Teachers’ Instrumentation of a Collaborative Dynamic Geometry Environment

Muteb M Alqahtani,Arthur B Powell

doi:10.24933/horizontes.v36i1.649

Muteb M Alqahtani, Arthur B Powell

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We draw on the theory of instrumental genesis (RABARDEL; BEGUIN, 2005) and the notion of co-action (HEGEDUS; MORENO-ARMELLA, 2010) to understand how teachers’ instrumentation of dynamic geometry environment (DGE) and how this instrumentation shapes their geometric knowledge. In small groups, six middle and high school mathematics teachers engaged in solving open-ended geometric problems in an online dynamic geometry environment for 15 weeks. Our analysis of their interactions indicates that the co-action between the teachers and the environment helped them appropriate the dragging feature of DGE, which shaped their understanding of geometrical relations, particularly dependencies. Designing tasks that support teachers’ effective appropriation of DGEs requires special attention to the co-active nature of DGEs. This study provides insights into aspects of learners’ collaborative interaction with certain technologies.

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With dynamic geometry environments (DGEs), the software provides feedback to the user after manipulating dynamic objects, which affects the user’s interaction with the software
CENTER FOR BEST PRACTICES; COUNCIL OF CHIEF STATE SCHOOL OFFICERS, 2010, p. 7), meta-analytic and large-scale studies indicate that teaching with technology cannot guarantee positive learning outcomes (CHEUNG; SLAVIN, 2013; HIGGINS; XIAO; KATSIPATAKI, 2012; KAPUT; THOMPSON, 1994; LI; MA, 2010; RAKES; VALENTINE; MCGATHA; RONAU, 2010; WENGLINSKY, 1998)
Our analysis focuses on understanding how the teachers appropriated Virtual Math Teams with GeoGebra (VMTwG) and how this appropriation shapes their geometrical understanding

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With dynamic geometry environments (DGEs), the software provides feedback to the user after manipulating dynamic objects, which affects the user’s interaction with the software. The environment reacts to the users’ actions through engineered infrastructure that responds according to the theory of geometry This reaction can inform the users’ actions and can shape users’ thinking. There is a gap in the literature about understanding how learners use technological tools collaboratively and develop their mathematical knowledge. To contribute to this understanding, we describe learners’ appropriation of online, dynamic geometry environment and its influence on their geometrical understanding. This paper responds to the question: How do learners appropriate an online, collaborative dynamic geometry environment and how do this appropriation and the environment’s coactive functionality shape their geometrical understanding?

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