Learning to teach through proving: In-service Primary School teachers’ understanding and use of proving while engaged in proof-based teaching

Abstract

This study investigates the effects of an intervention that has a focus on the development of in-service teachers’ proof-related assumptions and the way their understanding of the nature of proving is observable during their teaching. Three in-service teachers of a private school from Peru participated in the study. They were first engaged in an exploratory interview that consisted of two parts and gave access to the teachers’ initial proof-related assumptions. Based on the observations during the exploratory interview, refinements were made to an initial design of an intervention that aimed at supporting the teachers’ change from non-mathematical proof-related assumptions to the formation of mathematical ones. The development of the intervention was part of a two-year design-based research. Here the focus is on the second research cycle which is a refinement of the first cycle. The teachers used the insights they gained during the intervention to teach in their classrooms. Their teaching made visible their use of mathematical assumptions they had changed during the intervention and some new unexpected mathematical assumptions. This study does not only show the way these three teachers developed their own understanding. It shows that although the teachers might use mathematically-aligned assumptions, their warrants might not be mathematical. More importantly it shows the close relation among the teachers’ assumptions and the way it influences their development. It underscores the need for research that emphasizes a global view of individuals’ assumptions so that a real understanding of their development can be achieved. This study identifies the features of the intervention that may explain changes in the three teachers’ proof-related assumptions. Those features were extrapolated to make recommendations of what an intervention with similar goals should include. Suggestions for future research and some reflections are also included.