Teaching 3D geometry with dynamic environments in upper secondary classes: How to help students combine empirical perception and theoretical deduction?

Abstract

This study investigates a crucial didactical challenge for mathematics teachers when they integrate 3D dynamic geometry environments (3D DGEs) into upper secondary classrooms. The challenge concerns teachers’ regulation of the interaction of two processes—empirical perception (often intertwined with actions) and theoretical deduction—in student learning. We establish a framework to characterize teachers’ behaviour regarding the two processes of students, referring to it as the “coordination behaviour” framework. The framework is then applied to a case study involving an experienced French mathematics teacher. The analysis identifies three distinct patterns in the teacher’s coordination behaviour, revealing that despite her goal of fostering students’ theoretical deduction and empirical perception–action concurrently, she sometimes has to make compromises due to contextual and personal factors, leading to a diminished focus on one of these two processes. The results highlight the intricacy of teachers’ coordination in upper secondary classrooms integrating 3D DGEs. We therefore call for the development of teacher education programmes that specifically prepare teachers to address this challenge.