An Exploration of Teaching for Understanding the Problem for Geometric Proof Development: The Case of Two Secondary School Mathematics Teachers

Understanding the proof problem is necessary in the development of geometric proof in schools. This paper discusses findings from a qualitative case study which explored the mathematical work done by teachers in helping students to understand geometric proof problems. Data were generated from two teachers through video-recorded observations of 30 lessons and tape-recorded post-lesson interviews. Both types of data were analysed using thematic analysis which involved coding of the data relating to the first stage of Polya’s problem-solving framework. The findings suggest that supporting students to understand geometric proof problems involves several tasks, including defining key mathematical terms of the theorem, initiating activities for introducing the theorem and representing the theorem as a statement to be proved. Furthermore, conducting these aspects of mathematical work using empirical exploratory approaches offers students better opportunities to understand the proof problem. © 2019, © 2019 Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE).