Understanding functional dependency on Dynamic Geometry Systems (DGS): Napoleon and von Aubel Theorems on Geogebra

Abstract

Functional dependency is a term coming out of mathematical software terminology. It shows the dependency of one representation (either diagrammatic or algebraic) to one another in the form of a formula, a conceptual relation or an algorithm. In mathematics, it is important since it shows students’ understanding of those conceptual relationships if used properly. In this study, we have used representation of two mathematical theorems on DGS specialty of Geogebra: Napoleon and von Aubel Theorems. Both theorems are related with the geometrical relations of simple shapes as in the forms of squares and triangles. A class of 33 students divided into two lab groups were given randomly these two theorems without the knowledge of the names of the theorems to the students of Material Development course students. In each lab hour, students’ assignment to the theorems were related to their seat numbers in order hence no one could see the same theorem person seating next to a student. The main study was a teaching experiment. Results are analyzed according to correct reasoning, inconsistencies, lacking diagrams etc. Data demonstrate that these kind of theorem use in mathematics classroom may be possible by Geogebra use and may empower students to think mathematically. Functional dependency is not connected to the task, hence can be given in all types of tasks by Geogebra. It was interesting to see some students’ conjectures on the results of these two theorems.

Keywords

• Dynamic geometry
• understanding math
• functional dependency
• Geogebra

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