Pre-service teachers' noticing of structural thinking in mathematics

The importance of teachers' understanding and using mathematical structure is recognised but not well researched. Mathematical structure, when understood, connects mathematical concepts and builds powerful understandings of deep mathematical thinking. The research reported in this thesis is based on the premise that educating teachers to consider structural thinking in their teaching and learning processes will improve their mathematical content and pedagogical knowledge. The positive outcome of teachers using mathematical structure is that it encourages students to think structurally. In this study, I investigated two primary and three secondary mathematics pre-service teachers (PSTs) as they engaged in learning about mathematical structure through a professional learning program during their final undergraduate year. This study comprised two phases. The first phase involved the primary PSTs, the second involved the secondary mathematics PSTs. All PSTs completed an introductory and exit questionnaire either side of a professional learning program in which they participated in three cycles, each of which comprised a professional learning workshop, teaching a planned mathematics lesson, and a post-lesson interview or post-lesson reflection. Quantitative and qualitative data were collected from the two questionnaires, audio transcripts of the professional learning workshops and the post-lesson interviews, lesson plans, and videos of the PSTs' mathematics lessons. These data were analysed for the PSTs' understanding and use of a new framework, the Connecting, Recognising Patterns,Identifying Similarities and Differences, Generalising and Reasoning (CRIG) framework, to teach mathematical structure-a framework that refers to "noticing structural thinking". From the results of this study, I was able to identify that the PSTs came to appreciate the importance of mathematical structure through their familiarity with the new framework. Engaging in the CRIG framework proved to be effective in deepening the PSTs' mathematical content and pedagogical knowledge. However, their use of the CRIG framework when in-the-moment of teaching was not always reflected in their communications or pedagogical approach -- summary.