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PSYC*2650 Ch 14.pdf

9 Pages

Course Code
PSYC 2650
Anneke Olthof

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Chapter 14: Solving Problems Problem-Solving - the process through which you figure out how to reach your goals, starting from your current state General Problem-Solving Methods Problem-Solving as Search - as though you are navigating through a maze, seeking the best path to your goal - Newell and SImon described problem-solving as starting with an Initial State (the knowledge and resources you have at the outset) and working toward a Goal State - the problem-solver has a set of Operators (tools or actions that can change her current states) - Path Restraints - rule out some options or some solution, they may take the form of resource limitations or other limits - there is limited number of intermediate states that one can reach en route to the goal - Problem Space - the set of all states that can be reached in solving a problem - one option in solving a problem would be to trace through the entire problem space, exploring each branch in turn, this would guarantee you would eventually find the solution, if the problem was solvable, this is hopeless for most of the problems we face - narrowing your search would involve an element of risk that you may overlook the best option - need a problem-solving heuristic - in the domain of problem-solving, a heuristic is a strategy that guides you through the problem space - narrowing your search in a fashion that leads you to the problemʼs solution General Problem-Solving Heuristics Hill-Climbing Strategy - at each point, you simply choose the option that moves you in the direction of your goal - this is helpful for some problems e.g. finding something that smells bad in your house - it is limited though because many problems require that you start by moving away from the goal and then from this position, the problem can be solved Means-End Analysis - one starts by comparing the current state and the goal state - provides 2 different benefits: (1) the analysis highlights differences between where you are right now and where you want to, and in this way it helps you see exactly what you need to do to solve the problem, (2) it will often lead you to break up a problem into smaller subproblems, each with their own goal - by solving the subproblems one by one, you address the larger problem - by breaking a problem into smaller pieces, we make the initial problem easier to solve Working Backward- one can often solve a problem by using the goal as the starting point, rather than the problemʼs initial state - both means-end analysis and working backward appear frequently in peopleʼs problem-solving protocols - they are often effective and applicable to a large number of problems Mental Models and Mental Images - translating a problem into concrete terms, relying on a mental image or model Pictures and Diagrams - no difference between problem-solving through a picture and problem-solving via imagery - for other purposes there are important differences between mental images and pictures, with some problems more readily solved via imagery, and other problems showing the reverse - mental images have the advantage of being more easily modified than diagrams - if a problem solution depends on motion, then the problem may be more easily solved with imagery than with a picture - if a problem depends on more elaborate or detailed forms, problem solving through pictures will be more helpful Relying on Past Knowledge Problem-Solving via Analogy - we remember some other problem we have already solved and this will tell us, by analogy, how to solve the problem now before us - we derive the unknown solution from one that is already known - in the history of science and teaching, analogies have often played an important role - in a study, participants first read about a related situation and then presented with the tumor problem - when participants were encourage dot use the hint, 75% were able to solve the tumor problem, for participants without the hint, only 10% solved it Difficulties in Finding an Appropriate Analogy - despite the clear benefit of using analogies, people routinely fail to use them - e.g. participants read the general and fortress story, but no further hints were given - participants were not told this story was relevant to the tumor problem - 30% solved the tumor problem, fewer than 75% explicitly told that the fortress story was relevant to their task - in another study, first participants had to solve the “jealous husbands” problem and then asked to solve the “hobbits and orcs” problem - when the close relationship between these 2 problems was pointed out to the participants, they were considerably faster in solving the “hobbits and orcs” - if the relationship was not explicitly pointed out, they showed no benefit at all from this training - people do use analogies if suitably instructed, but spontaneous, uninstructed use of analogies seems relatively rare - in solving a problem about tumors, people ask themselves “what else do I know about tumors” but it wonʼt lead them to the “general and fortress” problem - this potential analogue will lie dormant in memory and provide no help - in order to create, or even to understand, an analogy, people need to get beyond the superficial features of the problem and think instead about the principles governing the problem - people can use analogies only if they figure out how to map the prior case onto that problem now being solved - this mapping process is sometimes difficult, and failures to figure out the mapping are common, providing another reason why people regularly fail to find, and fail to use analogies - mapping one problem onto another is easier if the 2 problems are similar in the particular - if instead, you have recently solved the “jealous husbands” problem, then the principles learned in this experience might be applicable to the new problem, but only via a step of translation Strategies to Make Analogy Use More Likely - with instruction, people could learn to ask themselves different questions when searching their memory - analogies usually depend on a problemʼs “deep structure” - the pattern of causal relationships within the problem, and how the problemʼs parts are interrelated - the problemʼs “surface structure” - how the causal relationships are manifested - is largely irrelevant - perhaps we can promote analogy use by urging people to pay attention to the deep structure from the very start, rather than attending to the problemʼs superficial content - Cummins presented participants with algebra problem, one groups was asked to analyze them one by one, they tended to categorize them in terms of superficial features - participants in the second group were explicitly asked to compare the training problems to each other, these participants tended to describe and categorize the problems in terms of their structures, paying attention to the underlying dynamic - Needham and Begg presented their participants with a series of training problems - some were told that they would need to recall these problems later on and were encouraged to work hard at remembering them - other were encouraged to work at understanding each solution, so that they would be able to explain it later to another person - when the test problems came, the participants in the second group were much more likely to transfer what they had earlier learned - those who had taken the “understand” approach were able to solve 90% of the test problems, the memorization approach only solved 68% - for the purposes of problem-solving, there is a preferred way to learn - you want to attend to the structure of a problem rather than to its surface, this increases the likelihood of finding analogies later on and the likelihood of benefiting from analogies - one way to achieve this is by comparing problems to each other, seeking parallels and points of similarity - the same benefit is observed if you simply spend time thinking about why a problemʼs solution is a solution - why it gets the job done - people are also helped by getting the right training problems that call attention to underlying structures Expert Problem-Solvers - discussion of problem-solving has important implications for education - if we want to teach students to be better problem-solvers, first we could teach them some of the heuristics that appear useful for problem-solving in general - second, analogies are plainly helpful in problem-solving, and so we could provide students with experience in the relevant domains so that they would have a basis from which to draw analogies - third, encourage students to approach the training problems in an appropriate way, and also to provide a basis for seeing the mapping between the training and test problems - expert problem-solvers use many of the techniques discussed here - experts tend to think about the problems in terms of their deep structure - experts are also more attentive to the problemʼs structure Chunking and Subgoals - experts also have another advantage, and it once again leads to a suggestion about how to train people so that they can become better problem-solvers - it is often helpful to break the problem into subproblems and create subgoals while working on a problem, and to work on these rather than aiming only at the end goal - these are often used by experts, and are supported by the expertsʼ understanding of the problemʼs deep structure - e.g. chess experts are particularly skilled in organizing a chess game - seeing the structure of the game, understanding its parts, and perceiving how these parts are related to each other - they could remember where more pieces were on the board because the group made “tactical sense” - the masters had memorized the board in terms of higher-order units and not the individual pieces, these units were defined according to their strategic function within the game - this perception of higher-order units doesnʼt just help memory, it also helps organize the expertʼs thinking - they can keep track of broad strategies without getting bogged down in the details, these units help set subgoals for the expert - in a study, participants were shown a new mathematical procedure, for some the key steps were labeled in a fashion that highlighted the function, for other there were no labels - those with labels were useful, participants given them were better able to use the new procedure in solving novel problems - nonexperts can therefore be trained to use subgoals The Nature of Expertise - experts have other advantages, including the simple fact that they know much more about their domains of expertise than novices do - takes an estimated 10 years to become an expert in a domain, need experience - experts also gain their experience through years of deliberate practice - aping careful attention to what they are doing, seeking feedback, and seeking explicit instruction - experts organize their knowledge more effectively than novices - studies indicate that expertsʼ knowledge is heavily cross-referenced, so that each bit of information has associates to many other bits - not only do experts know more, but they have faster, more effective access to what they know - experts may also differ from novices in the strategies they use - the key is not that experts know strategies that novices donʼt, instead they make better choices in which strategies they use, and they are also more effective in using the strategies - executing the strategies with greater skill and greater efficiency - experts are also well practiced in working in their domain, well practiced in solving problems - this practice helps them to sharpen their skills and establish certain routines for dealing witch commonplace tasks - these often allow an expert to recognize a new problem as being functionally identical to ones met earlier, the expert will give the problem no further thought, relying instead on the well-rehearsed routine Defining the Problem - one crucial difference between experts and novices is in how each groupʼs members define the problems they encounter - novices usually define problems in terms of their superficial features and this guides how they think about the problem and how they try to solve it - experts define a problem in their area of expertise in terms of the problemʼs deep structure or underlying dynamic - experts are more likely to break the problem into meaningful parts, more likely to realize what other problems are analogies to the current problem, so more likely to benefit from analogies - there are better and worse ways to define a problem - ways that will lead to a solution and ways that will obstruct
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