Developing an understanding of inclusion relationships among quadrilaterals through mathematical events

This study examined the impact of analysing mathematical events on prospective teachers’ conceptualisations of inclusion relationships among quadrilaterals. Grounded in the theoretical framework that emphasises the transformative potential of mathematical events for developing content knowledge, the study employed a mixed methods design with 20 prospective teachers. The intervention involved engaging participants in the critical analysis of three mathematical events, with data collected via pre- and post-tests and transcribed classroom observations. Initially, most participants struggled to identify these relationships, relying on non-critical attributes exclusive to prototypical examples rather than shape definitions. After the intervention, participants showed significant improvement in recognising inclusion relationships, using geometrical definitions and critical attributes to explain their responses. The observed improvements were related not only to the inclusion relationships discussed in the events, but also to inclusion relationships not discussed in the events, in the context of both verbal and visual tasks. The intervention enhanced the participants’ ability to extend concept images to non-prototypical examples.