Abstract
Encouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. As a contribution to the discourse, this article discusses the potential use in the classroom of The Geometer’s Sketchpad® (Key Curriculum Press, Emeryville, CA, United States) mathematics software in modelling the derivative and related concepts in introductory calculus. In an empirical study involving first-year non-mathematics major undergraduate science students, a hypothetical learning trajectory (HLT) was conjectured and implemented for students to experience the visualisation and multiple representations of calculus concepts on the Cartesian plane with a computer graphic interface. The utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. The HLT was partly informed by the historical development of the derivative as synthesised from the literature on the history of calculus and partly by the affordances, enablements, constraints and potentialities of Sketchpad itself. The findings of the study suggest that when exposed to the capabilities of this software, learners can experience Geometer’s Sketchpad® as an effective visualisation tool or instrument for the representation and learning of the derivative and related concepts in introductory calculus. However, the effectiveness of this tool is not a given or a foregone conclusion − it is a product of the teacher’s instrumental orchestration, gradual learner mastery of the software syntax and careful resolution of theoretical-computational conflicts that can arise during early use of the instrument.
Highlights
There is increasingly firm encouragement to integrate information and communication technologies into mathematics education curricula in many countries of the world today, aided and accentuated by an unprecedented global proliferation of digital technologies
The findings suggest that the introduction of technology into the classroom requires instrumental orchestration skills from the teacher, with which to facilitate the processes of instrumental genesis amongst learners
The qualitative results suggest that provided with individual computers and worksheets, learners can work collaboratively to achieve a reasonable understanding of the mathematical concepts at stake
Summary
There is increasingly firm encouragement to integrate information and communication technologies into mathematics education curricula in many countries of the world today, aided and accentuated by an unprecedented global proliferation of digital technologies. The imperative to introduce computing technologies into the classroom brings with it many new opportunities for learning and teaching, but is strongly encouraged from within the mathematical and scientific community itself. Today most problems in the ‘real world’, in the scientific community and society broadly, can only be tackled, modelled and investigated with the aid of computing technology. The problems engineers and scientists frequently investigate today almost as a rule lead to differential equations which can only be solved numerically. Computing technology is seriously challenging the very content and focus of aspects of traditional mathematics curricula at school and university, and gradually beginning to force curriculators to start grappling with the ‘uncomfortable’ question about what is still relevant and what is not, and which new skills are essential for a modern computing society
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