Analogy and Transfer : Encoding the Problem at the Right Level of Abstraction

Analogy and transfer studies belong to distinct research areas regarding both the theoretical frameworks and the experimental paradigms, although they both contribute to the fundamental question of the generalization of learning. The aim of this paper is to show that those fields might be reanalyzed within a common framework, emphasizing the role of the abstraction level at which the problem is encoded, which might contribute to an unified theory of generalization of learning. Analogy and transfer Analogy and transfer of learning, which are two distinct areas in cognitive psychology as the lack of cross references between the two fields illustrates, are both concerned with the same basic questions: how can what has been learned in a specific situation be generalized to new situations and what conditions are necessary and/or sufficient to generate transfer from one situation to another? We shall attempt to reanalyze both phenomena within the same theoretical framework and show how this analysis contributes to the fundamental question of the generalization of learning. Differences and similarities in the study of analogy and transfer. The prevailing theory of transfer, proposed originally by Thorndike and Woodworth (1901), is transfer between the learning and the test situations relies on common elements. This theory has more recently been revived in the contexts of learning complex devices and programming languages. In these contexts, the common elements are production rules, which have both a stimulus side (their conditions) and a response side (the action triggered by the conditions). The idea that the degree of transfer between two tasks is proportional to the relative number of productions rules they have in common, each task being described by a set of production rules corresponding to the allowable procedures, has received substantive confirmation in text editing and computer programming (Anderson & Singley, 1993; Bovair, Kieras & Polson, 1990). On the other hand, the analogy theories have been developed in the last two decades mainly through the works of Gentner (1983, 1989) and Holyoak (e.g. Holyoak & Thagard, 1989; Hummel & Holyoak, 1997, 2003) and their co-workers. While differing in many respects, both theories decompose the analogy process into several basic constituent processes (access, mapping, inference, evaluation, generalization) and distinguish several kinds of similarities (pragmatic, semantic, superficial, structural), which govern analogy process differently depending on the constituent at hand. Theories differ in the kind of similarities taken into account and in the way these similarities are involved within the constituent processes. Several differences distinguish the experimental paradigms used between transfer and analogy studies. (i) Most of the problems in the analogy studies concern story problems that may be solved by pure reasoning and do not involve any physical action. The solution consists in the verbal statement of a procedure in order to attain the goal and not in the effective attainment of the goal (e.g. Ross, 1989). The reverse is true for transfer studies: solution is reached through physical actions from initial to final states of the problem (e.g. Kotovski, Hayes & Simon, 1985). (ii) Due to the prominent use of verbal material in the analogy studies, the semantic content of the tasks is usually much richer and irrelevant features are more numerous than in the transfer studies; therefore the selection of features for mapping is more critical in analogy studies than in transfer studies. (iii) In analogy studies, the solution to the source problem is usually not worked out by the participant but provided by the instructions, as it is the case in traditional teaching situations, whereas in transfer studies, the solution is discovered by the participant; thus, what is transferred is more likely to be declarative knowledge in the analogy studies and procedural knowledge in transfer studies. (iv) In analogy studies, a problem, or several isomorphic problems, is (are) usually given only once, while in transfer studies, several trials may be given for the same task by varying the initial state and the goal. In this way it is possible to control the degree of prior training in transfer studies and to observe its effect on successive trials with the transfer problem. In spite of these differences, many similarities may be emphasized in the way tasks are analyzed and in the results obtained. In both approaches, a sharp distinction is made between the elements that belong to the structure of the problem, and for this reason are relevant to the solution, and those that should be ignored. The theorists of analogy distinguish between the structural features that are relevant to