Dynamic Geometry Manipulative Tasks: A Quantitative Approach

Abstract: This paper reports the results of a quantitative analysis of students ’ performance in ten dynamic geometry manipulative tasks. More than 250 Grade 6 students from about 90 primary schools in Hong Kong attempted the tasks in a mathematics competition. These tasks, set up with the software C.a.R. but accessible with an ordinary Java-enabled browser, require students to drag points (mostly vertices of polygons) in pre-constructed geometric drawings so as to obtain specific areas or shapes. They are designed in such a way that students have to exercise their understanding in elementary geometry while continuously transforming the geometric figures on the screen. Apart from these geometric tasks, there is also a paper (in multiple-choice format) that calls for general mathematical reasoning and knowledge. Correlation between the scores on the multiple-choice test and the performance on the dynamic geometry tasks is also studied. The correlation is only moderately positive, which tends to suggest that the dynamic geometry tasks are probing a kind of ability different from the general mathematical competence expected of a Grade 6 student. Results of the students in the ten dynamic geometry tasks are also analyzed in an exploratory manner. Factor Analysis renders an extraction of four factors, three of which can be possibly interpreted with partial reference to the content knowledge involved, namely, knowledge about symmetry, area and congruence. But, with a careful examination of the geometric contents as well as the design of some of the tasks, we suggest a distinctive element of exploratory interaction, as opposed to working with formulas and computation, that should help characterize the factors at a deeper level