From geometric representation to algebraic representation with dynamic mathematics software: the concept of parabola

Abstract

Mathematical concepts can be represented in different ways. Geometric and algebraic representations are the most well-known and formal versions. The algebraic representation is abstract view of the concept, while the geometric representation is rather visual. Teaching a concept by relationships between its different representations is one of the important components of mathematics teaching. This study aims to construct the concept of parabola with the relationship between its geometric and algebraic representations. This construction is planned as bidirectional. That is both from geometry to algebra and from algebra to geometry. Since curve of the parabola started to appear with its geometric views in mathematics history, geometric representation was chosen as starting point of the construction. A learning environment was designed in 4 phases by the help of facilities provided by the GeoGebra Dynamic Mathematics Software. This learning environment was applied in a sample course in which 23 students of the 11th graders of an Anatolian High school participated. The learning environment was found as practical from the feed backs of the students during the course. Furthermore, the activity, designed to manage the learning environment, provided the learners with an opportunity to examine some advanced properties of the parabola.