediately obvious how to get around the obstacle the problem is difficult.

Question 2

Explain Gestalt’s early approach to problem-solving.

Answer 2

• Establish how the problem is represented. How do we define the problem?
• To solve we generally need to restructure the problem.
• Kohler’s circle problem.

Question 3

Explain Kohler’s circle problem and how to solve it with the Gestalt approach.

Answer 3

• There is a circle with a radius r and a triangle inscribed in a quarter of the circle.
• To solve you need to move the triangle.
• Gestalt:
  insight: sudden realization of solution –> requires restructuring the problem.
  Shouldn’t experience much warning before the insight/ solution. Alternatively people could solve problems gradually.

Question 4

What is a warmth rating and how did Metcalfe and Wiebe investigate this?

Answer 4

Warmth rating –> indicator of how close you are to the solution.

Question: if ‘insight’ is real then the warmth ratings shouldn’t help or indicate when the participant is going to solve the problem.

• 2 kinds of problems (maybe some problems are insight and others need step by step approach (non-insight))
• Insight problems –> triangle and chain problem
• Non-insight problems –> algebra
• Results: insight problem –> don’t report getting closer, with algebra problems you do get steps.

Question 5

Obstacles to problem solving.

Answer 5

• Duncker’s candle problem.
  Only 50% solved the original problem. 90% solved the problem when they presented the matchbox empty.
• Maier’s two-strings problem.
  Again when experimenters casually hinted that strings could swing they did better.
• Fixation –> We are used to using objects/situations in a specific way.
• Functional fixedness –> think of objects only being used in the context for which they were designed.
  We are caught up in the typical way in which we use things.

Question 6

What is the goal state and how does it relate to how fast we can solve a problem?

Answer 6

When you present a problem, how close is it to the goal state?

When you present a problem as being closer to the goal state, people do better.

Question 7

What is a mental set?

Answer 7

A particular way of understanding a set of circumstances. It’s based on past experiences with similar problems.

Functional fixedness and fixedness itself are kinds of mental sets.

Question 8

Explain the water-jug problem.

Answer 8

• 3 jugs that hold different quantities of water.
• task: obtain the desired amount by pouring water back and forth.
• Interesting results for problems 7 and 8 –> Participants tried applying the same method as they had used for the first 6 problems when in fact the solutions were simpler.
• Mental sets get established and can hold you back a bit.

Question 9

What is the modern approach to problem solving?

Answer 9

The information processing approach.

Question 10

Explain the information processing approach (Newell and Simon, 1972)

Answer 10

Problem-solving = search for solution.
- Initial state
- Intermediate states
- Goal state
- To achieve a goal, you need to transform the initial state to the goal state. –> involves intermediate states + operators (allowable rules for change) to change the current state.
- Don’t mention insight, focus on step-by-step problems.

Question 11

Explain the tower of Hanoi problem.

Answer 11

You have a tower of disks and three pegs. You need to move the disks to move the tower to the third peg.
Operators –> You can only move one disk at a time, you can only move the top disk and you can’t have a bigger disk on top of a smaller disk.

In general, people do a means-end analysis –> reduce the difference between initial and end state, do this by creating sub-goals.

Question 12

Explain the mutilated checkerboard problem.

Answer 12

Two red corners are removed from the board. You are asked if you can cover the board with domino pieces. The answer is no. You need pairs of red and black to cover it with dominos.
Different versions of the problem:
- All white squares
- Regular checkerboard
- Alternating words (black and pink)
- Alternating words (bread and butter)

• People did best with bread and butter because it inspired the pair idea.
• It’s important how the problem is stated.

Question 13

When are problems easier to solve?

Answer 13

When they are presented in a form that is closer to the key representation.

Question 14

What is the relationship between analogies and problem-solving?

Answer 14

We use solutions to similar problems to help us with a new problem.

Give people a source problem –> an initial problem in which the solution is similar to the one of the target problem.
Russian marriage problem –> you are a matchmaker and you have several males and females. Can you match them all up? - Only if you have the same quantity of both.

If you give participants the Russian marriage problem first then they are a lot better at solving the mutilated checkerboard problem.