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

Abstract

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.

Keywords:

• Geometric proof development
• geometric proof problem
• problem-solving
• mathematical tasks

Acknowledgements

This study was kindly funded by the Norwegian Programme for Capacity Building in Higher Education and Research for Development (NORHED) under Improving Quality and Capacity of Mathematics Teacher Education in Malawi Project.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Lisnet Mwadzaangati http://orcid.org/0000-0002-4322-2864

Additional information

Funding

This work was supported by Norwegian Agency for Development Cooperation (NORAD) (grant number QZA-0483 MW1-13/0022).