Hong Kong preservice teachers' beliefs and attitudes towards teaching proof in school mathematics: a design-based research

Thesis

Researchers have suggested that proof is essential for the learning of mathematics and should be placed at the centre of school mathematics. Yet, many studies suggest that teachers have counterproductive beliefs and attitudes towards teaching proof in school mathematics, which are constraints on making proof central to school mathematics. This study developed an intervention of short duration that promotes preservice teachers’ more productive beliefs and attitudes towards teaching proof, which in turn can support preservice teachers’ future teaching of proof.

Design-based research methodology was used to develop the intervention, which involved four research cycles of implementation, evaluation, and revision. The intervention comprised three weekly two-hour workshops. Preservice teachers who enrolled in different initial teacher training programmes of different universities in Hong Kong were recruited to participate in the intervention. Data were collected from multiple sources, including a questionnaire, individual semi-structured interviews, and fieldnotes and recordings of the intervention. In Research Cycles 1‒3, data were used to assess changes in preservice teachers’ beliefs and attitudes towards teaching proof in school mathematics and evaluate early versions of the intervention, which in turn informed refinements of the intervention. In this thesis, I report the findings of Research Cycle 4.

The results indicated that, after the intervention, the preservice teachers developed more productive beliefs and attitudes towards teaching proof in school mathematics, namely, enhanced beliefs about the importance of proof in school mathematics, greater enjoyment and interest in proof, less anxiety about proof, and less negative responses when failing to prove, and became more open and felt more prepared to implement proof in their future teaching. Components of the intervention that facilitated the change in the preservice teachers’ beliefs and attitudes towards teaching proof have also been investigated.

This study can extend our understanding of multifaceted beliefs and attitudes which influence whether and how preservice teachers plan to implement proof in their future teaching, particularly from an East-Asian perspective, and the design principles for facilitating change in beliefs and attitudes towards teaching proof in school mathematics. In practice, the intervention developed in this study can promote preservice teachers’ more productive beliefs and attitudes towards teaching proof in school mathematics in a relatively short period.

Authors: Lee, GC-Y

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: design-based research; teacher beliefs; preservice teachers; proof and proving