This study investigated how dragging in a Dynamic geometry environment (DGE) influences fifth graders in understanding inclusive relationships among quadrilaterals. We selected students who correctly recalled quadrilateral definitions but did not understand inclusive relationships. An analysis revealed that the diagrams in the DGE influenced students’ responses to quadrilateral definitions, indicating that their concept definitions of the quadrilaterals are not stable. Six types of student cognitive behaviors associated with dragging in the DGE were identified. First, students could not understand that dragging can help them find all diagram examples constructed based on certain geometric properties. Second, students may only focus on diagram outlooks when dragging. Third, students may slightly drag vertices or segments to avoid big diagram changes. Fourth, students may focus on what diagrams they intended to drag without noticing the dragging process. Fifth, students may only use data shown in table to evaluate inclusive relationships. Sixth, students can notice generalization and specification in various dynamic examples. Additionally, the types of student evaluations on relationships between quadrilaterals were recognized. They were evaluations based on classification, intersection, and inclusive relationship. Implications and suggestions for research and practices about the use of dragging to learn inclusive relationships are proposed.
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A study of Dragging in Dynamic Geometry Environment in Developing Elementary School Students´ Understanding of Inclusive Relationships among Quadrilaterals
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