Analyzing the Performance of Grade 6 Students in Dynamic Geometry Manipulative Tasks: A Quantitative Approach

Abstract

This paper reports the results of a quantitative analysis of students’ performances in manipulative tasks in the dynamic geometry environment. 252 Grade 6 students from about 70 primary schools in Hong Kong attempted the geometric tasks in the context of a mathematics competition. These tasks, set up by the dynamic geometry software C.a.R. but accessible by an ordinary Java-enabled browser, required students to drag points (mostly vertices of polygons) in prepared geometric drawings so as to obtain specific areas or shapes. They were designed in such a way that students had to exercise their understanding about area, congruence or symmetry while continuously transforming the geometric figures on the screen. Results of these students in 10 geometric tasks of this kind are analyzed in an exploratory manner. By employing Factor Analysis, these ten items are grouped into three types. Results of our analysis display certain significant differences in students’ performance in different groups of geometric tasks, which in turn suggests distinctive groups of geometric concepts and skills involved in the tasks. Apart from these geometric tasks, there was also a paper (in multiple-choice format) that called for general mathematical reasoning and knowledge. Correlation between the scores on such multiple-choice questions and the performances on the dynamic geometric items is also studied. The weak correlation tends to suggest that the dynamic geometric items are probing a kind of ability different from the general mathematical knowledge expected of a Grade 6 student. While all these findings are based on quantitative analysis, we draw on the understandings of the designer of the geometric items as well as the experience of a few veteran primary mathematics teachers when reviewing these findings. We thus provide in this paper a careful examination of the geometric concepts and skills that possibly account for the significant differences revealed by the numerical data. This is believed to be one step closer to the incorporation of dynamic geometry into our school mathematics curriculum, particularly as a possible tool for alternative assessment of basic geometric concepts and skills at an elementary level.