Learning by Discovery: Children’s Performance in a Computer-Based Geometry Lab

Author: I-Fang Liu(Yu Lin Elementary School), Chao-Jung Wu(National Taiwan Normal University)

Vol.&No.：Vol. 53, No.1
Date：March 2008
Pages：87-111
DOI：10.6300/JNTNU.2008.53(1).04

Abstract：

Knowledge is constructed during the process of discovery. With the support of a computer-based environment, a learner can acquire concepts by imitating the ways in which mathematicians make discoveries. The purpose of this study is to investigate how the experience of manipulating variables affects children’s discovery of two geometrical rules—the interior angle property (the interior angles of a triangle add up to 180 degrees) and the exterior angle property (an exterior angle of a triangle equals the sum of the two opposite interior angles). We are also interested in understanding what experimental strategies children use to discover the rules. Fifty-two fourth grade students participated in this study. They were randomly divided into two groups: “interior angle” and “exterior angle” groups. It was found to be harder for students to discover the interior angle property than the exterior angle property. Moreover, the experience of manipulating variables significantly affected the discovery of the interior angle property. We found that four strategies were used by the students and most students used at least one of them. The “change all variables” strategy was used frequently and the discovery process of these children was not very efficient. Furthermore, the strategy chosen by a student tended to depend on the positive reinforcement of coming up with positive instances, which led students to think that positive instances were the only useful kind of information in the discovery process.

Keywords：geometrical conjectures, rule discovery, simulation of geometric concepts, strategies of experimental design, variable manipulation

《Full Text》