Problem-Solving PDF

6 Problem-solving Introduction Types of problems...

6 Problem-solving Introduction Types of problems Gestalt approach Information-processing approach Information processing and ‘insight’ Use of analogy in problem-solving Problem-solving in everyday life Summary Review exercise Copyright © 2003. Taylor & Francis Group. All rights reserved. Introduction The need to solve problems is a common feature of our lives. There are many different types of problem, ranging from simple to complex and trivial to life threatening. A well-known example of a complex, life-threatening problem arose in the space flight of Apollo 13. During the journey towards the moon, some 200,000 miles from the earth, there was an explosion and the spacecraft sustained extensive damage. This was announced to mission control in the famously understated message ‘Houston, we’ve had a problem.’ The problem was how to turn the spacecraft around and return to the earth whilst sustaining the lives of the three astronauts aboard with limited power, water and oxygen. Most of us do not have to deal with such dramatic problems, but nevertheless we deal with problems daily. You may be faced with 65 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT the problem of how to get home when you have missed the bus, how to get in touch with someone when you have lost their telephone number, how to help a friend who is unhappy, how to produce an excellent psychology essay, etc. Since the problems people deal with are so diverse we are faced with the question: ‘What is a problem?’ Garnham and Oakhill (1994, p.217) suggest that ‘Problems arise when people do not see immediately how to get from where they are (starting state) to where they want to be (their goal state).’ This description introduces a number of essential elements of problems. Every problem has a start state (or initial state) and this is the position you begin with. For the crew of Apollo 13 this was being in deep space in a damaged spacecraft, but if you are trying to write an essay the start state may be sitting with a blank sheet of paper in front of you. The goal state is the state you want to achieve (returning safely to the earth or producing a grade A essay). Something is only a problem if we do not know how to get from the start state to the goal state, since if we can immediately see how to achieve the goal state it is not a problem. For each problem there are different types of processes or actions that enable us to get from one state to another; these are called operators. For the crew of Apollo 13 the operators involved changes to navigation plans, conserving water, living in the lunar module, etc. Another feature of many problems is that the process of going from the start state to the goal state cannot be achieved in one stage – you have to pass through a number of inter- mediate stages to reach the goal state (see p.75). This chapter initially looks at problems that are designed by Copyright © 2003. Taylor & Francis Group. All rights reserved. psychologists and studied in laboratory settings. These problems are usually clearly defined and the start state, goal state and operators are specified. However, since most problems in real life are not well defined the chapter ends by examining problem-solving in real life. Types of problems There are many types of problems faced by people, both in laboratory studies and in everyday life, and many researchers find it useful to try to categorise them. For example, Robertson (2001) suggests that problems could be categorised according to the type of solution that is required. One way problems differ is in the level of knowledge needed to solve them. Some problems do not require much prior 66 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING knowledge to solve them (for example, the nine-dot problem on p.68); these are called knowledge-lean. However, other problems are knowledge-rich; that is, the solution requires prior knowledge (e.g. if I were to ask you to translate an article from a German news- paper you would need knowledge of German). The strategies used to find solutions to knowledge-lean problems can often be applied to a variety of problems and they are therefore domain-general. However, the strategies used to find the solutions to knowledge-rich problems are usually only useful to the particular type of problem and are therefore domain-specific. Problems can also differ in how well they are defined. When problems are well-defined the start state and the goal state are clearly identified. Furthermore, in well-defined problems the actions (or operators) which are allowed or prohibited are also known (see, for example, the Hobbits and Orcs problem on page 72). In ill-defined problems one or more of the parameters (start state, goal state, operators, prohibited operators) are not known. Problems can also be categorised as adversarial or non-adversarial. Non-adversarial problems are problems in which an individual or a group is required to find the solution to a problem but there is no competition with others. These problems are typically puzzles of some sort and are usually well defined but knowledge-lean and domain- general. Adversarial problems involve competition with other people and the goal is to defeat your opponent(s). These problems are typically games of some sort (such as chess) and usually knowledge-rich, domain-specific and less well defined than puzzles (although the rules or operators are explicit in adversarial problems the goal is beat the Copyright © 2003. Taylor & Francis Group. All rights reserved. opponent, not a specific state). The following discussion focuses on various approaches to under- standing non-adversarial problems before examining problem-solving in real life. (Readers interested in adversarial problems should refer to the ‘Further reading’ section at the end of the chapter and to Box 6.1 on p.79.) 67 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT Progress exercise Before studying the findings of research into problem-solving it is worth looking at some of the problems used by psychologists. Try solving them and note down the thoughts you have whilst thinking about each problem, or if you have a friend to work with act as ‘solver’ and ‘note-taker’ on alternate problems. 1. Nine-dot problem (see Figure 6.1) Draw four straight lines that go through all nine dots without taking the pen from the page or retracing your route. Figure 6.1 The nine-dot problem 2. Candle problem (based on Duncker, 1945) Copyright © 2003. Taylor & Francis Group. All rights reserved. First, collect together a candle, a box of matches and a box of drawing pins. The problem is how to attach the candle to a wall in such a way that it will not drip wax on the floor when lit. 3. The water jar problem (based on Luchins, 1942) Imagine you have three different-sized jars that can measure a precise volume of water. Jar A can hold 9 litres, jar B can hold 42 litres and jar C can hold 6 litres. The problem is how to measure 21 litres accurately. (The solutions are on pp.123–124 should you become too frustrated by any problem!) 68 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING Gestalt approach Some of the earliest psychological research into problem-solving was performed by Gestalt psychologists at the beginning of the twentieth century. The Gestalt approach originated in the study of perception and one of the basic ideas was that people perceive whole objects (rather than adding up the parts of an object). This approach was extended to problem-solving and the Gestalt psychologists believed that problem-solving required an understanding of the overall structure of a problem rather than focusing on each element of the problem in turn. Gestalt psychologists typically studied problem- solving by using verbal protocols (see p.6). They were more interested in the process of problem-solving than the solution, and verbal pro- tocols are a way of studying the process. From these studies of human problem-solving the Gestalt psychologists believed that solutions came from an insight into the problem and occurred when participants restructured the problem. Insight occurs when the participants are suddenly aware of the answer (i.e. the participant does not gradually work towards a solution, rather it appears in a flash). If you managed to solve the nine-dot problem in the progress exercise above you may have experienced insight. Once you realise that the lines do not have to be within the square formed by the dots the problem has been restructured. The concepts of insight and restructuring are illustrated by the Gestalt ‘two-string’ problem set by Maier (1931). In this problem participants were faced with two strings hanging from the ceiling and their task was to tie the two strings together. However, the strings were Copyright © 2003. Taylor & Francis Group. All rights reserved. set too far apart for the participants to reach both at once and if they held one string they could not reach the other. Maier left a number of objects lying on the floor and one solution to the problem was to use the pliers. If the pliers were tied to the end of one of the strings it acted as a pendulum and the string could be swung back and forth. The participant could then hold the other string and catch the swinging string. Some participants solved the problem quickly, and showed insight since they claimed that the solution suddenly came to them. Other participants needed help in restructuring the problem and Maier found that if he ‘accidentally’ brushed against the string to set it swinging participants who had been struggling suddenly saw the answer. The swinging string had enabled them to restructure the problem (although many claimed they were unaware of the hint). 69 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT Gestalt approach and thinking The Gestalt studies led to the idea that there are different types of thinking that can be applied to solving problems. Wertheimer (1945) distinguished between reproductive thinking and productive thinking. Reproductive thinking involves using previous experience of problem-solving to solve new ones. For example, if you were to learn a mathematical rule while solving one problem you could use this rule when faced with a similar problem. Whilst this approach can be useful it can also lead to problems since people do not notice the structure of the problem and may not see other simpler solutions. Reproductive thinking may be therefore ‘structurally blind’ (Robertson, 2001) and may result in a failure to find a solution or in an inefficient solution. Productive thinking, on the other hand, involves an under- standing of the underlying structure of the problem and is more likely to lead to a restructuring of the problem and an insight into the solution. Wertheimer (1945) illustrated the difference in the types of thinking by teaching two groups of students how to calculate the area of a parallelogram in two different ways. One group were taught to use a mathematical procedure that the area = length of base x perpendicular height (or h x b). The other group was taught to understand the formula by restructuring the parallelogram to form a simpler shape, a rectangle (if you cut one end off the parallelogram and place it at the other end you can form a rectangle). Both groups of students were able to calculate the area of parallelograms equally well. However, when faced Copyright © 2003. Taylor & Francis Group. All rights reserved. with other unusual shapes such as a circular segment missing at one end and a circular segment added at the other end the students who had learned the mathematical procedure could not calculate its area. They were using reproductive thinking and the formula they had learned did not help with the new problem. The participants who had been encouraged to focus on the structure of the original problem were able to calculate the area of other unusual shapes. Using productive thinking they were able to restructure other problems to find solutions. Reproductive thinking and problem-solving The Gestalt psychologists argued that there are a number of possible negative effects of past experience and reproductive thinking such as 70 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING problem-solving set and functional fixedness. Problem-solving set occurs when participants learn to solve a series of problems in a specific manner. The solution then becomes a habit (or a mental set) which is used even if a simpler solution is possible. For example, Luchins (1942) gave participants a number of variations of the water jar problem (see p.68). The control group of participants was asked to solve a series of problems that required different types of solution. The ‘set’ group was asked to solve a series of problems that all required a similar solution. All the participants were then presented with a critical test that could either be solved simply or by using a more complex solution based on that the set group had used. The control group tended to use the simple solution, but the set group tended to use the complex solution they had learned on previous trials. Functional fixedness occurs when we focus on the normal function of an object and therefore fail to appreciate that it could have alternative uses. This is illustrated in Duncker’s (1945) candle problem (see p.68). Many participants fail to solve the problem because they perceive the box containing the matches as a matchbox only and fail to recognise that it may have other uses – as a candleholder, for example. Evaluation of Gestalt approach The Gestalt approach has been very influential in the study of problem- solving. The basic method they used to study problems – verbal protocols – is still used in most research even now. Many of the problems they studied are still provoking debate some six decades after Copyright © 2003. Taylor & Francis Group. All rights reserved. they were first used. Eysenck and Keane (2000) point out that the information-processing approach (see p.73) owes much to Gestalt ideas such as productive thinking. However, despite the appeal of the Gestalt explanations of problem-solving there are a number of problems with the approach. Most of these stem from the vagueness of the concepts which the Gestalt psychologists used. For example, the notions of restructuring and insight are not clearly defined and there is little explanation as to why they occur or fail to occur. Both concepts seem to be intuitively accurate descriptions of solving problems but do not explain the underlying processes. 71 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT Progress exercise Try solving the following problems and, as with the previous exercise, record your thoughts as you try to solve them. 1. Tower of Hanoi (see Figure 6.2) Move the rings on peg A so that they form an identical arrangement on peg C. Only one peg can be moved at a time and a larger ring cannot be placed on top of a smaller ring. (NB: This is a simple version of this problem; the more rings the more difficult it becomes!) A B C Figure 6.2 Tower of Hanoi Copyright © 2003. Taylor & Francis Group. All rights reserved. 2. Hobbits and Orcs (see Figure 6.3) Imagine there are three Hobbits and three Orcs on one side of a fast- flowing river. Everybody in the party needs to cross the river but there is only one canoe and this can only carry two at a time. Getting the whole party across is complicated by the aggressive nature of the Orcs because if the Orcs outnumber the Hobbits on either bank they will kill those Hobbits. This includes any Orcs that come to the shore in the canoe. Hobbits, on the other hand, are peace-loving creatures and it does not matter if they outnumber the Orcs. The strong current means that at least one Hobbit or Orc has to be in the canoe to make the crossing in either direction. What is the least number of crossings with the canoe that need to be made to get the whole party safely across? 72 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING Start State H H H O O O Goal State H H H O O O Copyright © 2003. Taylor & Francis Group. All rights reserved. Figure 6.3 The Hobbits and Orcs problem (The solutions are on pp.124–128.) Information-processing approach Much of the information-processing approach to problem-solving stems from the work of Newell and Simon (1972). Their book Human Problem Solving describes and explains many of the key concepts of the information-processing approach. One of these key concepts is that, like computers, humans can only solve problems by analysing and manipulating information. In trying to solve a problem we have to use a number of sequential stages to reach the solution. Sometimes 73 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT these stages do not lead to a solution and we have to go back a few stages and try again. In the Tower of Hanoi problem on p.72, for example, one might think about putting the smaller ring on peg B and the middle ring on peg C before realising that the largest ring could not go on either peg. Newell and Simon called this type of mental representation of the problem the ‘problem space’. Once we know the initial state – and the operators we can use – the problem space is like the mental path we take to the goal state. Sometimes this will involve going down the wrong path and we have to go back to try another route. In a problem like that of the Hobbits and Orcs (p.72) the possibilities that can exist in the problem space increase with each successive move. Newell and Simon (1972) used these ideas to develop a computer program called the General Problem Solver (GPS). The GPS was designed as a model of human problem-solving and was based on studies of people solving problems. One important aspect of the GPS was the strategy it was programmed to use for solving problems. Based on their earlier work, Newell and Simon (1972) outlined two distinct problem-solving strategies. One strategy for solving problems is to use algorithms. This algorithmic method involves a systematic search of all the possible solutions to a problem until the correct answer is identified. For example, if you are asked to solve the following anagram, ‘u n q i e t o s’, you can find the solution by systematically examining all the possible solutions. So the next combination you try may be ‘u n q i e t s o’ and the next ‘u n q i e s t o ’, etc. Eventually a systematic search of the 40,320 possible combinations of these letters Copyright © 2003. Taylor & Francis Group. All rights reserved. would reveal one or more recognisable words. However, most research suggests that humans do not use this approach often because a search of all of the possible solutions takes too much time and effort. The alternative approach is to use rules of thumb that act as short cuts and enable a selective search for the most likely solutions. These rules of thumb are called heuristics, and are solutions that often work although they do not guarantee finding the correct solution. In the example of the anagram above there is a ‘q’ and a ‘u’, and we know that they go together in English; we also know that ‘ion’ is a common combination. These short cuts, or heuristics, would probably lead to the solution – in this case, ‘question’. However, this solution is not guaranteed. We could use the heuristic that ‘un’ is a common beginning to words and by focusing on this fail to find the correct solution. 74 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING The heuristic strategy Newell and Simon built into the GPS was means-ends analysis. Means-ends analysis was a heuristic device that was observed in human problem-solving. When faced with a complex problem we cannot usually find a solution that requires one operation (i.e. we cannot go straight from the initial state to the goal state); rather, we have to break the problem up into a series of sub-goals that we tackle one at a time. Each sub-goal is used to reduce the difference between the initial state and the goal state. Of course setting a goal does not guarantee that it will be achieved, and each sub-goal (or ‘end’) requires an operator (or ‘means’) to achieve it: hence the name ‘means-ends analysis’. In human problem-solving requiring a series of moves, like the Hobbits and Orcs problem, participants do not make moves steadily from the initial state to the goal state but pause before making groups of moves (e.g. Greeno, 1974). This seems to reflect sub-goaling: when the participant solves one sub-goal they make a series of moves before considering how to achieve the next sub-goal. The computer simulation of the means-ends analysis that Newell and Simon (1972) built into the GPS successfully mimicked the behaviour of humans on a number of problems. For example, Thomas (1974) found that human participants have difficulty with the Hobbits and Orcs problem because the most successful solution at one point requires two creatures to return across the river. This does not seem to reduce the difference between the initial state and goal state but to increase it, and participants are reluctant to make this move. (Look back at your notes for the previous exercise; did you get stuck after Copyright © 2003. Taylor & Francis Group. All rights reserved. move 5? Move 6 is the one which requires one Orc and one Hobbit to go back to the bank that they started on.) The GPS successfully mimicked this and the manner in which participants solved other problems Evaluation of the information-processing approach Newell and Simon’s work on the information-processing approach has had an enormous impact on the understanding of problem- solving. They put forward a theory that introduced a variety of key concepts in the area, such as the use of heuristics in problem-solving and a large body of research that examined the topic. Eysenck and Keane (2000, p.407) claim that the theory ‘makes substantial and 75 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT fundamental contributions to cognitive theory and to our understanding of people’s problem-solving abilities’. Despite this Newell and Simon eventually abandoned the GPS because it only applied to certain types of problem – specifically well-defined problems. However, most of the problems the people solve tend to be ill-defined (see p.67). In addition, people are often faced with several problems that they have to deal with at once, but the GPS was designed to solve problems one at a time (Matlin, 2002). Nevertheless the concepts that Newell and Simon introduced are still at the core of research and theory into problem- solving. Information processing and ‘insight’ The information-processing approach seems to work well on problems that require step-by-step solutions (such as the Hobbits and Orcs problem) where a sequence of moves are needed to achieve the goal state. However, this approach seems to have some difficulty in explaining the types of problems studied by the Gestalt psychologists, problems whose solutions require ‘insight’ (such as the nine-dot problem). Knoblich et al. (2001) suggest that such problems pose a double challenge for the information-processing approach. Firstly, why do people fail to solve these problems for some time when most have the ability to do so? Secondly, what is it that allows people to break the impasse and solve the problem? People do not receive any new information yet the answer frequently appears suddenly. This Copyright © 2003. Taylor & Francis Group. All rights reserved. raises the question of whether information processing can explain problems that seem to require insight. Some researchers have suggested that there is a distinction between insight and non-insight problems. For example, Metcalfe and Wiebe (1987) investigated participants’ ‘feeling-of-knowing’ (or FOK) as they attempted to solve both insight and non-insight problems. FOK is the individual participant’s estimate of how close they are to solving a problem. During non-insight problems the participant’s FOK gradually increased from very low (e.g. definitely do not know the answer) to high (e.g. getting very close to an answer). However, when attempting to solve insight problems the participant’s FOK remained low until just before the answer was found. This suggests that there is a distinction between the two types of problem. 76 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING Nevertheless, there have been a number of information-processing accounts of insight such as Kaplan and Simon (1990) or MacGregor et al. (2001). Robertson (2001) points out that the accounts tend to have many features in common and that these features, such as searching through a problem space or retrieving relevant operators from memory, are found in accounts of non-insight problem-solving. For example, Kaplan and Simon (1990) suggest that insight-type problems require a search for an appropriate problem space (see p.74) whereas non-insight problems require a search through a problem space for a solution. More recently, MacGregor et al. (2001) have proposed a computational model of participants’ performance on the nine-dot and similar problems. The model has a number of components which are typical of information-processing models, such as searching the problem and selecting moves that maximise the number of dots with a line through them (e.g. a difference-reduction heuristic). The model seems to predict a participant’s performance on the problems well and to explain why the problem cannot be solved initially and how the solution is reached. Robertson (2001) notes that ‘MacGregor et al. have succeeded in building a detailed process model of success and failure on abstractly defined problems.’ Use of analogy in problem-solving Another type of heuristic device for solving problems is to adapt solutions for similar problems from the past. This type of heuristic is the use of analogy. For example, if I find a solution to the problem Copyright © 2003. Taylor & Francis Group. All rights reserved. of how to cut five equal portions of a pie I can adapt that solution if faced with the problem of cutting five equal portions of a pizza. Analogies clearly have the potential to be a very useful problem-solving heuristic – but do people use them? One way of studying the use of analogies is to present participants with a problem together with the solution and then present them with an analogous problem. The participant’s performance can then be studied to assess whether they use the analogous solution or not. One example of this approach is a study by Gick and Holyoak (1980). They used an analogous problem to the ‘inoperable tumour problem’ that was originally posed by Duncker (1945). In the original problem participants are told of a patient who has an inoperable tumour that can only be cured by a strong dose of radiation. However, although weak doses of radiation do not harm 77 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT normal tissue the strong dose required to cure the tumour would not only destroy the tumour but the surrounding tissue as well. The solution to this problem is to aim a number of weak beams of radiation at the tumour from different angles. These weak beams do not harm the normal tissue but combine to form a strong concentration on the tumour. The analogous problem introduced by Gick and Holyoak (1980) involved a general trying to capture a fortress that can be approached by a number of roads. However, each of these roads is mined and any large group of troops would detonate the mines, although a small group would not. The solution is analogous to the solution to the inoperable-tumour problem since a number of small groups of troops can be sent down each road to form a large force at the fortress. Gick and Holyoak found that merely presenting the general’s problem did not improve participants’ performance on the inoperable-tumour problem, but if participants were instructed to use the analogy they performed better. There seem to be a number of factors that affect whether analogies are used or not. One factor that has been widely investigated is the degree of similarity of the analogous problems. These studies suggest that participants tend to focus on the superficial content of the problem (or the surface features) rather than the underlying similar- ities (or the structural features) or the principles of the problem and solution (Matlin, 2002). For example, if given two problems with similar surface features, such as treating an inoperable brain tumour and treating an inoperable lung tumour, participants can transfer the solution well. However, participants are less good at Copyright © 2003. Taylor & Francis Group. All rights reserved. transferring solutions between two problems with different surface structures but with the same essential structural features (such as the inoperable tumour and the general’s problem). Matlin (2002) also notes that solutions to problems are often context-bound. Thus a solution learned in one context is not easily transferred to another context or setting. Although a number of studies suggest most participants do not use analogous problem-solving well there are a number of methods for increasing the effective use of analogies. Matlin (2002) outlines four factors that seem to improve analogous problem-solving. She notes that the use of analogies increases if: 1. Participants are given explicit instructions to compare problems. 78 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING 2. Participants are shown several structurally similar problems before being given a similar one. 3. Participants are given a hint that the solution to an earlier problem may be helpful. 4. Participants study the structure of the problem rather than the surface features. However, these conditions do not usually exist in everyday life because when we encounter a problem we are not told to compare it to previous problems, nor are we guided to concentrate on the structural rather than surface features, etc. Therefore there is doubt about the relevance of analogies in solving real-life problems. Box 6.1. Adversarial problems: game playing and expertise In the studies of non-adversarial puzzle solving the problems used required novel solutions and were not based on previous knowledge (knowledge- lean problems). However, many problems people face are knowledge-rich and require practice or training to develop expertise in a topic. If my car failed to start I would not be able to fix it because I have no knowledge of how an engine works. I would have to call a mechanic who has knowledge of car engines and expertise in diagnosing and fixing engine problems. The study of adversarial problems has allowed researchers to investigate the development of expertise and to compare the difference in strategies between Copyright © 2003. Taylor & Francis Group. All rights reserved. novices and experts. Another feature of adversarial problems is that, like many real problems, the goal state is not well defined. In a game such as chess the goal state is to beat the opponent, but there is no set position for any of the chess pieces. Many of the studies of both adversarial problems and expertise have concentrated on chess for a number of reasons. Firstly, chess potentially presents a very complex problem and it is estimated that from an opening board there are 10120 possibilities (Garnham and Oakhill, 1994). Secondly, performance in chess can be evaluated, either by who wins or by using the agreed rating scale to measure the ability of any player (from novice to grandmaster). Much of the work on performance in chess stems from DeGroot (1965) who studied the difference between grandmasters and good players. He found that players considered a relatively limited amount of moves, and that, 79 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT surprisingly, the grandmasters did not consider more moves than the less- expert players. However, the grandmasters made quicker moves that were judged to be better. The limited consideration of alternatives shown by grandmasters is in contrast to computer chess programs which tend to consider a huge number of alternatives. For example, Deep Blue searches about 90 billion alternatives each move. This is clearly not possible for a human player, yet until recently computer ‘players’ could not beat the best human players. This suggests that human players must have some other means to achieve expertise rather than a detailed analysis of every alternative move and countermove. DeGroot proposed that experts differed in their knowledge of board positions. Grandmasters have a great deal of experience of playing chess and tend to study the games of other experts. This knowledge enables them to discount irrelevant moves and concentrate on a few likely ones. Other studies have shown that it is not just knowledge and memory that differentiates experts from non-experts – they also differ in the way information is used. Garnham and Oakhill (1994, p.226) point out that experts’ knowledge ‘is organised differently from that of novices, and it enables them to encode new information more efficiently’. For example, Chase and Simon (1973) asked three chess players of differing ability to replicate the position of pieces on a board. They recorded the timing of each glance at the board and how many pieces were placed on the second board after each glance. They found that the expert player recognised ‘chunks’ of the board quicker and was able to recognise more pieces with each glance than the novice could. Copyright © 2003. Taylor & Francis Group. All rights reserved. The study of games like chess has led to a great interest in experts, and it is an important topic in cognitive psychology. Apart from increasing our understanding of how people become expert the studies have led to the development of computer simulations of experts or ‘expert systems’. These studies have not been limited to chess or other adversarial games but to expertise in a wide range of human activity, including medicine, physics and writing. Although the nature of expertise may differ there seem to be some common features of experts. Robertson (2001) discusses a number of these features; among the most important are: 1. Experts tend to be expert in one area (or domain). 2. Experts are able to categorise problems quicker than novices. 80 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING 3. Experts are more efficient in perceiving chunks of information than novices. 4. Experts have efficient strategies for using long-term memory for dealing with tasks whereas novices tend to rely on short-term memory (which is limited). Problem-solving in everyday life Most of the problems described so far in this chapter have been well-defined problems that have been studied in controlled settings. However, the problems we encounter in everyday life are not well defined and often we have only a vague notion of the goal state and a poor understanding of the possible processes to achieve it. Furthermore, we frequently need to find solutions whilst dealing with various sources of distraction. This raises the question of the relevance of the formal studies of problem-solving. There is a danger that these studies only show how people solve abstract problems in psychology laboratories and have little to do with real life. An obvious way of addressing this issue would be to study ‘normal’ problem- solving in a natural setting such as home or work. However, there have been surprisingly few studies of this kind. Garnham and Oakhill (1994) have suggested a number of reasons for this. Firstly, unlike the laboratory-based studies, there is not a clearly recognised method for studying natural problem-solving. Secondly, there are problems Copyright © 2003. Taylor & Francis Group. All rights reserved. in understanding how the participants interpret the problem and their interpretation may be very different to that of the researcher. Finally, in contrast to the laboratory-based problems, real-life problems seldom have a correct or ideal answer and it is therefore difficult to assess the participant’s performance. Despite these problems there are a few studies of real-life problem- solving. For example, Carraher et al. (1985) studied the mathematical abilities of children selling goods in Brazilian street markets. They found that, despite a lack of formal education, the children solved complex mental arithmetic problems which related to their usual activities when they were tested on the streets. Carraher et al. (1985) also found that the children often used unusual methods to solve mental arithmetic problems. However, when they were moved to a more 81 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  LANGUAGE AND THOUGHT formal setting and asked to solve similar problems they did less well. It seems that, as with the more controlled studies, the ability to solve problems is not easily transferred from one context to another. Scribner (1984) looked at everyday problem-solving by studying different groups of workers in a dairy. As with the previous study, Scribner found that people used innovative and efficient methods for solving problems. One worker, who had to prepare cases and part cases for delivery, claimed not to count out the orders but to visualise the numbers needed. The workers at the dairy were better at finding optimal solutions to loading the deliveries than people, such as students, who had formal training in arithmetic. Garnham and Oakhill (1994) suggest that findings like these show that people are more adaptable and inventive in real life than in formal laboratory studies. Perhaps when problems are real and solutions bring tangible rewards (such as less walking backwards and forwards to prepare a delivery) people are more motivated to find solutions, or perhaps real-life problems have more relevance. Whatever the reason, Garnham and Oakhill (1994, p.271) claim the findings of the real-life problem-solving ‘indicate a need to be cautious in drawing conclusions about ordinary thinking from the results of laboratory studies of how people solve contrived problems’. Summary Problems are a common aspect of our daily lives and they occur when we cannot immediately perceive the way to goal state. One of Copyright © 2003. Taylor & Francis Group. All rights reserved. the earliest approaches to study problem-solving was the Gestalt approach. This approach emphasises the way problems are looked at as a whole and concentrated on insight methods of problem-solving. They suggested that solutions required restructuring of the problem. Although the Gestalt approach provided some useful methods of studying problems it did not provide an adequate explanation of problem-solving. A more recent approach to problem-solving is the information-processing approach, typified by the work of Newell and Simon (1972). They developed a computer program called the General Problem Solver (GPS) which used heuristic methods of solving problems. Heuristics are rules of thumb that can be used as short cuts to find solutions, but they do not always provide the correct solution (as opposed to algorithms that do find the correct solution in 82 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  PROBLEM-SOLVING a systematic way, although this can be slow). The heuristic used in the GPS was ‘means-ends analysis’. Solving problems with means- ends analysis involves breaking down the problem into sub-goals which help reduce the difference between the initial state and the goal state. Another heuristic that could be used for solving problems is the use of analogies. If a person learns or is shown the solution to one problem they should in theory be able to use this solution to help solve a similar problem. However, this heuristic is only used when the surface features of the problems are similar or if participants are given instructions to pay attention to the structural features. A number of studies of problem-solving in real life have suggested that people are inventive and adaptable and have led to doubts about the relevance of the laboratory-based studies. Write a brief description of the following approaches to the study of problem- Review exercise solving: 1. Gestalt approach. 2. Information-processing approach. 3. Use of analogies. List one positive and one negative criticism of each approach. Further reading Copyright © 2003. Taylor & Francis Group. All rights reserved. Garnham, A. and Oakhill, J. (1994) Thinking and Reasoning. Oxford: Blackwell. This is an advanced textbook that has a good chapter on problem-solving (non-adversarial problems). It also has an interesting chapter on game playing and expertise (adversarial problems). Robertson, S.I. (2001) Problem-Solving. Hove: Psychology Press. This book is aimed at undergraduates, but it is also very accessible to A-level students. It explains ideas very clearly and is written in an engaging and witty style. 83 Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.  This page intentionally left blank Copyright © 2003. Taylor & Francis Group. All rights reserved. Lund, Nick. Language and Thought, Taylor & Francis Group, 2003. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/cityuhk/detail.action?docID=199320. Created from cityuhk on 2024-11-22 07:40:52.