Commencing in April 2016, Kotaro Komatsu (Shinshu University, Japan), who is currently a Visiting Fellow at Southampton Education School, and Keith Jones, began a research project entitled Proofs and Refutations in Dynamic Geometry Environments (PRinDGE). The project is funded by the Japan Society for the Promotion of Science.

Following the work of mathematics philosopher Lakatos, this study uses the term proofs and refutations to refer to mathematical activity depicted in the figure. The process of proofs and refutations is essential in school mathematics because it can provide students with an opportunity to engage in authentic mathematical activity that represents how mathematical knowledge dynamically develops in the discipline. Nevertheless, there is still much to learn about how the activity can be facilitated in the classroom.

To address the research gap, our PRinDGE research project focuses on task design for fostering student activity of proofs and refutations with dynamic geometry software. In particular, we aim not only at developing tasks and task sequences that can be of practical use in classrooms, but also at making a contribution to mathematics education research by providing design principles that theoretically and empirically support the task design.

From left to right Mikio Miyazaki (Shinshu University), Keith Jones, and Kotaro Komatsu