Dynamic Geometry and Its Effects on Geometric Reasoning in Terms of Van Hiele Levels

Date of Graduation

Spring 2007

Degree

Master of Natural and Applied Science in Mathematics

Department

Mathematics

Committee Chair

Linda Plymate

Abstract

Dynamic geometry software allows the construction of figures using built-in properties from geometry. The usefulness of such software is that the user is capable of performing a variety of instantaneous transformations. Educators see this technology as an opportunity to increase understanding and assist students in developing proof. With the advent of dynamic geometry, teachers must look at its effectiveness in assisting student's development in geometric reasoning. This mixed design study analyzed significant effects that such programs have on the development of high school geometry student's ability to reason in terms of the van Hiele model. Questions also addressed affective changes through the use of Cabri. Data was collected through pre and post van Hiele reasoning test, a Likert-scaled pre- and post-survey, interviews, and artifacts. Pre and post test results revealed that there were no significant effects on student reasoning in terms of their van Hiele levels (p<.10); however, more students in the Cabri-assisted environment experienced an increase of their van Hiele level (p<.05). Observations and interviews showed that Cabri was not responsible for improving reasoning and proof capabilities. Knowledge of how to operate the Cabri dynamic environment was not enough; students needed to have foundational skills and an understanding of what a dynamic geometry environment was capable of doing. Few affective changes were experienced with the use of Cabri; the two classes studied already differed significantly in attitudes toward geometry and technology at the start of the study.

Keywords

dynamic geometry, reasoning, geometry, van Hiele, Cabri geometry

Subject Categories

Mathematics

Copyright

© Jesse E. Hiett

Citation-only

Dissertation/Thesis

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