On the Exploration and Problem Solving Related to Tangent Lines of Quadratic Curves via Dynamic Geometry

Objectives The purpose of this study is to explore methods of effective teaching the tangent line of quadratic curves in a dynamic geometric environment. Methods The exploratory software GeoGebra was used as a dynamic geometric environment, and the activity worksheets for exploring the geometric properties of the tangent line to quadratic curves were developed. The changes in students’ perspective of geometry appeared were examined and their influences were analyzed. Results The results show that the dynamic geometric environment is significant as a means for students to think geometrically by intuitive observation and explore the inherent properties of the tangent line to quadratic curves. Teaching from the perspective of geometry made students change their views that they need to memorize formulas and be familiar with the types of problems to learn quadratic curves. There is a positive response about changes in students understanding the problem situations and leading the solving process. Conclusions The result of this study provides some useful implications to geometry education that harmonize perspectives of analytic geometry and synthetic geometry.