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 –> Focus on an aspect of the problem that prevents us from arriving at the solution.
• 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.

Analogical training improves analogical transfer to problems with similar features. People are better at solving problems in the real world.

Question 15

What are experts? and how do they solve problems?

Answer 15

They are individuals who have completed extensive study and training and are widely viewed as being extremely knowledgeable, skilled, etc, in their field.

They solve problems faster and more accurately than beginners.

Experts analyze problems using structural features more. They are faster at solving problems overall, but they spend more time analyzing the structural features.

They are better at solving problems in their fields but they are no better than others at solving problems in general. Although, sometimes they are overconfident and make claims in other areas.

Sometimes less experiences scientists make big breakthroughs because they are not yet confined to a way of thinking.

Question 16

What is creativity? and what processes does it involve?

Answer 16

Innovative thinking
Novel ideas
New connections between existing ideas

Divergent thinking –> open-ended; a large number of potential solutions

Practical creativity –> often involves analogical transfer
De Menstral –> Velcro
Odon –> parallel between cork and birth

Question 17

What are Basadur’s 4 steps?

Answer 17

1) Problem generation
2) Problem formulation
3) Problem solving
4) Solution Implementation

Question 18

Is experience always good?

Answer 18

Too much experience can hurt.

Question 19

What is brainstorming and when is it most useful?

Answer 19

Many ideas are generated without censoring them in groups.
More ideas are generated individually.

Question 20

Explain Finke’s creative cognition.

Answer 20

They gave participants different components, and they asked them to come up with inventions and how they can be used (Pre-inventive forms –> rough initial ideas).

Judges said that some of the inventions had potential.

If we encourage and reward creativity, people can get better at it.

Question 21

What mental disorders are hypothesized to be related to creativity?

Answer 21

Bipolar disorder and schizophrenia
–> Most research suggests that there is no direct connection
–> Indirect link: family members of people with these disorders are more associated with creative professions
–> Latent inhibition (ability to screen out irrelevant stimuli is reduced in creative people and people with some mental illnesses.
–> Low LI predicts increased creative accomplishment, especially in people with high IQs

Question 22

Explain how analogical transfer is used to solve problems concerning Gick and Holyoak’s (1980) radiation problem.

Answer 22

Target problem: Radiation problem
Source Problem: Fortress story

• Only target problem: 10% solved
• Source problem: 30% solved
  –> When reminded of the source problem 75% solved it

Analogical transfer varies dramatically. Sometimes, even when people have a source problem, they don’t apply it.

Question 23

What are the three steps that Gick and Holyoak propose for successful analogical transfer?

Answer 23

1) Noticing the relationship
2) mapping correspondence between source and target
3) Applying mapping

Question 24

What might facilitate noticing/mapping? Explain with relation to Gick and Holyoak (1983 and 1987).

Answer 24

An important obstacle to analogical transfer is only focusing on surface features instead of the structure features (underlying features that govern the solution).

Manipulated source/target surface and structural features.
- Invented the lightbulb problem.
- Result: greater surface or structural similarity improved target solution.
–> This makes sense for structural, but it could be conflicting for surface as it might lead to focusing on non-essential aspects.

*Humans are not great at noticing structural similarities.

Question 25

What is analogical encoding training and how can it be implemented? Use Gentner and Golding-Meadow's experiments as examples.

Answer 25

- Problems are compared and structural similarities within them are determined. People do get better at solving problems with similar structural features.