Scandinavian Journal of Psychology, 1988, 29, 85-94

Mental models and problem solving: Three challenges to a theory of restructuring and insight

HENRY MONTGOMERY Department of Psychology, University of Gothenburg

Montgomery, H.: Mental models and problem solving: Three challenges to a theory of restructuring and insight. Scandinavian Journal of Psychology, 1985,29, 85-94

The Gestalt psychologists’ view of restructuring and the associated phenomenon of insight is discussed and related to findings in modern cognitive psychology. In line with Ohlsson (1984b) it is assumed that search in semantic memory is an indispensable part of restructuring. However, in contrast to Ohlsson‘s (1984b) information processing theory of restructuring and insight the present paper focuses on the role of mental models. It is asserted that the Gestalt approach to problem solving is compatible with the idea that a mental model is manipulated. The paper discusses three assumptions of restructuring and insight, all of which are related to mental models: (a) restructuring involves manipulating a mental model; (b) the experience of insight is based on “seeing” something in a mental model; (c) restructuring aims at realizing structural balance in a mental model. TO assess the validity of these three assumptions is seen as a challenge to future research on human problem solving.

Henry Monlogmery, Department of Psychology, University of Gothenburg, BO.K 14158, S-400 20 Goteborg, Sweden.

Long before the launching of modern cognitive psychology the Gestalt psychologists attempted to understand thought processes involved in problem solving. In particular, they focused on the phenomenon of restructuring, i.e. when the problem solver finds a new way of viewing the problem situation. Restructuring was assumed to be the crucial event in produc- tive problem solving. The Gestalt psychologists saw a close connection between restructuring and another phenomenon in problem solving, viz. the experience of insight. This experience occurs as a result of a successful restructuring. The problem solver is then able to “see” how the problem can be solved.

Modern cognitive psychology has undoubtedly sharpened the understanding of human thought processes. We now have powerful and relatively precise concepts, like semantic networks and specific operators or heuristics, by which human thinking can be described and even simulated step by step. Using this conceptual apparatus, can we also understand restruc- turing and insight in problem solving? TO what extent is it possible to capture the Gestalt approach to restructuring and insight by concepts from modem cognitive psychology?

Ohlsson (1984b) addressed the above questions and concluded that two important theories in modern cognitive psychology, the information processing theory of problem solving and the semantic network theory of memory, account in a parsimonious manner for the phenomenon of restructuring as discussed by the Gestalt psychologists. The former theory implies, accord- ing to Ohlsson, that restructuring occurs when the problem solver changes his representation of the problem in such a way that the applicability of particular problem-solving operators is affected. Semantic memory theory sheds light on the cognitive processes underlying a restruc- turing event. These processes were assumed to be of two kinds, viz. (a) retrieval processes which search semantic memory for concepts that can be used for reinterpreting some part of the given situation and (b) attempts to propagate a new interpretation to other parts of the problem-solving situation. Insight is hypothesized to occur when the problem solver can reach

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the goal state by constructing a short enough path that he can think through in his head. Ohlsson’s line of reasoning was later elaborated by Keane (1985).

The discussion thus initiated by Ohlsson (1984b) is continued here. In line with Ohlsson, I will assume that search in semantic memory is necessary for restructuring and insight to occur. However, inspired by the writings of the Gestalt psychologists and by findings in modern cognitive psychology I will make three additional assumptions about these phenomena. All three assumptions are related to the idea that mental models are important components of human thinking. The three assumptions are: (a) restructuring involves manipulating a mental model; (b) the experience of insight is based on “seeing” something in a mental model; (c) restructuring aims at realizing structural balance in a mental model. When an appropriate structural balance has been attained the problem solver experiences insight.

MENTAL MODELS AND GESTALT PSYCHOLOGY

The ability to create and manipulate mental models of hypothetical or real phenomena in physical reality has been assumed to be a fundamental characteristic of human thinking (Gentner & Stevens, 1983; Johnson-Laird, 1983; Johnson-Laird et al; 1984). Mental models are models of something. They represent more or less accurately affairs in the world. However, there are also other mental representations. Johnson-Laird (1983) distinguishes between three types of mental representations, viz. propositional representations, images and models. Images are closely related to models inasmuch as they correspond to different viewsof a particular model (e.g. the mental model of a pyramid may be viewed from different angles). Propositional representations are characterized as “strings of symbols composed from a finite vocabulary” (Johnson-Laird, 1983, p. 151). The main difference between propositional representations and mental models is that the former type of representation has an arbitrarily chosen syntactical structure whereas the structure of mental models is structured analogously to the corresponding state of affairs in the world. The analogical structure of mental models implies that problems can be solved by “reading off’ a mental model. This is because when the problem is solved the structure of the model will be analogous to the structure of some hypothetical or real state of affairs in the world corresponding to the solution of the problem.

Mental models have a number of properties in common with physical objects although they may represent more or less abstract states of affairs in the world. They can be inspected and specific characteristics of the model can be read off. They have a finite size and cannot directly represent an infinite domain (Johnson-Laird, 1983, p. 398). They can be manipulated in ways which correspond to operations that can be done with physical objects. Also in models that represent abstract states of affairs elements may be moved and grouped in different ways.

A large number of studies have presented evidence for the use of mental models, or of related mental constructs such as images (e.g. Gentner &Stevens, 1983; Johnson-Laird, 1983; Kosslyn, 1980; Shepard, 1978) In the present paper it will be assumed that the use of mental models is indeed a fundamental characteristic of human thinking. As a working assumption, it will be taken for granted that insightful problem solving as a rule involves the manipulation of a mental model. However, the validity of this assumption needs to be further tested in future research.

To my knowledge, the Gestalt psychologists did not explicitly use the term “mental models”. However, it often appears that their descriptions of problem-solving processes are compatible with the idea that a mental model is manipulated. Duncker (1935/1945) obviously referred to a phenomenon corresponding to mental models when he discussed a possible solution to Kant’s classical problem: How is synthetic knowledge a priori possible? Duncker

Scand J Psycho1 29 (1988) Mental models and problem solving 87

expresses this problem as follows: how is it possible to directly understand that a fact “b” follows fromanother fact “a”. For example, how can we understand directly that a>b and b>c implies a>c. Duncker gives the following answer:

I can demonstrate the meaning of “greater” on all kinds of objects. With the help of the concepts so obtained a clear “paradigmatic” situation, “a greater than b and b greater than c”, can be constructed. From the situation SO constructed, the fact, “a greater than c” may now be read OH. Yet-and this is the important point-this fact was not needed in the construction of the situation, the “foundation” from which it is now being read off (p. 49).

Duncker adds “We shall call a situation ‘paradigmatic’ if it is constructed for the mind’s eye by the exclusive use of the concepts expressively contained in the premises”.

The use of the terms “reading off’, “constructing” and “the mind’s eye” clearly suggests that Duncker was referring to a concept corresponding to mental models. Hence, Duncker’s solution to the problem of how synthetic knowledge or evidence is possible, according to the above quotation, could be expressed as follows: synthetic knowledge can be obtained by “reading off’ facts from a mental model which were not used for constructing the model. Duncker makes strong claims for the importance of synthetic evidence in human thinking and, hence, indirectly for the importance of mental models. He writes: “The kind of experience in which synthetic evidence occurs represents the psychological medium of all productive think- ing . . .” (p. 52).

In his book Productive thinking the Gestalt psychologist Wertheimer (1935/1959) offered a number of concrete examples of how problems are solved in an insightful way. I t appears that for all these examples Wertheimer described operations that could be seen as analyses or transformations of a mental model. Table 1 presents data supporting this assumption. The table gives an analysis of four of Wertheimer’s (1945/1959) demonstrations of “productive” problem solving. In each case the problem-solving process is based on some sort of model of the problem situation. The model is described as an image of a physical object (Problems 1 and 3), as a concrete example of elements of the problem situation (Problem 2) or as a schematic network-like description of the problem situation (Problem 4). For each problem it is shown how the problem is solved by carrying out various operations on the model. As already indicated the operations may be divided into two groups, viz. (a) analytical operations such as identifying subwholes and grouping of items, and (b) transformational operations such as moving items, shrinking parts of the model, or recentring the model. The analytical operations imply that patterns are discovered in the model without changing the model as such whereas the transformational operations imply that the model is changed in some way or another. Common to both types of operations is that they are analogous to operations that may be carried out with a physical object.

Kohler, another well-known Gestalt psychologist, also investigated how humans (and apes) solve problems. In his last book The task of Gestaltpsychology he stated that in “the solution of a problem . . . we suddenly become aware of new relations, but these new relations appear only after we mentally changed, amplified or restructured the given material”. This statement obviously refers to some kind of mental object the character of which is changed as a result of the problem-solver’s operations with the object. Moreover, the operations referred to may correspond to operations carried out with a mental model (in particular the “amplifying” operation).

Thus, it appears that the Gestalt psychologists’ descriptions of problem-solving processes are compatible with the notion of manipulating a mental model. Still, it is interesting to speculate how the Gestalt psychologists would answer if they were asked whether their view of problem solving is consonant with the mental model notion. It is obvious, I believe, that

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Table 1. Analysis of restructuring in problem solutions described by Wertheimer ( 1 9 6 / I Y S Y )

Problem no. 1 2 3 4

Problem Find area of Ficd principle for Find sum of Two boys, A and B, play parallel- sum of ascending exterior badminton. A is older than logram arithmetic series angles of B and wins all the time. B

polygon refuses to play any more. What should A do to keep the game going?

Lack of ___t

1+2. . . . .9+10 Initial model of problem situation

Restructuring Ascending Descending by 1 by 1

1+2. . . . .9+10 c

. . . . . . . . . . . . . . . . . . .

1+10

Operations Identification of Grouping Identification subdhole of subwholes. Moving subwhole Shrinking

(sides of polygon)

r u n e cannot go

Game

Aim game of to y r a m e go can on

keep the ball going as long as Game possible

Recentring

Information Concept of rectangle Concepts of ascending Complete angle ? retrieved Formula for area of and descending series around a from semantic rectangle point=3W memory Problem Area-area of rectangle Sum-n(n+l) Sum of angles= See above solution Area=base Xaltitude 2 n.2R +360

Note. Dotted line=equality.

Duncker’s answer would be “yes”, and perhaps also Wertheimer would say “yes”, but I am not sure about what Kohler would say. Henle, a representative of the Gestalt school in contemporary psychology, asserts that manipulation of mental models is far from the Gestalt psychological approach (Henle, personal communication, 10 December 1987). She refers to Kohler (1969) who stated that the essential change leading to an intellectual discovery “tends to occur outside the mental field, and that only the result appears on the mental stage” (p. 160). Kohler stressed the role of physiological brain processes in human thinking (see, e.g., Kohler, 1938/1966,1969), and, apparently, to a lesser extent than Duncker and Wertheimer viewed thinking as a conscious mental activity. In modem cognitive psychology mental processes and structures are not necessarily assumed to be conscious and, hence, as I see it, all transformations of a mental model do not need to be conscious. Similarly, the term manipula- tion of a mental model does not mean that every operation on the model is intentional or

Scand J Psycho1 29 (1988)

conscious but rather that there is a common direction in these operations in a given problem situation. Obviously, this statement is in line with Kohler’s thinking. In The tusk of Gestalt psychology his last words read: “At least this part of nature, the human brain, seems to operate in a most selective fashion. It is the direction of its operations which is truly remarkable” (Kohier, 1969, p. 164). TO conclude, given the above clarifications of how I use the concept “manipulation of a mental model” Kohler would perhaps agree that his line of thinking is compatible with this concept.

Mental models and problem solving 89

MENTAL MODELS AND RESTRUCTURING

In the present paper it is assumed that the analogical structure of a mental model implies that the problem solver experiences his model of the problem situation as an object which he can inspect and manipulate. To do the right things with that object is a goal of the problem-solving process. The resulting change of the mental model (via transformational operations) or of how the model is viewed (via analytic operations) is assumed to correspond to restructuring in the Gestalt psychological sense.

Assuming that restructuring results from manipulating a mental model, what implications does such an assumption have for the idea put forward by Ohlsson (19846) that restructuring is mediated by search in semantic memory? It goes without saying that certain conceptual and general world knowledge is needed for constructing and interpreting a mental model and this knowledge has to be stored in some kind of memory. For example, to solve Wertheimer’s parallelogram problem it is necessary to know the concept of “rectangle” and it is also necessary that the solver knows the formula for the area of the rectangle. In line with Ohlsson (19846) I will assume that the memory in which the relevant knowledge is stored is organized as a semantic network. Also in line with Ohlsson (1984b) I will assume that the application of a certain concept for describing a given situation may require search processes in semantic memory. For example, activating the concept “rectangle” may lead to a search for a proposi- tion stating the formula for the area of a rectangle. Sometimes, the results of a search process may help the solver to restructure his model of the problem. For instance, the solving of Problem 2 (Table 1) involves activation of the concept “mathematical series”, which may lead to activation of the concept “decreasing mathematical series”, which in turn may help the solver to discover relations between elements of the model that can be used for solving the problem.

To summarize so far, I have assumed that two processes may be operating in restructuring, viz. (a) manipulations of a mental model and (b) search in semantic memory. The interesting question now is which of these processes, if any, is the decisive or crucial one in a restructuring event. I interpret Ohlsson (19846) to mean that the search process is the crucial one. Putting the emphasis on the search process would mean that the main problem in restructuring is to find an appropriate path from the (model of) the problem situation to the node standing for a certain concept (retrieval) and then finding a path back from that node to the problem situation (propagation). The actual restructuring is here seen as resulting from the propaga- tion operation, which in turn is dependent on retrieval operations. From this perspective the manipulation of the mental model would be seen either as “inspections” of various parts of the model to provide input to the retrieval process or as operations determined by the outcomes of propagation processes in semantic memory. The “inspections” may follow some standard procedure like inspecting all lines in a given geometrical figure.

Putting the emphasis on the manipulation of the mental model would mean that the crucial difficulty in a restructuring event lies in making the appropriate manipulations of the model. In other words, the manipulations will not follow automatically from the outcomes of search and

90 H. Montgomery Scand J Psycho1 29 (1Y88)

propagation processes in semantic memory. What, then, makes people introduce the appropriate changes of given material in a problem situation (i.e. to make the appropriate mental model manipulations)? Wertheimer’s (1945/1959) answer would be that it is important to be in close contact with the “true” structure of the problem. For example, he describes productive thinking in problem solving as follows: ‘I. . . there is at bottom a desire, the craving to face the true issue, the structural core, the radix of the situation. . .” (p. 236). The finding of the “true” structure may be facilitated by retrieving relevant information from semantic memory but a “Gestalt“ approach implies that it is stressed that the search for relevant information be guided by an appropriate perception of the problem situation. Wertheimer (1945/1959) gives many examples of how people do not solve problems in this way, but rather in a blind, mechanical manner, and because of this fail to find a productive solution. I interpret Wertheimer to mean that productive solving largely results from a certain attitude, that is, a motivation to go to the roots of a problem, to let the problem “take over”. In other words, as I interpret the Gestalt psychologists, restructuring is not only a question of search but a search which is guided by a certain attitude to the problem. In terms of mental models this means that in productive problem solving the solver repeatedly asks him/herself Do I use a correct model? Are there further possibilities to explore and transform the model in a way which is consonant with the given problem requirements?

Rephrasing the Gestalt approach in information processing vocabulary implies that a decisive step in a restructuring event is to find the appropriate input to search operations in semantic memory (e.g. to find the appropriate “trouble regions” in the parallelogram pro- blem). Another decisive step may be to find Out how the output of a search operation (“propagation” in Ohlsson’s (19846) theory) be used for solving the problem. For example, in Problem 2 semantic memory search may result in retrieval of the concept of a descending series, which in turn implies that the model is seen as both an ascending and a descending series. However, it is not obvious that this way of organizing the model implies that compon- ents of the model are grouped as shown in Table 1. This grouping must be discovered although it is certainly facilitated by the information retrieved from semantic memory. In the following sections of the paper we will discuss in some detail how and when a solver discovers (or finds) the solution of a problem.

MENTAL MODELS AND INSIGHT

In his book Onproblemsolving, Duncker (1935/1945) has achapter called “On total insight or evidence”. In this chapter he develops his ideas on synthetic evidence which we discussed above. From this perspective insight is simply seen as the psychological counterpart of synthetic evidence, that is, the experience of or grasping of such evidence. We assumed earlier that Duncker by synthetic evidence referred to certain evidence that can be “read off’ from a mental model. Hence, insight occurs when the individual “reads off’ synthetic evidence from a mental model. Similarly, to have insight about how a problem can be solved is equivalent to “reading off” (synthetic) evidence from a mental model.

The term “insight” (in German “Einsicht”) implies that something is “seen”, although “insight” of course is not equivalent to any seeing, but to a kind of seeing which implies some sort of understanding. The Gestalt psychologists stressed that “insight” is the perceiving of “relations” (and not of isolated stimuli or aspects) (see, e.g., Kohler, 1969, pp. 152-153). In problem solving, the Gestalt psychologists apparently assumed that insight is a necessary condition for finding a good solution. In other words, it was assumed that the problem-solver perceives relations which imply that the problem is solved. Since a mental model is regarded as being more or less analogous to a physical object, it can be “inspected” or “seen” by the

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problem solver. This “inner seeing” provides the necessary data for manipulations of the model.

Kohler used the term “insight” in a very broad sense (see e.g. Kohler, 1929, Ch. X; 1969, Ch. IV). For him “insight” also referred to grasping of relations in ordinary perception and, hence, insight was not necessarily seen as equivalent to a n “inner seeing”. However, given that a problem is solved by some kind of mental restructuring, which Kohler assumed, and given that “insight” refers to seeing something, then it follows that the insight resulting from a restructuring event refers to an “inner seeing”.

In general, the Gestalt psychologists stressed the importance of “seeing” the right things when solving a problem. This emphasis on “seeing” is evidenced by the large number of drawings in Duncker’s and Wertheimer’s works illustrating how problems can be interpreted and restructured. Thus, the “seeing” that is associated with insight could be taken in a fairly literal way if one assumes that the insight occurs when the individual “sees” something in a mental model. For example, in Wertheimer’s parallelogram problem by imagining how one of the two end triangles moves to the other end one can see how a rectangle is formed.

In his attempts to define “insight” from an information processing frame of reference, Ohlsson (19846) arrives a t the following definition: “Insight occurs when a representational change brings the goal state within the horizon of mental look ahead” (p. 124). By “horizon of mental look ahead” Ohlsson means how far the problem solver has worked through a problem in his head or , to use Ohlsson’s more poetic language, “ the tips or leaves on the search-tree developed during mental look-ahead”, where “mental look-ahead’’ simply seems to corres- pond to the thought processes going on in problem solving. It appears that Ohlsson’s seemingly elaborate line of reasoning reduces t o the idea that insight is the same as solving a problem in one’s head from a given representation.

Ohlsson’s definition of insight does not explain the special feeling of understanding, of self evidence, which is usually associated with the experience of insight. That the phenomenon of insight has this character was strongly emphasized by the Gestalt psychologists (see, e.g. Ohlsson’s ( 1 9 8 4 ~ ) own review of the Gestalt approach). It is also clear that Ohlsson’s definition goes directly against what the Gestalt psychologists meant by “insight”. Wertheimer (1945/1959) gives several examples how a problem can be solved blindly without real insight. Such a “blind” problem solving may certainly occur in the problem-solver’s head and, hence, be perfectly compatible with Ohlsson’s definition of insight.

The definition suggested in the present paper explains better the special character of the experience of insight. People usually find it hard to deny what they can see with their own eyes. To see a solution in a mental model presumably has such a n undeniable character, which, in turn, will give rise to feelings of understanding or self evidence. In the following section we will discuss a question which now may be asked: How has the solver analysed a problem situation (i.e. manipulated his mental model of the situation) when he sees how the problem is to be solved?

Mentul models and problem solving 91

RESTRUCTURING, INSIGHT, AND THE FINDING OF A BALANCED STRUCTURE

The Gestalt psychologist’s answer to the above question would be: When the solver sees how to solve the problem the situation fonns a good Gestalt. Wertheimer (1945/1959) described this end state of a problem-solving process as follows: “. . . a state of affairs that is held together by inner forces as a good structure in which there is harmony in the mutual require- ments, and in which the parts are determined by the structure of the whole, as the whole is by the parts” (p. 239).

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The key word of the above quotation is “harmony”. It is obvious from Wertheimer’s writings that good Gestalts in problem solving are characterized by some sort of harmony or balance. In this way the good Gestalt will be a structure in which the parts determine the whole and vice versa. Accordingly, productive thinking involves “that inner structural relations- fitting or not fitting-be sought among such disturbances (gaps, trouble regions, etc.) and the given situation as a whole and among its various parts” (Wertheimer, 1945/1959, p. 235).

By going through Wertheimer’s examples of productive thinking I have tried to synthesize what harmony or balance means in this context. First, it appears that the harmony or balance holds among certain parts of a mental model of the problem situation. Table 1 exemplifies how these parts are delimited and/or constructed in a problem-solving process. Second, it appears that when a good Gestalt is at hand each of the crucial parts of the mental model is balanced somehow by another part of the model. More precisely, each crucial part is equal in some respect to some other crucial part (e.g. with respect to area in Problem 1, sum of numbers within each part in Problem 2, angle size in Problem 3, and requirements of game from each player in Problem 4, see the dotted lines in Table 1). Third, the equality relations in a balanced structure are not arbitrary but point to the solution of the problem. The solution can be seen in the pattern created by the equality relation(s) found in a mental model. In this way “the parts are determined by the structure of the whole, as the whole by its parts”.

The type of structure now described may be called a baluncedsrrucrure. Possibly, the notion of balanced structures is particularly appropriate when a general principle can be inferred from a mental model, i.e. a principle which holds for many different realizations of a mental model. Most of Wertheimer’s problems appear to be of that type. However, there may be insightful solutions of other types of problems where the notion of balance in the above strict sense is less appropriate. For example, this may be the case for problems which are solved by realizing a new way of using a particular object (e.g. that a hammer be used as a pendulum in Maier’s (1970) well-known problem).

Ohlsson (19844 notes that the Gestalt psychologists view restructuring as a move towards a better structural balance. Obviously, this is a correct observation. The analysis in Table 1 shows that it may be possible to describe in an exact way what is meant by balance in a specific problem situation. Still, the balance concept does not seem to have been explicitly incorpor- ated into current information processing theories of problem solving, including Ohlsson’s theory of restructuring in problem solving (see Greeno & Simon’s, in press) recent review of research in this area). On the other hand, the balance concept and related notions such as equilibrium play a fundamental role in theories of human thinking in addition to modern cognitive psychology, e.g. in balance theory in social cognition, see Fiske &Taylor (1984) and in Piaget’s developmental theory, see Ravel1 (1963). It may be an important task for modem cognitive psychology to find out how and when notions of balance serve as guidelines for problem solving and restructuring.

How can it be that a balanced structure in a mental model actually helps the individual to find the correct solution of a given problem. Perhaps part of the answer is that balanced structures are relatively easy to generalize. For example, in Problem 2 it is easy to find the general principle asked for (the sum of a series) by generalizing the equalities noted in the mental model. This holds true provided that the equality relation is defined in a sufficiently general way. In Problem 1 it is important to realize that the equality relations between the ends of the parallelogram holds irrespective of how the parallelogram is orientated. By making appropriate manipulations of the mental model the solver may verify that the equality relation possesses the intended generality. For instance, in Problem 1 he may rotate the parailogram to check that the equality between the two ends of the parallelogram holds for different orienta- tions of the parallelogram. Thus, it seems that the relative ease by which generalizations could

Scand J Psycho1 29 (1988) Mental models and problem solving 93

be made from mental models (perhaps not only with respect to equality relations) has to do with the possibility of making various manipulations with the model.

The above line of reasoning implies that a balanced structure may provide the bridge between the relatively concrete and specific mental model and a more general and abstract principle that is asked for in the problem. Perhaps the finding of such a bridge is often the core of the experience of insight, i.e. that a correct solution can be seen in the mental model.

Obviously, the notion of structural balance may function as a general guideline for the selection of appropriate manipulations of a mental model as well as for search in semantic memory. By noting lack of balance-“trouble regions” or “gaps”-the problem solver may find suitable starting points for these operations. Similarly, decisions about how to proceed after having carried out a certain operation (e.g. after having retrieved a concept from semantic memory) may be guided by the notion of structural balance. As already indicated, it appears that little is known about these matters from modern research on problem solving. However, it seems safe to say that to the extent that the finding of structural balance is important for an appropriate restructuring it will be important for the problem solver to be sensitive to lack of balance and for possibilities of finding balance in his mental model, if any, of the problem situation. Hence, in addition to having access to relevant information from semantic memory it will be important to manipulate the mental model in a productive way.

CONCLUSIONS

Despite the massive amount of research conducted in recent years on human problem solving there has been a limited interest in how the problem solver restructures an initial representa- tion and, as a consequence, understands the problem better. The need for research in this domain has been emphasized by Greeno & Simon (in press) in their recent review of research on human problem solving and reasoning. By contrast, the recent literature in cognitive psychology abounds with research on “mental models” (for a review, see Rouse & Morris, 1986). However, the concept of “mental models” tends to be used in a very general sense being more or less equivalent to any specific representation of a particular content domain (cf. Carroll, 1985). In the present paper and in line with the view put forward by Johnson-Laird (1983), “mental models” has been used in the sense of a structure which is analogical with a corresponding structure in the world.

Ohlsson (19846) attempted to integrate the notions of restructuring and insight with the information processing theory of problem solving but did not include mental models in his line of reasoning. Although Ohlsson rightfully points out that restructuring may be related to search in semantic memory he misses important issues emphasized by the Gestalt psycholo- gists in his account of restructuring and insight. These issues include (a) the operations of groupings, subwhole identification, recentring, etc, that the Gestalt psychologists associate with restructuring, (b) insight regarded as “inner seeing”, and (c) the notion of balanced structures. These issues underline the importance of acquiring an appropriate understanding of a problem but do not easily lend themselves to the detailed step-by-step description of a problem-solving process, which typically is required by information processing theory. (See, however, Greeno (1983) for an attempt to computer simulate some of the operations that are associated with restructuring.)

In the present paper I have tried to show that the three above-mentioned issues are compatible with the view that problem solving proceeds by manipulating a mental model. It may be an interesting challenge for future research to assess the validity of this tripartite view of the role played by mental models in restructuring and insight.

94 H . MontEomery Scand J Psycho1 29 (1988)

This paper was supported by a grant from the Swedish Council for the Humanities and Social Sciences. I wish to thank Carl Martin Allwood, Anders Biel, Sven Hemlin, Mary Henle, and an anonymous reviewer for their comments on previous versions of the paper.

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