Geogebra, tool for mediating knowledge in the teaching and learning of transformation of functions in mathematics.

Abstract

As a teacher of mathematics, I always taught the topic functions (graphs such as linear, quadratic, hyperbola, exponential, trigonometric functions) in the same way all of my twenty-three years in the profession. I often assumed that the learner understood a concept that had been presented only to find, in subsequent lessons, that the learner could not recall it or talk about it. I referred to the constant value c in the function f (x) = ax² + c or f (x) = ax² + bx + c as the y-intercept informing my learners that it is a point on the y-axis of the Cartesian plane. I also taught transformation of functions as the vertical and horizontal shift without much visual demonstration beyond pen and paper. Whilst using dynamic mathematics geometry software, last year namely, Geogebra, I realized that this section could be taught more effectively through interaction with this software. Geogebra, is a freely available interactive dynamic software for the teaching and learning of mathematics that combines geometry and algebra into a single user-friendly package. Within this research I set out to explore firstly, the function of Geogebra, as a pedagogical tool and mediating artifact in the teaching and learning of transformation of functions in secondary school mathematics; and secondly whether interaction with these virtual manipulatives enhance the understanding of mathematics concepts. The study is rooted in a social constructivist view of learning and mediated learning and the approach used is a case study. The research was carried out in an independent school that involved 8 learners. My data consisted of feedback from two sets of student worksheets, the first being from prior to using the Geogebra applets and the other from post engagement with the applets, classroom observations during the practical use of Geogebra and finally with learner interviews. On analysis of the data it seems that the introduction of Geogebra did indeed influence the educational practice in three dimensions, namely: the development of mathematical ideas and concepts through computer-based teaching and the role Geogebra plays in the understanding of and visualization of certain mathematical concepts in high school algebra topics.