Problem Solving (3)

Question 1

What is Isomorphism?

Answer 1

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

Question 2

What is an Analogy?

Answer 2

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

Question 3

What prior knowledge is there into problem solving?

Answer 3

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’

Question 4

What is the atom/solar system analogy?

Answer 4

• 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

Question 5

What is analogy and creative thinking?

Answer 5

• 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

Question 6

What is analogy and problem solving

Answer 6

• 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

Question 7

What is the radiation problem?

Answer 7

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

Question 8

What was Gick & Holyoak’s (1980) study that used the fortress problem?

Answer 8

• 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

Question 9

What study did Kean, (1987) conduct?

Answer 9

• 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

Question 10

What is analogy spotting and what does it do?

Answer 10

• 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)

Question 11

What is categorising and comparing analogy spotting?

Answer 11

• 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

Question 12

How can we understand a/the problem in/when using analogy spotting?

Answer 12

• 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

Question 13

What is meant by analogy and expertise?

Answer 13

• Memory isn’t enough difficulty wise with analogies
• understanding and comparing helps
• what processes does this use? - e.g. schema induction?

Question 14

What study did Novick & Holyoak, (1991) conduct?

Answer 14

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

Question 15

What study did Novick, (1988) conduct?

Answer 15

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)

Question 16

What are experts (in relation to problem solving)?

Answer 16

• 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?)

Question 17

What is the template theory?

Answer 17

• Information stored as a template
• template = (in) abstract form
• can apply it

Question 18

What are Chess playing experts?

Answer 18

• DeGroot’s chess players
• well defined problem(s)
• ranked players on an international scale

Question 19

Who was/is DeGroot, (1965)?

Answer 19

• 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?

Question 20

Discuss the Chess playing experts study/research

Answer 20

• 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

Question 21

What did McGregor and Howes, (2002) do/study/find?

Answer 21

• Experts don’t remember actual board positions

- they remembers the attack/defence relationship between pieces which would require an adjustment to the template theory

Question 22

What did Charness, Reingold, Pomplun and Stampe, (2001) do/study/find?

Answer 22

• 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

Question 23

What is Chunking?

Answer 23

• 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

Question 24

What is meant by quantity leads to quality?

Answer 24

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

Question 25

What is the Template Theory?

Answer 25

Gobey and Waters, (2003):

Findings:

• Found chunking can’t easily explain:
• A) the higher order representations that chess masters have
• B) the speed with which chess masters select their moves
• ‘Chunks of moves’ used frequently are organised into templates
• each template has a core of information (like a chunk), plus slots (pieces in each configuration which are dependent upon the stage in the game)

Question 26

What are other benefits of being an expert?

Answer 26

Novick and Sherman, (2003):

Procedure:

• Asked experts and non-experts to solve 5 letter anagrams
• then to choose amongst statements that explained how they came to the solution

Findings:
- Experts = more likely to choose option that the solution just seemed to ‘pop out’ of nowhere

Conclusions:
- Have the experts over learned maybe?