Week 7: Problem solving

Question 1

Overview

Answer 1

1. Problem solving (Problem 1 - building furniture)
   
   2. Analogical problem solving (Problem 2 - school work)
2. Expertise (Problem 3 - cludo)

Question 2

Defining problems: IGOR

Answer 2

I - Initial state of the problem. Clear description of how everything is set up at the beginning of the problem.
G - Goal state - what the problem should like at the end
O - Operators - the actions to be taken to get to the goal
R - What you are not allowed to do (operator restrictions)

Question 3

Types of problems (4)

Answer 3

well-defined

ill-defined

knowledge-rich

knowledge-lean

Question 4

Well-defined problems

Answer 4

– All aspects of a problem are clearly specified
(know end goal & have the resources to do it)
(e.g. an anagram)

Question 5

Ill-defined problems:

Answer 5

Aspects of the problem are imprecisely specified
(e.g. trying to organise a surprise party - there’s lots of components with not one right answer)

Question 6

Knowledge-rich

Answer 6

Can only be solved with relevant knowledge and expertise
(e.g. need relevant knowledge of exam content to pass)

Question 7

Knowledge-lean

Answer 7

– Do not require knowledge
– Most information to solve problem available in the initial problem statement
(e.g. a jigsaw puzzle - don’t need existing knowledge)

Question 8

Gestalt approach: Distinguishes between 2 types of thinking in problem solving

Answer 8

1) Reproductive

2) Productive

Question 9

Reproductive thinking

Answer 9

Systematic re-use of previous experience (apply existing knowledge/ experience)

Question 10

Productive thinking

Answer 10

Novel restructuring of a problem (previous experience isn’t enough, so have to think of something new)
Problems requiring productive thinking solved using INSIGHT.

Question 11

Insight

Answer 11

• Involves a sudden restructuring of a problem (i.e. eureka moment)
• Experience of suddenly realising how to solve a problem

e.g. the mutilated chess board problem

Question 12

Facilitating insight

Answer 12

• hints!
• Hints can be effective without conscious awareness of task relevance - study found pps more able to solve pendulum puzzle when told to swing arms before the task

(even subtle ones, where an example is given)

Question 13

Facilitating insight: Incubation

Answer 13

– Problem is put to one side for some time
(e.g. sleeping before trying to decide something)

• subconscious mind continues to work towards a solution
• forget previous strategies to adopt a new approach

Question 14

Facilitating insight: Changing the problem representation (3 methods within this)

Answer 14

Block = can’t have insight, so need to change the representation:

CONSTRAINT RELAXATION: change the assumptions of what you think you can’t do

RE-ENCODING: some aspects of the problem representation reinterpreted

ELABORATION: new problem information is added to the representation

Question 15

Example of constraint relaxation

Answer 15

the nine-dot problem

Involves drawing four straight lines that go through all nine dots without lifting your pencil off the page

Assume that the lines must remain within the confines of the square formed by the dots

key to insight that you realise you don’t have to stay within the box

Question 16

Past experience: effects on problem solving?

Answer 16

• Past experience increases our ability to solve problems
  
  • However, we can be misled by our past experience
• Functional fixedness
• mental set

Question 17

Functional fixedness

Answer 17

• Mistakenly assume that a given object has a limited number of uses
• Duncker (1945)
  – Nail candle to wall using pins? X
  – Melt candle with matches and stick to wall? X

    – Empty pin box, use empty pin box to hold candle, and pin to wall!

Question 18

Mental set

Answer 18

• Tendency to use a familiar problem-solving strategy that has proved successful in the past
  – Allows similar problems to be solved rapidly
• Three water jars problem
  • Luchins (1942)
    – Second problem solved successfully only by 36%
    – Solution: fill jug A completely (28), then tip excess into C (28-3=25)
    – Used a familiar problem-solving strategy that had proved successful, but was inappropriate for new problem

Question 19

Tower of Hanoi: Newell and Simon

Answer 19

– We have very limited short-term memory capacity and processing is typically serial (one step at a time)
– How do we solve problems given our limited capacity?
– Used knowledge-lean problems

Question 20

Heuristics (“rules of thumb”)

Answer 20

• Easy to use and often produce correct answers
• Means-end analysis
  – Note the difference between the current problem state and the goal state
  – Form a sub-goal to reduce the difference between the current and goal states
  – Select a mental operator (e.g., move or moves) that permits attainment of the sub-goal

Used to REDUCE MENTAL CAPACITY

Question 21

Cognitive misers

Answer 21

• Someone who is typically economical with their time and effort on tasks requiring thinking
• takes shortcuts that don’t always work
• Cognitive Reflection Test
  – Provides evidence of the extent to which people are cognitive misers

Overlap with use of heuristics
– Misers resort to simplest strategy
– Unlike heuristics (used due to limited capacity), misers are reluctant to engage in effortful processing rather than because they cannot

Question 22

Analogical problem solving

Answer 22

• Involves solving problems using analogies
  
  • Analogies involve a comparison between current/previous problems, and highlighting similarities
  • Very important in everyday life

– Deal with novel situations by relating them to situations encountered previously

Question 23

Types of similarity

Answer 23

There are three main types of similarity between problems:

Superficial similarity

Structural similarity

Procedural similarity

Question 24

Superficial similarity

Answer 24

solution-irrelevant details are common to the two problems (i.e. the problems look similar on the face of things)

Question 25

Structural similarity

Answer 25

causal relation among some of the main components are shared by both problems (share the same elements to it)

Question 26

Procedural similarity

Answer 26

procedures for turning the solution principle into concrete operations are common to both problems (share the same procedure)

Question 27

Analogy detection example:

Answer 27

the tumor problem - want to destroy tumor but not the healthy cells - how? Can gain insight by the 'conquering the fortress' problem - answer is to space out and attack from multiple angles Analogy detection: * When participants told story would help them solve tumour problem, 80% solved * However, only 40% did so when not informed of the relevance of the story – Lack of superficial similarities between the two stories (when not told the relevance of the 2 problems) ○ The features shared by two problems important, helping people to see the relevance § (Gick & Holyoak, 1980)

Question 28

Expertise (Problem 3)

Answer 28

* Considerable specialist knowledge – Very efficient at problem solving – High-level of thinking as a result of practice * KNOWLEDGE RICH problems – knowledge beyond that contained within the problem

Question 29

Chess expertise

Answer 29

* Advantages to studying chess playing: – Can measure chess players’ level of skill very precisely based on their results from other players (ELO ranking system) – Detailed longitudinal data of tournament performance over time. * Why are some people better than others? – PRACTICE! ~1,000h to become a grandmaster

Question 30

Is this because of better visual memory?

Answer 30

Study where grandmaster did remember positions on a chess board more than novice, however.. * Difference in performance not due to better visual memory generally – When presented with positions that were unlikely to arise, experts no better than novices * Chess players possess more chess-related information in long-term memory – Accessed rapidly – Narrow-down possible moves to consider

Question 31

Medical expertise

Answer 31

can make rapid and accurate diagnoses

Question 32

How can we identify the diagnostic strategies used by medical experts vs novices?

Answer 32

Eye tracking and medical expertise - track focus of attention Several differences found between medical experts and novices – Shorter fixations (could more rapidly detect what was going on) – Faster first fixations on task-relevant information – More fixations on task-relevant information – longer saccades (rapid eye movements - straight to the important info)

Question 33

Eye tracking: what does it provide evidence for?

Answer 33

Consistent with: – Information-reduction hypothesis, efficient and selective allocation of attention – Holistic model, experts extract information from a wider area with each fixation

Question 34

Plasticity

Answer 34

Plasticity = changes in structure/function of the brain that affect behaviour and are related to experience Does expertise also cause modifications within the brain? London Taxi drivers - “The Knowledge” – Greater volume of grey matter in posterior hippocampus than novice drivers – But correlational evidence = issues with causation (i.e., cannot be sure that acquiring The Knowledge causes hippocampal changes.)

Question 35

Deliberate practice

Answer 35

Prolonged, deliberate practice over many years essential to become an expert

Question 36

Deliberate practise: 4 aspects to it

Answer 36

1. Appropriate level of difficulty 2. Feedback 3. Repeat task 4. Correct errors Reduces the negative effects of limited memory capacity – Rapid transfer of information from long-term memory