12. PROB SOLVING Flashcards
What is insight?
- sudden comprehension, realisation to a problem solution
- involves reorganisation of mental representation in a situation that was not initially obvious
What is restructuring?
- Process of changing the problem’s representation
- restructuring is often the outcome of insight
What is an eg. that demonstrates insight?
Eg. Metcalfe and Wiebe (1987) distinguish between insight and noninsight probs. Predicted that ppl working on insight probs will not be good at predicting how near they r to a solution as insights appear suddenly. While ppl working on noninsight probs would be more likely to predict as it is a methodological process
- IP parti had to make ‘warmth’ judgements every 15 secs while working on prob
- NIP parti were given algebra questions
RESULTS: IP parti ratings began at 2, didnt change much until they jumped from 3-7 at the end but NIP parti began at 3 and gradually increased till the end. IP hence do occur sudddenly.
What is fixation, and hence functional fixedness?
- fixation is ppl’s tendency to focus on specific characteristics of the problem that keeps them from arriving at a solution.
- functional fixedness focuses on familiar objects and the uses of those objects only.
Describe 2 experiments that can explain functional fixedness
- Duncker’s (1945) Candle problem
- there is a vertical corkboard mounted on the wall
- given materials like candles, matches in matchbox, some tacks
- task is to mount the candle on the corkboard so it will burn without dripping wax on the floor
- SOLUTION: matchbox can be used as a support rather than container
- when duncker did this he showed one group with small card board box containing materials while another, but the boxes were empty
- group with boxes as containers found prob more difficult than group with empty boxes
- Maier’s (1931) 2 string problem
- parti had to tie 2 strings tgt that were hanging from the ceiling, but was diff as the strings were so far apart it was impossi
- objects given were pliers and chair
- SOLUTION: they had to create a pendulum with the pliers and swing it within the person’s reach
- 37/60 ppl failed to do so as they were focused on the usual function of pliers
- Maier then gave a hint by brushing against one of the string and set it in motion
- 23/37 people were able to then solve within a minute
What can functional fixedness lead to?
- mental set
- it is a preconceived notion about how to approach a problem
- this is determined by a person’s experience of what has worked in the past
Describe the Luchin’s Water Jug problem and what it can explain
- explains how a mental set can arise out of the situation created as a person solves a problem
- mental set: preconceived notion about how to approach a problem and is determined with person’s experience of what has worked in the past
Eg.
- partis task is to obtain a required volume of water
- given 3 empty jars for measurement
- partis presented with the prob. A= 21 quarts, B= 127 quarts, C= 3 quarts
- the desired amount = 100 quarts
- mental set group: luchin presented problem 1 as a demo and had participants solve probs 2-8. this established a mental set for using the demo formula: B-A-2C
- no mental set group: partis just solved probs 7-8. in this case, they werent exposed to the demo formula
- luchin wanted to know how partis in no mental set grp solve 7-8.
- RESULTS: only 23% of mental set group used a simpler solution for 7-8, but all the partis of the no mental set group used the simpler solutions.
- HENCE mental set can influence problem solving cause of the preconceptions about the functions of the object (candle, 2 string eg.) , and also of preconceptions about the way to solve a problem (water jug)
Describe the tower of Hanoi problem
- Move the discs one at a time from one peg to another
- A disc can be moved only when there are no discs on top of it
- A larger disc can never be placed on top of a smaller disc
initial state- conditions at the beginning of a problem
goal state- solution to the problem
subgoals- small goals that create intermediate states that are closer to the goal. they may appear to increase the distance to the goal, but in LR can result in shortest path to the goal
- Newell and Simon states that Means-end analysis can solve this problem
- Means-end analysis: reduce the differences between initial and goal state by creating subgoals
Describe an example that demonstrates restructuring.
Restructuring- Process of changing the problem’s representation, and is often the outcome of insight
Eg. Mutilated Checkerboard problem (Kaplan and Simon)
- checkerboard has 64 squares that can be completely covered by placing 32 dominos on the board
- here, each domino will cover 2 squares
- Qn: if we eliminate two corners of the checkerboard, can we now cover the remaining squares with 31 dominos? Partis to ans yes or no and rationale of their ans
- partis must realise that each domino covers 2 squares, and the squares must be of different colours
- hence removing two corner squares make it impossible to solve the problem
- Kaplan and Simon hypo that versions of this game will more likely lead partis to become aware of the principle to solve
- blank: board with all blanks squares
- color: alternating black and pink sqaures
- the words blank and pink on the board
- the words bread and butter on the board
- RESULTS: partis in bread and butter group solved the prob twice as fast as those in the blank group and required fewer hints (1 hint vs 3.14 hints in blank group)
- HENCE, solving a prob is easier when info is provided that points people towards the correct repre of the prob.
What is a source problem that can solve the Mutilated checkerboard problem?
Eg. The Russian Marriage problem
- 32 bachelors and 32 unmarried women in a village
- the matchmaker managed to arrange 32 satisfactory marriages
- one night 2 bachelors got into a fight of strength and died
- can the matchmaker through some quick arrangements come up with 31 heterosexual marriages among the 62 survivors?
- ans is NO
this eg. parallels the mutilated checkerboard prob as instead of males and females being paired up, light and dark squares are. people who read this story are usually able to solve the prob if they realize the connection between couples in the story and the alternating squares.
- this process of noticing connections between similar probs and applying the solution for one problem to other probs is called analogical transfer.
What is an analogy and what is analogical transfer?
analogy- using the solution to a similar prob to guide solution of a new prob. it is also called analogical problem solving
analogical transfer- how well ppl can transfer their experiences from solving one prob to solving another similar prob.
What are the 2 key problems of analogical transfer?
- target problem- the prob which the parti is trying to solve (checkerboard)
- source problem- another problem that shares some similarities with the TP and illustrates a way to solve the TP (russian marriage prob)
Describe Duncker’s radiation problem and what concept does it illustrate?
You are a doctor faced with a patient who has a malignant tumor in the stomach. It is impossible to operate on the patient but unless the tumour is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumour. if the ray reaches the tumour at a sufficiently high intensity, the tumour will be destroyed. but, at this intensity, the healthy tissue which the ray passes through on the way to the tumour will also be destroyed. at lower intensities, the ray is harmless to healthy tissue, but it will not affect the tumour either. what type of procedure might be used to destory the tumour and also avoid destroying healthy tissue
- ANS: use low intensity rays directed at the tumour at the same time
- many people couldnt solve it and only 10% could
Gick and Holyoake then had another group of partis read and memorize the fortress story. In the story, the dictator’s fortress corresponds to the tumour and the small groups of soldiers sent down different roads correspond to the low intensity rays that can be directed at the tumour.
- after partis heard this, they begin to work on the radiation prob.
- 30% were able to solve it
- 10% improvement over the 10% who solved the problem
- BUT, 70% still unable to solve the prob, after reading the fortress story.
- THIS SHOWS THAT many people cant make the connection between SP and TP
What are the 3 steps of Gick and Holyoake’s process of analogical problem solving?
- Noticing- there is an analogous rls between SP and TP
- Mapping- there is a correspondence between SP and TP, use SP to solve TP
- Applying- the mapping to generate a parallel solution to the TP
What is analogical encoding and what does it do?
- the process by which 2 problems are compared and similarities between them are determined
- it helps people to notice similarities in TP and SP in analogical problem solving
