A Study of Geometric Construction in Dynamic Geometry Environment “GeoGebra”: A Proposal and Verification of the Category Focused on the Concept of “Degree of Freedom of Points”

Abstract

The purpose of this study is to reconsider and propose a framework for the category of geometric constructions in dynamic geometry environments. This framework is theoretically considered from the concept of “degree of freedom” for points, which concerns the essence of dynamic geometry environments, and then is empirically verified as to its validity and usefulness for the geometric constructions of the subjects. The conclusions of this study are 1) geometric constructions in dynamic geometry environments are classified into 5 types, and these types are related in terms of the state of recognition of geometrical figures, 2) the constructors moves type (2) and (3) and, it is necessary that we reconsider the 2 types and their relation. The results of this study contribute to promoting the utilization of technology in mathematics education in compulsory education.