![]() ![]() 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 utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. 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. #ZOOMMATH 500 REGISTRATION KEY SOFTWARE#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. From these dynamics, finally, we will sketch some perspectives for further researchĮncouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. In the fifth section, we analyze the influence of this evolution for rethinking the instrumental approach itself. In the fourth section, we underline the influence of this evolution for rethinking the role of the teacher. Next, we evidence the evolution of this notion, giving more importance to its role in learning processes. We situate this notion as an element of the dialectics instrumentalization-instrumentation grounding the instrumental approach. ![]() In this article, we will first address our general view on mediated action, before introducing the notion of instrumentalization, as adapting a tool for adopting it as a support of one’s mathematical activity. This type of use has evolved over the time, keeping a strong link with general definitions above, pointing out the creative potential of an agent (performing, arranging, scoring, making something instrumental….), in the frame of an orchestra. In mathematics education, the noun “instrumentalization” has been more frequently used than the verb “to instrumentalize”. “To instrumentalize” is generally defined as “to perform (a piece of music) using a musical instrument or instruments” or “To arrange or score (a piece of music) for instruments, especially for an orchestra”, or “To make or render (something) instrumental to accomplishing a purpose or result to use as a means to an end”. This journey through history and schooling represents a good occasion to address some questions: Are there ‘‘good’’ contexts in which to develop mathematical instruments? Are there ‘‘good’’ teaching practices which assist students’ instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed. ![]() Our ‘‘visits’’ to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. The issues related to the use of tools and technologies in mathematical education are now widely considered. In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. ![]()
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