Abstract
Generalization and proof are defining activities within mathematics, yet the focus of "school" proof has often been on form over meaning, on established results rather than exploration and discovery. Computer-based microworlds offer opportunities for students to notice and describe patterns, formulate generalizations, and generate and test mathematics conjectures. This paper examines the work of a group of middle and high school students who used a microworld for transformation geometry to investigate the composition of reflections. The students‘conjectures are described in terms of a learning paths chart for the task, as well as through a detailed analysis of the work of one pair of students. A general scheme for describing informal exploration and reasoning prior to formal proof is offered, and the role of social support in the learning of proof is discussed.
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Edwards, L.D. Exploring the Territory Before Proof: Student‘s Generalizations in a Computer Microworld for Transformation Geometry. International Journal of Computers for Mathematical Learning 2, 187–215 (1997). https://doi.org/10.1023/A:1009711521492
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DOI: https://doi.org/10.1023/A:1009711521492