On August 14, 2003, a power failure caused millions of people in the northeastern and midwestern United States and eastern Canada to lose their electricity. A few days later, after most people had their electricity restored, experts still did not know why the power failure had occurred and said it would take weeks to determine the cause. Imagine that you are a member of a special commission that has the task of solving this problem, or some other major problem. How could the processes described in this chapter be applied to finding a solution? What would the shortcomings of these processes be for solving this kind of problem?
Scholars Portal PDF Export Towards a theory of thinking Author(s) Glatzeder, Britta ; Goel, Vinod ; Mèuller, Albrecht A. C. von Imprint Berlin ; London : Springer, c2010 Extent p. Topic BF Subject(s) Thought and thinking; Thought and thinking -- Physiological aspects Language English ISBN 9783642031298, 3642031293 Permalink http://books.scholarsportal.info/viewdoc.html?id=370306 Pages 26 to 44 3B.M. Glatzeder et al. (eds.), Towards a Theory of Thinking, On Thinking, DOI 10.1007/978-3-642-03129-8_1, © Springer-Verlag Berlin Heidelberg 2010 There is no problem so big it can’t be run away from. – Charles Schultz Abstract Problem solving and thinking are inseparably linked together. We propose that a theory of thinking has to consider and incorporate the notion of problem solving. In this chapter, we review the most important accounts of problem solving and hope to convince the reader that problem solving may provide an ideal framework for developing a theory of thinking. We start with a broad summary on the Gestaltist perspective. The Gestaltists per se understood thinking as problem solving. They invented a large body of theoreti- cal concepts and ingenious tasks that until now influence cognitive psychology in general and unexpectedly affects the development of the information processing account also. However, this influence becomes less and less explicit and is not appropriately recognized. We hope to stress this connection and bring it back to the readers’ minds. Nevertheless, the Gestaltist approach has its weaknesses and meth- odological flaws, which will be dealt with in this chapter. A large section is dedicated to the information processing account that still dominates the problem solving literature as a clear and proper account for describ- ing and defining human problem solving. We elaborate on the differentiation between well and ill-defined problems and provide several foundations and models derived from this account. Nevertheless, the information processing account has its limits and we conclude with some extensions of the classical account and provide an integrative model for insight problem solving. M. Öllinger (*) Parmenides Center for the Study of Thinking, Munich, Germany e-mail: [email protected] V. Goel Department of Psychology, York University, Toronto, Canada Department of Psychology, University of Hull, UK e-mail: [email protected] Problem Solving Michael Öllinger and Vinod Goel 4 M. Öllinger and V. Goel 1 Introduction In this chapter, we will focus on the study of thought processes through the study of problem-solving. Problem solving can be understood as the bridging of the gap between an initial state of affairs and a desired state where no predetermined opera- tor or strategy is known to the individual. For example, consider the following task: 3 × 4 = ? This task does not constitute a problem for most adults. They can automati- cally produce the result from memory. For a 7-year-old child, on the other hand, who is learning to multiply, it is a problem. The child has to consciously apply rules and procedures to bridge the gap between the initial problem state and a solution state. For a 2-year-old the situation is not recognizable as a problem because the child lacks the knowledge and semantics to understand what he/she is being asked to do. In the following sections we will review psychological theories on problem solv- ing, beginning with the work of the Gestaltist psychologists, and the subsequent development within the framework of information processing theory, and then point out two outstanding challenges that the information processing framework needs to confront and overcome. 2 The Gestaltist Perspective At the beginning of the last century, the Gestaltist approach (Wertheimer 1912, 1925, 1959; Koffka 1935; Katona 1940; Duncker 1945; Köhler 1947) emerged as a countermovement to the dominant learning theory of Behaviorism. For the Gestaltist, thinking was not a reproductive recombination of learned associations but the meaningful effort to understand the fundamental nature and affordances of the given problem situation and the desired goal as a whole. They assumed that thinking obeyed similar basic principles (Gestalt laws) as perception. The Gestaltist idea was that, as in the flipping of the Necker Cube, there are also major transitions during the process of problem solving characterized by restructuring the given information in new and nonobvious ways. Restructuring reveals the fundamental structure of the problem. Problem solving was viewed as a process of transforming a disturbed Gestalt into a good Gestalt (“gute Gestalt”). It is a goal directed behav- ior that clears out existing barriers in the service of gaining a desired end (for an overview see Ash 1998; Öllinger and Knoblich 2009). Between 1914 and 1917 Wolfgang Köhler investigated chimpanzees on Tenerife island. He addressed the question of whether chimps are able to solve problems in an intelligent way. He hoped to find evidence against the Behaviorist dictum that animals solve problems by pure trial and error (Thorndike 1911; Köhler 1921, 1925). He claimed that intelligent behavior can be observed when the obvious way to the goal is blocked by a barrier. That is, intelligence is used to elude existing barriers in new and unfamiliar situations. He created situations in which his apes had to solve problems. Sultan, the star pupil, was asked to get a banana that was out of reach. There were two sticks lying around in the compound. After a few minutes 5Problem Solving Sultan purposefully joined the sticks together and successfully fished for the banana. For Köhler these findings provided evidence that some animals were able to solve problems not simply by blind and mindless trial and error attempts, but by insight into the affordances of the given situation. Max Wertheimer the most famous and influential Gestaltist was particularly interested in the sudden moment of restructuring that accompanied insight in a given problem. Wertheimer contrasted productive thinking (Wertheimer 1959) with reproductive thinking (Thorndike 1911). He was certain that productive thinking is superior to reproductive thinking, because it is characterized by gaining deep insight into the relations of the given problem constituents and their role in the given task, and the resulting solution. Wertheimer worked on a general psychologi- cal theory of problem solving that can be applied to various phenomena, ranging from low-level perceptual phenomena, to solving problems like crypt arithmetic, to explaining great scientific inventions, to problems in the social domain (Wertheimer 1959). Restructuring was the basic mechanism for resolving problems across a wide range of domains. The Gestaltists demonstrated what they meant by “restructuring” in a series of elegant examples (Wertheimer 1925, 1959). Figure 1a depicts a typical example. The task is to determine the area of the isosceles triangle, given the length of the side s and the angle at the apex (90°). At first glance people might try to determine the two segments g and h in order to apply the triangle formula ½ g × h for the area. This is a laborious approach. However, rotating the triangle reveals that the triangle can be understood as one half of a square with the diagonal g and the side with the length s (Fig. 1b). Now, the area can be determined by the simple formula s × s / 2. Restructuring the given situation requires a problem solver to overcome the reproductive tendency to compute the triangle area in the usual way and see it in a new way as part of a larger good Gestalt. Another problem that Wertheimer analyzed was the famous enumeration prob- lem solved by the young Gauss. The task was to add as quickly as possible the sum Problem h a b g S Solution S h g S Fig. 1 Wertheimer’s Triangle problem (a). The task was to determine the area of the given tri- angle. Insightful solution of the problem (b) 6 M. Öllinger and V. Goel of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10. Anecdotally, it is said that almost imme- diately Gauss proclaimed “Here it is!”, and he showed his disbelieving teacher the correct solution (see Fig. 2). The reproductive solution requires stupid blind successive addition of consecutive numbers. However, Gauss found a productive solution in terms of a general principle of arithmetic progression ((n + 1) × (n/2); n = length of a series). Of course, the longer the series the more effective is the productive approach. The reader is invited to try both approaches on a series from 1 to 100. Probably the most important Gestaltist work on problem solving was reported by Karl Duncker in his Monograph: On Problem-Solving (Duncker 1945). Duncker extended the basic principle of restructuring by a general framework that views problem solving as a stepwise process situated in a problem space which people navigate by means of strategies or heuristics. Duncker anticipated some concepts that later became the fundamentals of Newell and Simon’s Problem Space Hypothesis (Newell and Simon 1972). Duncker also introduced a number of classical problems, like the radiation prob- lem and the candle problem, into the literature. The radiation problem asked the following question: Given a human being with an inoperable stomach tumor, and rays which destroy organic tissue at sufficient intensity, by what procedure can one free him of the tumor by these rays and at the same time avoid destroying the healthy tissue which surrounds it? (Duncker 1945, p. 1–2). This has proved to be a fairly difficult problem. The solution is to use more than one laser of weak intensity and arrange them in a way that their rays exactly meet right in the heart of the tumor. The superimposed radiation destroys the tumor and does no harm to the surrounding tissue. In Duncker’s studies, participants were asked to “think aloud” or verbalize thoughts and ideas as they are attended to, while solving the problem. This technique has become an important methodical instru- ment, within information processing theory, for mapping intermittent steps in thinking processes onto cognitive models (Schooler and Engstler-Schooler 1990; Ericsson and Simon 1993; Schooler et al. 1993, Goel and Pirolli 1992). Duncker analyzed the thinking-aloud protocols and systematically developed graphs, such as in Fig. 3. 55 5 ∗ 11 11 1 2 3 4 5 6 7 8 9 10 11 11 11 11+ + + + +++++++++ Fig. 2 Gauss’ Enumeration Problem. Determine the sum of the given series. The trick is to re-cluster the problem elements and multiply the number of clusters. In this case the value of a cluster is 11 and there are 5 of those clusters 7Problem Solving T as k