Unfortunately, most of the research on memory has concentrated on deliberate and voluntary remembering. This applies both to the classical storehouse tradition and the constructive ecological tradition. The pure memory tasks, such as free recall, cued recall, and recognition tests, all have the drawback that they study memory in isolation. What we really need for understanding the complex interactions between memory and reasoning is the study of spontaneous remembering, i.e., remindings that happen spontaneously in the context of a problem-solving activity. In particular, we are interested in spontaneous remindings of analogous situations and problems.
On the other side, the sparse research on memory within an analogy-making framework has ignored the constructive view on memory and has concentrated on how people select the most appropriate episode from the vast set of episodes in LTM. We will not review these studies in any detail since Hummel and Holyoak (1997) have done this already elsewhere, we will only mention some basic findings. It has been established that the existence of similar story lines or similar objects (objects with similar properties) is a crucial factor for analogical reminding (Holyoak & Koh, 1987; Ross, 1989; Gentner, Rattermann, & Forbus, 1993). That is why remote analogies are very rare and difficult to achieve (Gick & Holyoak, 1980). However, Dunbar (this volume) demonstrates that people, both in natural settings and in the experimental laboratory, are able to produce remote analogies based on shared relations in both domains. Actually, the role of similarity between the relations in both domains has never been seriously studied. What has been studied and established is that structural correspondences (similar objects playing similar roles in similar relations) does not have much effect on reminding. It can possibly facilitate reminding under certain circumstances, but only when there is general similarity between the domains or story lines (Ross, 1989; Wharton, Holyoak, & Lange, 1996). Dunbar (this volume) and Ross and Bradshaw (1994) present evidence for encoding effects on remindings, i.e., that reminding is facilitated when the subjects perform similar operations on the material at study and test, and when they focus on the same aspects (relations or properties) in both cases. Spencer and Weisberg (1986) have found context effects indicating that even the same or similar environmental context can facilitate reminding. Unfortunately, there is not much research on the dynamics of the process of reminding (or reconstructing), on the completeness and accuracy of the resulting descriptions of the old episodes, and on how these reconstructions depend on the target problem.
The following subsections briefly review some results obtained by the AMBR research group illustrating the possible effects reasoning can have on reminding, memory on reasoning, and perception on memory and reasoning.
A recent experiment looked at human memory in the context of analogical problem solving. It was designed as a replication of Holyoak and Koh's (1987) Experiment 1. A think-aloud method was used, however, and the accuracy of the base story was measured as it was being recalled. The participants were college students taking an introductory cognitive science course. As part of the class on thinking, they discussed the radiation problem and its solution. Three to seven days later they were invited by different experimenters to participate in a problem-solving session in an experimental lab. They had to solve a version of the lightbulb problem. Almost all subjects (except one who turned out not to have attended the class discussing the tumor problem) constructed the convergence solution and explicitly (in most cases) or implicitly made analogies with the radiation problem. We were interested in how complete and accurate their spontaneous descriptions of the tumor problem story were.
It turned out that remembering the radiation problem was not an all-or-nothing event. Different statements from the story were recollected and used with varying frequency. Thus the application of several X-rays on the tumor was explicitly mentioned by 75% of the 16 students participating in the experiment; the statement that high intensity rays will destroy the healthy tissue was mentioned by 66% of the subjects; and the statement that low intensity rays will not destroy the tumor was mentioned by only 25%. Finally, no one mentioned that the patient would die if the tumor was not destroyed. All this demonstrates partial recall of the base. Our hypothesis is that the elements that tend to be reproduced are the ones that correspond to pragmatically important elements in the target. This hypothesis remains to be tested and corresponding experiments are under development.
On the other hand, there were some insertions, i.e. "recollections" of statements that were never made explicit in the source domain description. Thus one subject said that the doctor was an oncologist, which was never explicated in the radiation problem description (nor should it be necessarily true). Another subject claimed that the tumor had to be burnt off by the rays, which was also never formulated in that way in the problem description.
Finally, there were borrowings from other possible bases in memory. Thus one subject said that the tumor had to be "operated by laser beams" while in the base story an operation was actually forbidden. Such blendings were very frequent between the base and the target. Thus 7 out of the 11 subjects who spontaneously re-told the base (radiation) story mistakenly stated that the doctor used laser beams (instead of X-rays) to destroy the tumor. This blending evidently results from the correspondence established between the two elements and their high similarity.
In summary, the experiment has shown that remindings about the base story are not all-or-nothing events and that subjects make omissions, insertions, and blendings with other episodes influenced by the mappings established with the target problem.
Memory in its turn, having its own life independent of reasoning, can influence the reasoning process. One example of this is the influence that our immediate or very recent past has on reasoning. Thus people are always in a particular memory state when they start solving a problem. This state is determined by what they have been doing and thinking about immediately before they switched to the new task. This state will typically be unrelated to the current problem but can nevertheless have an influence on how it is solved. This memory state is characterized by the person's currently active concepts, generic facts, rules, particular past episodes, goals, plans, and so on. In an attempt to partially control this memory state, Kokinov (1990, 1994a) carried subjects through a series of problem-solving tasks. The problems were chosen from a variety of domains (algebra, geometry, physics, commonsense, etc.), so that there were no apparent relations among them. The problems were presented to the subjects one by one and in different orders in the different experimental groups. Among the series of 10 problems there were typically two which were covertly related and which we anticipated to interact. The expected interaction was that the early problem would prime the other, i.e., induce a memory state that would facilitate solving the later problem.
The experiment demonstrated that when the target problem was preceded by different priming problems subjects may solve it in different ways. Since the solution of the priming problem was known to the subjects in advance (a commonsense problem like how to prepare tea in a glass) the only effect that its presentation had on the subjects was making certain concepts, facts, rules, or episodes more accessible. This turned out to be crucial for the following problem-solving process, as the performance of the subjects in the task rose from 12% to 44%. In some cases we demonstrated that people can be influenced to find different solutions of the same problem depending on the specific priming provided. The experiment also studied the dynamics of the process by manipulating the length of the time interval between the priming and target problem (by making people solve distractor problems in between). The results showed that the priming effect decreased exponentially with the course of time and disappeared within about 25 minutes in this particular study. Thus immediately after priming the rate of successful performance was 44%, about 5 minutes later it declined to 29%, and after 25 minutes it was back at the control level of 12%. Schunn and Dunbar (1996) have also demonstrated priming effects on problem solving. Their results indicate that subjects were not aware of the priming effect.
Kokinov (1989) demonstrated that memory about general facts such as "which is the lightest chemical element?" is also sensitive to recent experience. The experiment demonstrated priming effects on recall of such general facts. Many experiments have demonstrated priming effects on particular concepts. For instance, studies in social psychology have demonstrated that a particular priming can affect the use of various prototypes in characterizing a person or person's behavior (see, Bargh, 1994, for a review).
Based on a prediction derived from an earlier simulation of analogy-making (Kokinov, 1994a), the AMBR research group started to look for context effects, i.e., how the perception of incidental elements of the environment during the problem-solving process can alter it. Thus Kokinov and Yoveva (1996) conducted an experiment on problem solving in which seemingly irrelevant elements of the problem solver's environment were manipulated. The material manipulated consisted of drawings accompanying other problems which happened to be printed on the same sheet of paper. There was no relation between the problems and the subjects did not have to solve the second problem on the sheet. However, these seemingly irrelevant pictures proved to play a role in the problem-solving process, as we obtained different results with the different drawings. We used Clement's (1988) spring problem as target:
Two springs are made of the same steel wire and have the same number of coils. They differ only in the diameters of the coils. Which spring would stretch further down if we hang the same weights on both of them?
The problem description was accompanied by the following picture ( Figure 2).
Figure 2. Illustration accompanying the target problem.
In different experimental conditions the drawings used to accompany a second unrelated problem on the same sheet of paper were different: a comb, a bent comb, and a beam ( Figure 3).
Figure 3. Illustrations accompanying the irrelevant problems in the various experimental conditions.
The results obtained in these experimental conditions differed significantly. In the control condition (no second picture on the same sheet of paper) about half of the subjects decided that the first spring will stretch more, the other half "voted" for the second one, and only a few said they will stretch equally. In the comb condition considerably more subjects suggested that the first spring will stretch more. In the bent-comb condition considerably more subjects preferred the second spring. Finally, in the beam condition more subjects than usual decided that both springs will stretch equally. Our interpretation is that the illustrations activate certain memory elements that, once activated, start to play a role in the problem-solving process. For example, the image of the bent comb probably activates concepts such as "bending" and facts such as "thicker teeth are more difficult to bend." This knowledge is then transferred (incorrectly in this case) by mapping teeth to springs, bending to stretching, and concluding that "thicker springs are more difficult to stretch."
Similar results, although not that dramatic, were obtained in the think-aloud experiment described in Section 2.4.1. Subjects who had to solve the lightbulb problem were divided into two groups. In the control group there were no other problems on the sheet of paper, whereas in the context group the following problem was presented on the same sheet ( Figure 4).
The voting results from the parliamentary elections in a faraway country have been depicted in the following pie-chart. Would it be possible for the largest and the smallest parties to form a coalition which will have more than 2/3 of the seats?
Figure 4. Illustration accompanying the context problem.
The results were the following: in the context group all 7 subjects who produced the convergence solution to the lightbulb problem used three laser beams (7:0), while in the control group no one said three: two subjects said they would use two or three beams and the rest said they would use either two or several beams (2:5). The difference is significant at the 0.01 level.
Finally, Kokinov, Hadjiilieva, and Yoveva (1997) have demonstrated that subjects were not aware of the manipulations and the possible context effect of the second illustration. The context condition was contrasted with an explicit-hint condition in which subjects were invited to use the same picture during the problem-solving process. The results from the hint condition were significantly different. Moreover, in some cases when a hint was given to use the picture subjects were less successful in solving the target problem compared to the control condition, while when they seemingly ignored the picture they were still influenced by it and showed better performance compared to the control.
The results from all the experiments described in this subsection demonstrate that sometimes perceiving small changes of a seemingly arbitrary element of the environment can radically change the outcomes of the problem-solving process (blocking it, or guiding it in a specific direction).
Another effect that perception can have on reasoning has been demonstrated by Keane, Ledgeway, and Duff (1994). They have shown that the specific order of perceiving the elements of the target can also influence the problem-solving process. We call these perceptual order effects to contrast with the memory order effects described in Section 2.3. We hypothesize that the mapping process in its turn influences perception. For example, the currently established mapping may guide the attention and thus influence the selection of details to be perceived and their order. We do not have experimental support for this hypothesis yet. We call this potential influence mapping effect on perception.
The conclusion from this short review is that perception, memory, and reasoning strongly interact during the problem-solving process and must be studied and modeled together. The next subsection attempts to summarize all these results and to describe the constraints they entail for models of analogy-making.
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