Embodied instrumentation in a dynamic geometry environment: eleven-year-old students’ dragging schemes

Abstract

Digital technologies for mathematics education are continuously developing. Still, much remains unknown about how students use these tools and how this affects learning. For example, tablets nowadays come with multi-touch options that allow for a more embodied approach to geometry education, compared to mouse interactions. However, little is known about how students use these opportunities to develop bodily-based conceptualizations of geometric concepts in a touch-based dynamic geometry environment (DGE). The aim of this study was to investigate students’ dragging schemes from an embodied instrumentation perspective and to identify the types of embodied-dragging schemes that the students use, while transforming one type of parallelogram into another. Fifty-seven 11-year-old students worked on a task on transforming a given parallelogram into a rectangle and next into a square, using a tablet-enabled DGE. Results showed that students used three types of embodied dragging schemes: (a) action-perception dragging guided by perceived prototypical images of shapes, (b) sequentially-coordinated dragging based on initial perception and then utilizing the affordances of the artefacts, and (c) adaptive dragging, effectively integrating action-perception loops and geometrical properties. In schemes of types (b) and (c), geometric properties of the constructed shapes emerged and guided students’ action-perception loops. As a conclusion, this description informs teachers, textbook authors, and designers of digital assessment on how to design student activities. From a theoretical perspective, the embodied instrumentation lens provided a fruitful approach to study student–tool interactions in geometry that does justice to the bodily foundations of mathematical cognition.