Problem solving - Prior knowledge in problem solving PDF

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Having knowledge prior to solving problems in order to solve them ...

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Prior Knowledge in Problem Solving Egan & Greeno (1974)  

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Experience with a related problem helps to solve it o Experience is a key factor in problem solving People with lots of experience (experts) in a particular area (domain) seem to be able to solve problems much better than non-experts or even merely experienced people Had Köhler’s chimps already seen somebody standing on a box to get the fruit? Is this why they acted this way?

Isomorphism   

Isomorphic: Corresponding or similar in form or relations Newell & Simon suggest that we navigate problem spaces Isomorphic problems will have similar problem spaces hence similar solutions

Problem solving by analogy   

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Analogy is a comparison of the structure/relationship between the attributes of two different things/problems/situations A successful analogy does not involve comparing (or mapping) the details (attributes): it involves a mapping of the relationship between attributes Types of comparison o Useful comparison e.g. a jam jar could be used as a jam jar, but also to store plants, make a snow globe or be a cool light o Less useful comparison  e.g. a toothbrush and a hairbrush are both brushes and very similar, but only one of them will clean your teeth  e.g. there are two type of mice: a computer mice and a live mouse – don’t plug the wrong one into the computer! Atom/solar system analogy (Rutherford) o Atoms/solar systems are alike in that they both involve smaller objects orbiting around larger ones and this rotation is caused by a central force o The relationship is important, not the identity of the objects

Analogy and creative thinking: spotting similarities between problems has been identified as part of creativity and is thought to be a key feature of expertise 

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Early work on analogy focussed on case studies of creative people in the sciences (Hadamard, 1954; Mednick, 1962) or across areas of expertise (Koestler, 1964) o These studies suggest that expertise allows people to compare the similarities between very different ideas and see new connections across domains (areas) of knowledge  Famous analogies have characterised the similarities between the function of the heart and a pump (Harvey) and Rutherford’s atom/solar system analogy Although experts and creative people use analogies, do the rest of us? Gick & Holyoak (1980) examined the use of analogies in problem solving by giving

Introduction to Cognitive Psychology – Problem Solving: Lecture 3

participants Duncker’s (1945) ‘Radiation Problem’ to solve (which normally only has a 10% success rate) o The Radiation Problem: A patient has a tumour. Surgery will kill the patient. The tumour is resistant to chemotherapy. Radiation destroys the tumour but at intensities high enough to destroy it will also destroy healthy tissue. Participants are given a hint in the form of the fortress problem  The fortress problem shows soldiers that need to cross a landmine to reach their destination. The landmine will go off when repeatedly stepped on, but not if only one soldier steps on it. The problem is shown to participants, who need to figure out that in order for the soldiers to reach their destination, one soldier must go over only one landmine o 10% of participants solved the radiation problem. 40% of participants who had previously seen the fortress problem solved the radiation problem. I participants were given a hint that the fortress problem was useful in helping solve the radiation problem, success doubled to 80% Analogy spotting    

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LTM is huge – many memories are stored, but what information is useful to this problem? People can recognise analogous problems, but this is not easy Wharton, Holyoak, Downing, Lange, Wickens & Melz (1994) found ‘deep’ analogies are used if they can be made distinct from competing memories Keane (1987) o Lack of superficial similarities made analogies difficult to spot (e.g. the fortress does not look like a patient) o In a lecture, he presented participants with either a story about a surgeon using rays to cure a brain tumour (analogous in structure to the radiation problem) or the fortress problem and then had them try to solve the radiation problem a week later o 88% of participants initially given the brain tumour story correctly solved the radiation problem compared with 12% given the fortress problem Categorise or compare? o Novices tend to rely on surface similarities rather than structural/relationship similarities (Holyoak & Koh, 1987) o Cummins (1992) presented participants with algebraic problems. One group were asked to categorise the problems, the other to compare the problems to one another. The categorise group relied on superficial details whilst the comparison group paid attention to the problem’s underlying structure Understanding the problem o LTM isn’t the only problem o Needham & Begg (1991)  Gave participants a series of training problems. One group were told to try and understand the solution to each problem whilst the 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 69% of the text problems Conclusion to analogy spotting o Spotting analogies helps you solve problems o LTM is big – which analogy do you go for? o Strategies to help

Introduction to Cognitive Psychology – Problem Solving: Lecture 3

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Tell them analogy is useful Ask people to compare Ask people to understand to problem  A bit like LOP and memory? (This may or may not be a useful analogy)

Analogy and expertise    

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Memory isn’t enough to explain difficulties with analogies: understanding and comparing helps What processes does this use? More examples: better at analogy spotting (Gick & Holyoak, 1983) o Schema induction? Novick & Holyoak (1991) o Students with different maths abilities to solve a training problem and then several analogous problems (used the same underlying mathematical principles) o There was a positive relationship between ability and expertise Novick (1988) o Students of different maths ability to sot problems by type o Better at maths = sort problems by formulae to solve the problem (useful analogy) o Worse at maths = sort them by similarities in the working of the maths question (superficial) Experts o Experts appear to not only have a large body of domain specific knowledge, it appears to be interlinked/cross referenced so that each bit is associated with other bits which may explain the level of abstraction needed to make use of analogies (Bedard & Chi, 1992; Eylon & Reif, 1984; Heller & Reif, 1984) o Accumulation of knowledge is necessary in order to find analogies (multiple examples in Gick & Holyoak 1983; Needham & Begg, 1991) o Hayes (1985) and Holding (1985) suggest that it takes at least 10 years to become an expert in a domain o 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? Template theory: Information is stored as a template. Template = abstract form. Can apply it! DeGroot’s chess playing experts (1965, 1966; DeGrott & Gobet, 1996): Well defined problem. Ranked players on international scale o DeGroot (1965): Compared 5 grandmasters and 5 experts – grandmasters were faster than experts. Grandmasters’ moves were rated as better by an independent panel of experts. Grandmasters did not consider a greater number of moves than experts (breadth-first), nor did they think more moves ahead (look-ahead) – so, how are they doing it? Do grandmasters have a different representation to experts? o Chess playing expertise: DeGroot showed board positions from games (for 2-15 seconds), then asked subjects to recreate the positions. 91% accuracy level in grandmasters vs. 41% in expert players. Chase & Simon (1973) tried random positions and found no difference amongst three subjects  McGregor & Howes (2002): Experts don’t remember actual board positions – they remember the attack/defence relationship between pieces which would require an adjustment to template theory

Introduction to Cognitive Psychology – Problem Solving: Lecture 3

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Charness, Reingold, Pomplun & Stampe (2001): Eye movements of expert chess players. 80% of experts’ fixations (lasting less than a second) were on tactically important pieces, compared to 64% of intermediate players’ fixations

Chunking o In addition to better memory for board positions, Chase & Simon (1973) found that better players tended to chunk pieces. Players looked at a board and reproduce it on another board. Players placed groups of pieces on the board and grandmasters produced more tactically relevant groups of pieces Quantity leads to quality o Simon & Gilmartin (1973) suggested that chess masters have learned 50,000 board positions (chunks of pieces) o Newell & Simon (1972) suggest that masters 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 – they are selecting among moves they’re already learned Template theory o Gobet & Waters (2003) found that chunking cannot easily explain a) the higher order representations that chess masters have and b) the speed with which chess masters select their moves o ‘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 are dependent upon stage in the game) Other benefits of expertise o Novick & Sherman (2003) asked expert and non-experts to solve 5 letter anagrams and then to choose amongst statements that explained how they came to the solution. Experts were more likely to choose that the solution just seemed to ‘pop out’ of nowhere  Overlearned? Becomes so embedded in our brains that it happens naturally

Introduction to Cognitive Psychology – Problem Solving: Lecture 3...