Curriculum, Classroom Practices, and Tool Design in the Learning of Functions Through Technology-Aided Experimental Appr
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CURRICULUM, CLASSROOM PRACTICES, AND TOOL DESIGN IN THE LEARNING OF FUNCTIONS THROUGH TECHNOLOGY-AIDED EXPERIMENTAL APPROACHES
ABSTRACT. The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a ‘transposition’ of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic geometry and spreadsheets. The paper focuses then on the potentialities of classroom use of computer algebra packages that could help to go beyond this shortcoming. It looks at a contradiction: while symbolic calculation is a basic tool for mathematicians, curricula and teachers are very cautious regarding their use by students. The rest of the paper considers the design and experiment of a computer environment Casyope´e as means to contribute to an evolution of curricula and classroom practices to achieve the transposition in the domain of algebraic activities linked to functions. KEY WORDS: classroom practices, computer algebra, computer tool design, curriculum, dynamic geometry, experimental approaches, functions, instrumentation, praxeologies, spreadsheet, transposition
1. INTRODUCTION At the present time, mathematics curricula – especially at secondary level in France – recommend the use of computer tools and this use is not uncommon in classrooms. It is then possible to go beyond a ‘laboratory approach’ of the educational use of computers and to address as a whole the issues of curriculum, classroom practices, and relevance of software applications offered for students. Research about technology in education indeed broke off with considering a mechanical influence of new tools on curricula and classroom practices. To be successful, technological innovation has to offer new opportunities for current curricular concern and to be compatible with viable classroom practices (Ruthven and Hennessy, 2002). At a more general level, Human Computer Interaction (HCI) researchers stressed for 10 years that ‘Laboratory-based usability studies are (only) part of the solution’, and are best preceded by ‘‘careful field
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studies’’ to address question like: ‘how technology can fit into users’ actual social and material environments; the problems users have that technology can remedy; the applications that will promote creativity and enlightenment. . .’ (Nardi, 1996). The approach of this paper will be first to consider existing combinations of curriculum, practices and tools, and then, analysing possible limitations, to look into potential new combinations. These new combinations include new curricula and practices but also new tools. That is why a concern of this paper will be about technological tool’s design. Taking into account the limitations of existing software in view of curriculum and practices, and of their possible evolution, this paper will consider a project that a team including the author is currently developing: the Casyop
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