The effects of a professional development program on teachers' beliefs and teaching of mathematical proofs

Abstract

Although proof is a primary way that people communicate mathematically, it is not a strand of mathematics that is well taught in schools. Little research has been done on how professional development programs might improve this teaching. This study investigated the effects of a professional development program on in-service geometry teachers' beliefs and teaching practices of proof. Six participants in a high school participated in a 20 hour professional development program. All participants took part in pre- and post- interviews. In addition, two participants had their classes observed before and after the professional development program when they were teaching proof. In order to describe how the participants' beliefs and teaching practices changed after the professional development, the interviews were coded using a frame work from Knuth (2002a, 2002b). Classroom observations were coded using the Instructional Quality Analysis Rubric (Junker, 2006). Changes were then mapped onto the Interconnected Growth Model (Clarke & Hollingsworth, 2002). Results showed that after the professional development program, the participants stated they felt that it was important to include inductive reasoning components in proof tasks to create insight and provide motivation for formal proof writing. Classroom observations showed that the participants were attempting to implement such tasks in their classrooms but their level of implementation varied and depended highly on their beliefs prior to the professional development program. Future research will use the results of this study to modify the professional development program and implement it with a new cohort of teachers. Also, future research will analyze similar professional development programs in other courses of mathematics such as Algebra 1 and middle school mathematics.