An experimental approach to the derivative using Geogebra.

Abstract

This qualitative research study was carried out with six Grade 11 pupils from a school for boys in Pietermaritzburg, South Africa. Its main intentions were to explore if the computer software Geogebra could aid pupils in discovering the differentiation rule for elementary polynomials and to assess the effectiveness of Geogebra in enhancing the development of concepts related to the derivative. Geogebra is a free dynamic computer software program that combines geometry and algebra into a user friendly mouse driven package. The study was informed by constructivism and Kolb’s (1984) experiential learning theory. One-to-one task-based interviews were the main data collection strategy. Analysis of the data, in an interpretive paradigm, suggested that Geogebra can indeed provide the necessary support required by the pupils to deduce inductively the differentiation rule for elementary polynomials. The results also suggested that the evolution of the general result follows a linear process and as such the strategic sequencing of the task-based activities is of paramount importance. Additionally, all the students who successfully deduced the result displayed high levels of conviction regarding its generality and they expressed a need for an explanation. This arguably sets the tone for the teaching of the formal proof, which in this case serves to explain why the empirically derived result is always true. The study also found that the experience with the Geogebra applets might help students resolve conceptual difficulties associated with the derivative. In particular, it explored the effect of the Geogebra experience on the students’ ability to solve non-routine graphing problems involving the first derivative. Analysis of the results produced some insights that may be important for instructional design. It found that students concentrate on either the degree of the polynomial or the derivative as a function of x. The ability to correlate the two aspects leads to the successful solution of the problem, and evidence from the interviews indicated that Geogebra has a role to play in helping pupils reconcile these concepts.