Paper 1: Analysis of Achievement for Understanding Geometry

The purpose of this study was to investigate the effectiveness of a mathematics professional development course. More specifically, in this study we examine whether geometric experiences have an impact on level of performance in mathematics. The van Hiele (Fuys, D., Geddes, D., & Tischler, R., 1988) model of geometric understanding provided a research framework from which to view geometric understanding. This model suggests five levels of understanding that should be taken into consideration when examining levels of geometric thinking: Visual, Descriptive/Analytic, Abstract/Relational, Formal Deduction/Proof, and Rigor. The sample under study was three cohorts of practicing elementary teachers and mathematics coaches engaged in a 50-hour P-5 Mathematics Endorsement course entitled Understanding Geometry. Data collected through pre- and post-tests provided evidence that participants made significant improvement in geometric content knowledge and levels of understanding, thus verifying the effectiveness of their professional development experience. Also, this study points toward the importance of participants’ entering level of understanding for achieving the course objectives