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

• Published in: Educational studies in mathematics Vol. 113; no. 2; pp. 181 - 205
• Main Authors: Pittalis, Marios, Drijvers, Paul
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2023; Springer; Springer Nature B.V
• Subjects: Cognition; Education; Educational Technology; Geometric Concepts; Geometry; Instrumentation; Instruments; Learning Strategies; Mathematics; Mathematics Education; Mathematics Instruction; Parallelograms; Perception; Preadolescents; Rectangles; Students; Study and teaching; Tablet Computers; Technology Uses in Education; Cyprus; Dynamic geometry; Primary education; Embodied instrumentation; Dragging; Instrumental genesis; Mathematics education; Embodiment
• ISSN: 0013-1954; 1573-0816
• DOI: 10.1007/s10649-023-10222-3

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.