Relational Reasoning is in the Eyes of the Beholder: How Global Perceptual Groups Aid and Impair Algebraic Evaluations
Year: 1991
Type: article
Abstract: Relational Reasoning is in the Eyes of the Beholder: How Global Perceptual Groups Aid and Impair Algebraic Evaluations David Landy ([email protected]) Department of Computer Science, Indiana University Address Robert L. Goldstone ([email protected]) Department of Psychology, Indiana University Address Motivation Experiment 2 Relational reasoning—reasoning that depends on the interactions of multiple elements, rather than on the intrinsic properties of the elements—is both ubiquitous and challenging. For example, children find it difficult to respond to relational commonalities when object-based similarities are present (Gentner & Rattermann, 1991). Since overt symbol systems such as algebra are external constructs, their terms can contain perceptual regularities. Models of symbolic reasoning, however, typically ignore perceptual regularities (Anderson, in press). It is reasonable to wonder whether people make use of available domain- general grouping processes when parsing mathematical structures. The purpose of the experiments described here is to evaluate whether algebraic grouping is sensitive to visual grouping. If processing is strictly symbolic, then the manipulation of perceptual regularities should not affect judgments; however, if people use visual grouping to help them parse expressions, then they should make more errors in cases where the perceptual grouping gives an incorrect answer, and be more accurate when visual grouping supports the standard order of operations. The materials were identical, except that the variables in the original expressions were replaced by complex terms (see Figure 1, 3-4). Instead of manipulating the spacing of the terms, we manipulated the similarities of these internal structures. In congruent cases, terms around the multiplications had similar structures, while in incongruent cases, terms around the additions had similar structures. Again, performance was significantly worse in incongruent cases only when grouping affected the correct answer (accuracies = 81.1%, 78.8%, and 75.8% on grouping- matters trials, 92.6%, 90.8%, 91.8% on grouping-irrelevant cases. An ANOVA analysis reveals that both congruent and incongruent cases when grouping matters are significantly different from neutral performance, (n=28, p .1 on a repeated measures ANOVA). Experiment 1 establishes that spacing affects algebraic grouping judgments, but the effect might be limited to physical proximity. Experiment 2 explores another perceptual regularity, regular structure, in order to evaluate whether that also affects grouping. Figure 1: Sample stimuli. (1) incongruent, answer depends on the grouping. (2) congruent, answer does not depend on grouping. (3) incongruent. (4) congruent. References Anderson, J. R,. (in press). Human symbol manipulation within an integrated cognitive architecture. Cognitive Science. Gentner, D., Rattermann, M. J. (1991). Language and the career of similarity. In S. A. Gelman & J. P. Byrnes (Eds.), Perspectives on thought and language: Interrelations in development (pp. 225-277). London: Cambridge University Press.
Authors: David Landy, Robert L. Goldstone
Institution: Indiana University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W234546729