Problem Solving (3) Flashcards
What is Isomorphism?
Things that look the same
Isomorphic: an adjective, corresponding to or similar form and relations
Newell and Simon suggest:
- We navigate problem spaces
- isomorphic problems will have similar problem spaces, hence having similar situations
What is an Analogy?
A comparison between 2 types of problems, a way of thinking about 2 things in the same way
- An analogy = a comparison of the structure (or relationship) between the attributes of 2 different things/problems/situations
- a successful analogy does NOT involve comparing (or mapping) the details (attributes) - it involves a mapping of a/the relationship between attributes
What prior knowledge is there into problem solving?
Egan and Greeno, (1974):
- Experience with a related problem helps complete it = experience is a key factor in problem solving
- people with a lot of experience in a specific area/domain (experts) seem to be able to solve problems much better/easier than non-experts (novices) or even merely/slightly experienced people
- Spotting similarities between problems has been identified as part of ‘creativity’
- it is thought to be a key feature of expertise
- this is referred to as problem solving by ‘analogy’
What is the atom/solar system analogy?
- Atoms/solar systems are alike
- both involve similar objects orbiting around larger ones and this rotation is caused by a central force
- the relationship is important, NOT the identity of the objects
What is analogy and creative thinking?
- Early work on analogy focused on studies of creative people in sciences e.g. Hadamard, (1954) or across areas of expertise e.g. Koestler, (1964)
- these studies suggest expertise allows people to compare similarities between (very) different ideas and see new connections across domains of knowledge
- famous analogies have characterised similarities between function of the heat and a pump (harvery), and Rutherford’s atom/solar system analogy
What is analogy and problem solving
- Experts and creative people use analogies; (what about the rest of us?)
- Gick and Holyoak, (1980 and 1983) examined the use of analogies in problem solving
- participants received Duncker’s (1945) ‘radiation problem’ to solve = only had a 10% success rate
What is the radiation problem?
AN EXAMPLE:
- a patient has a tumour
- surgery to remove it etc. will kill the patient
- tumour is also resistant to chemotherapy
- radiation therapy destroys the tumour but at intensities high enough to also destroy healthy (brain) tissue
- students are given a hint = fortress problem
What was Gick & Holyoak’s (1980) study that used the fortress problem?
- Roughly 10% of participants solved the radiation problem
- 40% of participants who had previously seen the fortress problem solved the radiation problem
- if participants were given a hint that the fortress problem was useful in helping solve the radiation problem, the success doubled to 80% of participants solving the radiation problem
What study did Kean, (1987) conduct?
- Lack of superficial similarities made analogies difficult to sport e.g. fortress doesn’t look like a patient?
- in a lecture, researcher(s) presented the participants with either a story about a surgeon using rays to cure a brain tumour (analogous in structure to radiation problem) OR the fortress problem and then had them try to solve the radiation problem a week later
- 88% of participants initially given the brain tumour story correctly solved the radiation problem
- compared with 12% of those that were given the fortress problem
What is analogy spotting and what does it do?
- The long term memory is huge and can store many memories - what information is useful to this problem?
- people can recognise analogous problems, but it isn’t easy
- Wharton, Holyoak, Downing, Lange, Wickens and Melz, (1994) found these ‘deep’ analogies are used if they can be made distinct from competing memories
- Helps you solve problems
- the long term memory is big - which analogy do you go for?
Strategies to help choose: - Tell them the analogy is useful
- ask people to compare
- ask people to understand
(a bit like levels of processing and memory)
What is categorising and comparing analogy spotting?
- Novices tend to rely on on surface similarities rather than structural/relational similarities (Holyoak and Koh, 1987)
Cummins, (1992):
- Presented participants with algebraic (maths) problems)
- 1 group were asked to categories problems
- the other group were asked to compare the problems to one another
Cummins found:
- The ‘categorise’ group relied on superficial details
- whilst the ‘comparison’ group paid attention to the problems’ underlying structure
How can we understand a/the problem in/when using analogy spotting?
- Long term memory isn’t the only problem
- Needham and Begg, (1991) gave the participants a series of training problems
- 1 group were told to try and understand the solution to each problem
- others were told to just remember the problems
- participants in the ‘understand’ group correctly applied analogous solutions to 90% of the text problems
- participants in the ‘memory’ group correctly applied analogous solutions to only 69% of the text problems
What is meant by analogy and expertise?
- Memory isn’t enough difficulty wise with analogies
- understanding and comparing helps
- what processes does this use? - e.g. schema induction?
What study did Novick & Holyoak, (1991) conduct?
Method:
- Researchers got students with different maths abilities to solve a training problem and then several analogous problems (both used the same underlying mathematical principles)
Findings:
- There was a clear positive relationship between (level of) ability and (level of) expertise
What study did Novick, (1988) conduct?
Method:
- Research got students that had different maths abilities to sort problem by (their) type
Findings:
- Better at maths = sort the problems by formulae to solve the problem (useful analogy)
- worse at maths = sort the problems by similarities in the wording (superficial)
What are experts (in relation to problem solving)?
- Experts appear to not only have large body of domain specific knowledge; it appears to be interlinked or cross referenced so that each bit is associated with other bits which may explain level of abstraction needed to make use of analogies
- accumulation of knowledge e.g. Gick and Holyoak, (1983) - it is necessary in order to find analogies
- Hayes, (1985) suggest it takes at least 10 years to become an expert in a domain
- knowledge seems to be organised so that it cross-references the structural similarity and allows it to be used differently e.g. applied to problems
- (stored like a template?)
What is the template theory?
- Information stored as a template
- template = (in) abstract form
- can apply it
What are Chess playing experts?
- DeGroot’s chess players
- well defined problem(s)
- ranked players on an international scale
Who was/is DeGroot, (1965)?
- Compared 5 grand masters and 5 experts
- grand masters = faster than experts
- grand masters moves = rated as better by an independent panel of experts
- grand masters didn’t consider greater number of moves than experts (breadth-first) nor did they think more moves ahead (remember look-ahead) - (how are they doing it?)
- do grand master have a different representation to experts?
Discuss the Chess playing experts study/research
- This should be amenable to memory tests
Procedure:
- DeGroot showed board positions from games for 2-15 seconds
- then asked the subjects/participants to recreate the positions
Findings:
- 91% accuracy level in grandmaster
VS
- 41% in less expert players
- Later on in another/extended study Chase and Simon, (1973a and b)
- they tried random positions and found no other differences amongst their 3 subjects
What did McGregor and Howes, (2002) do/study/find?
- Experts don’t remember actual board positions
- they remembers the attack/defence relationship between pieces which would require an adjustment to the template theory
What did Charness, Reingold, Pomplun and Stampe, (2001) do/study/find?
- Eye movements of expert chess players:
Findings:
- 80% of experts’ fixations (lasting less than a second) were tactically important pieces
- compared to 64% of intermediate players’ fixations
What is Chunking?
- In addition to better memory for board positions, Chase and Simon found that better players tend to ‘Chunk’ pieces
Procedure:
- Players had to look at a board and reproduce it on another board
Findings:
- Players placed groups of pieces on the board and grandmasters produced more tactically relevant groups of pieces
What is meant by quantity leads to quality?
Simon and Gilmartin, (1973):
- Suggested chess masters have learned 500,000 board positions (chunks of pieces)
Newell and Simon, (1972):
- Suggested master have also learned what to do when confronted with particular chunks of pieces and that this explains why they produce better moves, faster than ‘lesser’ players - i.e. they are selecting among moves they have already learned
