Exploring the Use of Dynamic Geometry Manipulative Tasks for Assessment

Abstract

This paper discusses the potential use of dynamic geometry environment to examine quantitatively students?
 understanding of geometrical knowledge through their performance in manipulative tasks. Most of the studies on the impact of dynamic geometry computer environment tend to focus on students?
 performance in open-ended explorations or problem solving tasks by means of detailed observations, analysis of individual works and in-depth interviews, aiming to understand the nature of geometric investigations or explorations afforded by the interactivity possible in such environment. A different focus of study is proposed here, which considers dynamic geometry environment as a means to assess students?
 geometrical knowledge based on an analysis of their responses made quantifiable in specially designed manipulative tasks. These tasks elicit students?
 responses to mouse dragging of points in pre-constructed dynamic figures. Students?
 prior knowledge of how to use dynamic geometry software is not assumed. Their responses will be described by and recorded as a prescribed parameter value designed for each task. This will give a set of data describing a range of students?
 performance on tasks specifically designed to assess students?
 conceptions of certain geometrical knowledge. The design of these manipulative tasks is explained, with some examples from a recent computer-based mathematics contest for Secondary 1 students. Responses to these contest items illustrate a range of outcomes while students attempt to adjust continuously geometric quantities, such as length, angle and area, to complete the required configurations. Further analysis of the distribution of these responses in some items reveals the nature and varieties of approaches adopted by the students. This will lead to considerations of developing the tasks into diagnostic tests.