Recent research on geometry education: an ICME-13 survey team report

Abstract

This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.

Pre-Service Mathematics Teachers’ Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms

“…One theme in geometry education where prototype phenomenon has been applied is the classification of geometric shapes (Hershkowitz 1990). This prototype phenomenon has been and continues to be the subject of research and, it is argued to be one of the causes of difficulties in understanding the inclusion relations of quadrilaterals (Fujita, 2012;Sinclair, et al, 2016). Various studies emphasized that it is an obstacle preventing the acquisition and adoption of hierarchical relationships between them, as classifying quadrilaterals (Fujita, 2012;Fujita & Jones, 2007;Okazaki & Fujita, 2007).…”

Use of theories and models in geometry education research: A critical review

“…Moreover, the critical review of the literature reveals that there is a dearth of studies exploring the multilingual context of geometry classes. Sinclair et al (2016) published a review article focusing on the research contribution since 2008 in the field of geometry education. Interestingly, the article fails to mention the complexities arising due to the multilingual context of teaching and learning of geometry.…”

Volume 2. Proceedings of the Interdisciplinary STEM Teaching and Learning Conference

“…Both the PSMTs and the researcher felt the need to modify some of the geometry tasks that the researcher developed for the study by incorporating the dragging feature of dynamic geometry environments (DGEs), such as The Geometer's Sketchpad and GeoGebra. Especially, under the background of the rapid development of mobile devices and touch technology, the use of the dragging feature of DGEs in teaching and learning proof and reasoning has been discussed more and more widely and has become an ongoing research trend in mathematics education (Mariotti, 2014;Sinclair et al, 2016). Furthermore, introducing the dragging feature of some easily accessible DGEs to my secondary geometry content classes can provide PSMTs with a handy tool to explore the meaning and applications of counterexamples in writing proofs.…”