Enhancing geometric reasoning.

Geometry is an important part of the mathematics curriculum. However, students are not demonstrating strong conceptual knowledge of this subject. The research of Van Hiele and Van Hiele-Geldof has focused on the concept of thinking levels in geometry and the role of instruction in raising levels of thinking. This paper describes a field trial of a supplemental geometry unit intended to raise Van Hiele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels and attitudes toward geometry, as well as field-tested activities yielding the most positive results, are presented. Educators can benefit from this application of the Van Hiele model of geometric thinking, since the thought processes involved in learning geometry are explained, along with teaching techniques and tools for assessment. By having teachers become more aware of their students' cognitive skills, attitudes, and misconceptions, teaching practices and student achievement can be enhanced.