Learn a Mathematical Structure: A Study Based cn Elements of a Potential Theory Which Relates

The study was designed to describe the basis of a potential mathematics learning theory founded on the relationship between language and thinking, to relate the subjects ' overt verbalization and performance after they had been taught a mathematical structure, to relate overt verbalization and the number of discovered rules, and to examine the strategies used. Forty girls, 11-12 years old, were randomly assigned to one of four instructional situations: (1) subjects talk aloud while doing mathematical activities and then are silent, (2) subjects are silent while doing the activities and afterwards answer questions and explain findings, (3) subjects verbalize both during and after the activities, and (4) subjects do not verbalize either during or after the activities. A machine wired to embody the Klein-Four Group structure was used as a manipulative aid. Among the results found were: (1) subjects performed better, retained more and discovered more rules when they were silent while doing the activities and afterwards answered questions and explained findings; (2) there was significant interaction between learning and questioning; (3) the subjects ' overt verbalization during questioning did not accelerate learning; and (4) the nature of the rule and the number of discovered rules influenced performance. (Author/DT) eU