Can interactive visualization tools engage and support pre-university students in exploring non-trivial mathematical concepts?

https://doi.org/10.1016/j.compedu.2009.10.001Get rights and content

Abstract

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational contexts. This seems to be the case with educational visualization tools. Much evidence about the effectiveness of these tools appears to be more suggestive than based on empirical evaluations. In this paper, we attempt to fill this gap and provide empirical evidence for the use of visualization tools in supporting exploratory and other learning-related activities. In particular, we aim to investigate whether visualization tools can be used to engage pre-university students in exploring non-trivial mathematical concepts. We focus particularly on this age group and content domain because of the difficulty these students may encounter when trying to investigate more challenging mathematical concepts. Also, it is during their formative years before university that students’ predisposition and likeness towards mathematical ideas are formed. We report in this paper a study assessing whether a visualization tool, whose design was informed explicitly by research from information visualization and human–computer interaction, could engage pre-university students in their exploration and learning of more advanced mathematical concepts. Students who participated in this study came from multiple grade levels and have diverse cognitive and language skills as well as preferences towards mathematics. The results of this study indicate that visualization tools can effectively engage these students and support their exploration of non-trivial mathematical concepts, only if the tool is designed such that it can cater the diverse needs of these students.

Section snippets

Introduction and background

The main goal of this paper is to explore whether computer-based visualization tools can be used to engage pre-university students, especially at lower grades, in exploring non-trivial mathematical concepts. In pursuance of this goal, a mathematical visualization tool was designed and implemented, and an empirical study was subsequently conducted with the tool. The tool, described in more detail later, is intended to support the exploration of three-dimensional (3D) geometrical shapes with

Mathematical background

The mathematical context chosen to conduct this research is 3D geometry, more specifically, Platonic and Archimedean solids. Platonic solids are 3D shapes having planar faces; each face is a regular polygon; all faces are congruent; and, all angles between pairs of adjacent faces are identical to each other (Coxeter, 1991, Devlin, 2003). As such, they look identical from every vertex. The cube, for instance, is a Platonic solid, as it is composed of only squares, with three squares meeting at

Results

This section reports results of the empirical study, presented in two subsections: (1) test achievement results, which include statistical analysis of the Geometry Test results; and (2) response to SVT, which includes participants’ reactions towards and feelings about the tool.

Summary, conclusions, and future work

In this research, we have attempted to investigate whether visualization tools can be used to engage pre-university students across multiple grades in their exploration and learning of non-trivial mathematical concepts. Our hypothesis has been that this is possible, only if a visualization tool is designed appropriately—i.e., using relevant visualization and interaction design principles and techniques. To perform this research and test our hypothesis, a visualization tools was designed and an

Acknowledgements

This research has been funded by the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank Jim Morey for providing the foundational source code upon which this research could be further developed. The authors would also like to thank the students who participated in this study and, specially, the teachers who were so supportive of this research. Finally, the authors would like to thank all the reviewers for their comments and suggestions for improvement.

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