Conclusion: prospects for developments and research in secondary geometry education

This chapter concludes the collection of chapters, each of which expands on the papers presented during the Topic Study Group on the teaching and learning of secondary school geometry at ICME-13. In articulating a vision for where the field of secondary school geometry could go in the near future, the chapter revisits issues of methodologies for data collection and data analysis. The chapter proposes how new technologies could be integrated into research and practice in secondary school geometry and outlines some of the questions that the field might expect to address with the aid of such technologies

Enabling anticipation through visualisation in mathematising real-world problems in a flipped classroom

Meta-analyses of findings from flipped classroom studies in mathematics classrooms to date need to be treated with caution until the teachers and students involved develop mindsets that maximise and integrate the learning potential of both the out-of-classroom and in-classroom learning environments. Rather than a flipped classroom being used as a means to get through the curriculum, it can be used to enrich the curriculum. The question addressed is: Could a flipped classroom provide both vicarious experiences and fostering of critical thinking skills associated with modelling? A local secondary school implementation is used to illustrate how the approach could build meta-knowledge about mathematical modelling and facilitate associated critical thinking skills such as anticipating and visualisation to expand the learning experiences of secondary mathematics students