This study investigated how junior high school students conjecture geometric properties in a dynamic geometry software (DGS) environment. Using the proceduralized refutation model as an intermediate theoretical framework, we particularly examined the process and the difficulties that students may have when conjecturing. Specifically, we referred to DGS as an “example generator” and combined it with spreadsheets to support students in conjecturing geometric properties. A total of 15 seventh grade students participated in this study. Based on the qualitative analysis and quantitative data, we demonstrated that (1) the complexity of the relationship among measurements involved in a geometric property and the possibility of visualizing that property play important roles in determining students’ performance when conjecturing in a DGS environment; (2) being able to effectively classify geometric objects was the key to successfully perceiving geometric properties and relationships embedded in geometric diagrams; (3) decomposing and recomposing diagrams aided students in recognizing embedded geometric properties; (4) the ability to drag a geometric diagram into different shapes in a DGS environment did not guarantee the ability to discern supportive and counter examples or the ability to use those examples to correct false conditional statements; and (5) a lack of knowledge specific to DGS environments, particularly those related to dragging, hindered students’ effective construction of diagram examples. Additionally, we identified three types of conjecture approach: induction by randomly generating a finite number of discrete examples, conjecture by systematically making examples, and conjecture by dynamically altering examples.
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Junior High School Students Conjecture Geometric Properties in a Dynamic Geometry Software Environment
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