## 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.