The aim of this study is to explore, in a dynamic geometry environment (DGE), the operation models of the geometric thinking of college students. To achieve this, we conducted a case study. We recorded the process of geometry exploration activities by math-major college students, interviewed them, and interpreted their operation models of thinking through a qualitative analysis. The results are summarized as follows: (1) When students observe the dynamic representations generated by dynamic geometry software (DGS), they seldom react immediately, and instead engage in geometric thinking before they carry out appropriate dragging. (2) The apparent actions and intrinsic mathematical properties of dynamic representations tend to inspire students’ conjectures. Students then mentally manipulate mathematical objects and analyze possible dynamic behaviors to confirm their conjectures. Finally, they are able to produce a declaration. This process is a basic model for geometric thinking. (3) Students manipulate mathematical objects mentally based on the complexity of operation, and then decide whether to use a DGS-specific claim or conjecture in geometric thinking. (4) Students explore geometry properties in DGE under the constant interactions between geometry experiments and geometric thinking.
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Analyzing College Students’ Geometric Investigation within the Dynamic Geometry Environment
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