A Cognitive Analysis of Solutions for Verbal, Informal, and Formal‐deductive Reasoning Problems

Abstract

A previous study of new item types for the analytical measure of the GRE General Test found that the items loaded on three of four separable factors that were labeled verbal reasoning, informal reasoning, formal-deductive reasoning, and quantitative reasoning. The present study examined the issue of how processing differed for these item types in the context of a problemspace framework. Protocols of examinees solving a small set of problems aloud were collected. These protocols were examined with respect to two phases of the problem-solving process: problem representation and problem solution. For formal-deductive items, all the information necessary to solve the probJem was provided in the problem statement. The representation of formal-deductive items involved the use of meaning-reduced tokens and spatial diagrams. The units involved in the representation of informal reasoning and verbal reasoning item types included meaningful propositions and meaning-emphasizing paraphrases. Reference to common background knowledge occurred. The analysis of the problem-solution phase focused on the processes of evaluation, (judgments of the cczreccness of an option) and justification (statements of an argument or of evidence for why an option was or was not correct). First, the order of these processes was found to differ for formal-deductive items and other item types. Secondly, item solutions varied in terms of the kinds of justifications that were offered by the examinees for accepting or rejecting options. These results illustrate how the addition of some item types to the GRE analytical measure will expand the variety of reasoning skills assessed. Implications of these results for cognitive models of reasoning are also discussed.Acknowledgments

Relationships Among Multiple‐choice Reasoning Items and a Constructed‐response Generating‐explanations Task

“…In formal reasoning, the procedures typically involved include converting propositions to symbolic form, combining these propositions to deduce new information, and determining whether symbolic relationships are in accord with the rules of the system. This is the kind of reasoning applied in formal deductive systems such as logic and mathematics and is quite similar to the kinds of processes people use to solve analytical reasoning problems (Enright, Tucker, & Katz, 1995). In contrast, informal arguments consist of conclusions or hypotheses supported by reasons and are evaluated in terms of their soundness.…”

“…The formal-deductive factor consisted of analytical reasoning items, and the items that loaded on the informal reasoning factor included a version of analysis of explanations, numerical reasoning items (another item type involving explanations), and a number series item. Subsequently, Enright et al (1995) using protocol analysis, found that there were many commonalities in the way examinees reasoned about some of the item types that loaded on the verbal and informal reasoning factors, and these processes were quite distinct from the way people solved analytical reasoning items. In terms of representational tactics and the ordering of the processes of evaluation and justification, items that loaded on the verbal and informal reasoning factors were very similar.…”