AN EXPLORATION OF MATHEMATICAL KNOWLEDGE FOR TEACHING GEOMETRIC PROOFS

Abstract

Previous studies showed that secondary school students fail to understand geometric proof development because they are not offered effective learning experiences. However, the studies do not describe the knowledge required by teachers to conduct effective geometric proving lessons. This study explored mathematical knowledge for teaching geometric proofs (MKT-GP) with an aim of providing insights into its content knowledge (CK) and pedagogical content knowledge (PCK). The categories of cognitive activation (COACTIV) model by Baumert and Kunter (2013) were used as overarching theory to inform the study in formulation of research questions, data analysis and presentation of findings. Qualitative case study design was utilised to generate and analyse data. Data were generated from four secondary school teachers through pencil and paper tests, individual interviews, and lesson observations. Both deductive and inductive thematic analyses were conducted on the data to provide CK and PCK for teaching geometric proving. The study has proposed the following categories of CK for geometric proof development: Geometry content knowledge, geometric reasoning, geometric deductive reasoning, problem solving skills and algebraic reasoning. The study has also proposed several sub-categories of PCK relevant for good assessment of students’ thinking, implementation of cognitively activating tasks, for explaining and representing geometric proofs. These include to knowledge of identifying causes of mistakes, knowledge of providing good guidance to students, knowledge of exploratory activities, knowledge of problem solving skills, and knowledge of good teaching and learning materials.