Instrumental Appropriation of a Collaborative, Dynamic-Geometry Environment and Geometrical Understanding

To understand learners' appropriation of technological tools and geometrical understanding, we draw on the theory of instrumental genesis (Lonchamp, 2012; Rabardel & Beguin, 2005), which seeks to explain how learners accomplish tasks interacting with tools. To appropriate a tool, learners develop their own knowledge of how to use it, which turns the tool into an instrument that mediates an activity between learners and a task. The tool used in our study is the Virtual Math Teams with GeoGebra (VMTwG) environment. It contains a chat panel and multiuser version of GeoGebra. The learners are seven middle and high school mathematics teachers who participated in a professional development course in which they collaborated synchronously in VMTwG to solve geometrical tasks. We use conventional content analysis to analyze the work of a team consisting of two high school teachers. Our analysis shows that the teachers' appropriation and application of the dragging feature of VMTwG shaped their understanding of geometrical relations, particularly dependencies. This informs the broader question of how and what mathematical knowledge learners' construct using certain technologies.