Week 7: Problem solving Flashcards
Overview
- Problem solving (Problem 1 - building furniture)
- Analogical problem solving (Problem 2 - school work)
- Expertise (Problem 3 - cludo)
Defining problems: IGOR
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)
Types of problems (4)
well-defined
ill-defined
knowledge-rich
knowledge-lean
Well-defined problems
– All aspects of a problem are clearly specified
(know end goal & have the resources to do it)
(e.g. an anagram)
Ill-defined problems:
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)
Knowledge-rich
Can only be solved with relevant knowledge and expertise
(e.g. need relevant knowledge of exam content to pass)
Knowledge-lean
– 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)
Gestalt approach: Distinguishes between 2 types of thinking in problem solving
1) Reproductive
2) Productive
Reproductive thinking
Systematic re-use of previous experience (apply existing knowledge/ experience)
Productive thinking
Novel restructuring of a problem (previous experience isn’t enough, so have to think of something new)
Problems requiring productive thinking solved using INSIGHT.
Insight
- 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
Facilitating insight
- 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)
Facilitating insight: Incubation
– 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
Facilitating insight: Changing the problem representation (3 methods within this)
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
Example of constraint relaxation
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
Past experience: effects on problem solving?
- Past experience increases our ability to solve problems
- However, we can be misled by our past experience
- Functional fixedness
- mental set
Functional fixedness
- 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!
Mental set
- 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
- Luchins (1942)
Tower of Hanoi: Newell and Simon
– 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
Heuristics (“rules of thumb”)
- 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
Cognitive misers
- 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
Analogical problem solving
- 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
Types of similarity
There are three main types of similarity between problems:
Superficial similarity
Structural similarity
Procedural similarity
Superficial similarity
solution-irrelevant details are common to the two problems (i.e. the problems look similar on the face of things)
Structural similarity
causal relation among some of the main components are shared by both problems (share the same elements to it)
Procedural similarity
procedures for turning the solution principle into concrete operations are common to both problems (share the same procedure)
Analogy detection example:
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)
Expertise (Problem 3)
- 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
Chess expertise
- 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
Is this because of better visual memory?
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
Medical expertise
can make rapid and accurate diagnoses
How can we identify the diagnostic strategies used by medical experts vs novices?
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)
Eye tracking: what does it provide evidence for?
Consistent with:
– Information-reduction hypothesis, efficient and selective allocation of attention – Holistic model, experts extract information from a wider area with each fixation
Plasticity
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.)
Deliberate practice
Prolonged, deliberate practice over many years essential to become an expert
Deliberate practise: 4 aspects to it
- Appropriate level of difficulty
- Feedback
- Repeat task
- Correct errors
Reduces the negative effects of limited memory capacity
– Rapid transfer of information from long-term memory
