Developing Prospective Elementary School Teachers?Expertise with Dynamic Geometry

Abstract

Dynamic geometry packages offer abundant opportunities to explore and solve problems and to reflect about geometric phenomena. Even students with limited experience with the formalities of geometry are keen to use dynamic geometry, and this study explored the use of prepared files and associated activities to introduce pre-service elementary school teachers to dynamic geometry. The prospective teachers in the study were enrolled in geometry content courses in which they used the prepared files to complete a set of calculator-based dynamic geometry activities. The activities were developed in pilot tests during which pre-service teachers with no previous experience with calculator dynamic geometry worked on and later evaluated the activities. In the activities the future teachers constructed altitudes, angle bisectors, medians, and perpendicular bisectors for triangles. Then they animated the triangles and wrote conclusions and conjectures based on the concurrency of the straight objects they had constructed and the vertex angle measures of the triangles. In a concluding part of the activities, the pre-service teachers constructed and measured triangles bounded by the constructed straight objects and the original triangles, and made conjectures based on these measures and reanimations of the triangles. Results showed that the simpler layout of the calculator platform made it an appropriate technology for the elementary school grades and an excellent tool for prospective teachers to utilize in their own geometric investigations. Findings also indicated that the prepared files enabled the pre-service teachers to construct straight objects and polygons and to measure and animate these figures during the introductory activities. Application of a cognitive framework with four levels of tools and four access characteristics confirmed that the framework modeled the future teachers? work within the dynamic geometry environment. As a result, the prospective teachers used the prepared files with the activities to develop their expertise with the tools and access features detailed in the theoretical framework.