International perspectives on the teaching and learning of geometry in secondary schools

Abstract

This book is one of the outcomes of Topic Study Group 13 at the 13th International Congress on Mathematical Education, which took place in Hamburg, Germany, in the summer of 2016. Our Topic Study Group (TSG-13) concerned the teaching and learning of secondary geometry and the chapters in this volume include revised versions of most of the papers presented at the main meetings of the group. Also included are a handful of the shorter papers associated with TSG-13 in the context of short oral communications. In this brief introduction we orient the reader to these papers by first providing an organizer of the focus of our study group. The International Congress in Mathematics Education gathers researchers and practitioners in mathematics education and pursues a goal of inclusiveness across all sorts of boundaries. In particular, the boundaries between research and practice are often blurred in ICME and this surely applied to our Topic Study Group 13 in ICME-13. Therefore, to orient the reader to the chapters in the book, it might be useful to describe the territory or field of practice associated with the teaching and learning of secondary geometry. As we engage in such a description, we might benefit from using the metaphor of map-making as a guiding principle. Borges’s short story On exactitude in science uncovers the futility of expecting that a map be produced on a scale 1:1. Yet the value of maps as containers of geographic knowledge and as resources for travelers cannot be overemphasized, even if the existence of different kinds of projection techniques reminds us that any map has limitations in what it affords its readers. Different maps afford us different kinds of insight on the territory.