Preservice Mathematics Teachers’ Instrumental Genesis and Their Development of Geometric Knowledge in a Dynamic Geometry Environment

The emergence of dynamic geometry software influences the teaching and learning of geometry among learners of all ages. Relying on the theory of instrument, this study examined the relationship between preservice mathematics teachers’ instrumental genesis and their development of geometric knowledge when solving geometry construction problems with the Geometer’s Sketchpad (GSP). Data analysis revealed the coevolution between instrumental genesis and geometric knowledge. Two preservice secondary mathematics teachers’ explorations on two geometry problems are shared to illustrate this coevolutionary relationship. This relationship can be summarized as the following. Guided by his prior knowledge of geometry and GSP techniques, the participant first used particular GSP tools to obtain a geometric figure possibly through a non-constructible method. Through manipulating this geometric figure by various modalities of dragging and measuring as well as other instrument-mediated actions, the participant observed new geometric properties. The participant then used this newly developed knowledge to guide his GSP usage, which led him to create a dynamic figure or develop an alternative construction. This process might go through multiple iterations. It highlights the dynamic interactions among the learner, mathematical task, and technological tool, through which new geometric knowledge and meaningful ways of using technology emerge.