An Investigation of Student Conjectures in Static and Dynamic Geometry Environments

Abstract

This study was designed to investigate the mathematical conjectures formed by high school geometry students when given identical geometric figures in two different types of geometric environments. Student conjectures formed in a static geometry environment were compared with those formed in a dynamic geometry environment generated by dynamic geometry software. These conjectures and the environments in which they were formed were examined both quantitatively and qualitatively. Results indicate that students who used dynamic geometry software made more relevant conjectures, fewer false conjectures, and the conviction in the correctness of their conjectures was higher when compared to students working in a static geometry environment. These differences were found to be statistically significant using linear regression analysis. Qualitative data was collected by means of participant observations, a survey instrument, selected participant interviews, and a qualitative analysis of the conjectures made by the students in each environment. Qualitative analysis focused on the following themes: Student concepts of conjecture and proof, student preferences concerning each environment, the kind of language used in the conjectures formed in each environment, the ability to find counterexamples using dynamic geometry software, the “dragging” techniques used by the participants using dynamic geometry software, and the students conviction in the output generated by dynamic geometry software. Results indicated a strong preference for the dynamic environment and a high conviction in the output generated by dynamic geometry software. The language used in forming conjectures in the dynamic environment was noticeably different and reflected the environment itself. The participants’ concept of proof included both inductive and deductive frames when dynamic geometry software was available, and many of the students had difficulty with forming and finding of counterexamples using dynamic geometry software when confronted with a false conjecture.