1-Artigue-powerpoint

1-Artigue-powerpoint - Learning mathematics in a CAS...

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Unformatted text preview: Learning mathematics in a CAS environment : Learning mathematics in a CAS environment : the genesis of a reflection about instrumentation the genesis of a reflection about instrumentation and the dialectics between technical and and the dialectics between technical and conceptual work conceptual work Michle Artigue Universit Paris 7 & IREM Summary Summary Introduction The progressive development of the theoretical frame The unexpected complexity of instrumental genesis The institutional status of instrumented techniques Revisiting the relationships between technical and conceptual work: the epistemic value of instrumented work and techniques Introduction Introduction An evident contrast between: the impregnation by technology of most social and professional practices the limited penetration of these into the educational world Behind this constrast, an opposition of values that CAS technology makes specially clear From the professional and social sides: A pragmatic relationship to technology, Recognising that technology is not of an evident access, Accepting the fact that technology strongly shapes our practices and perspectives From the educational side: A vision of technology which remains mainly a pedagogical one, technology being asked to serve values defined independently from it An attitude that leads to see technology as something transparent with respect to knowledge and values Some dangerous associations Some dangerous associations Technology, by taking in charge the technical side, leaves the mind free for conceptual reasoning and provides new means for that Reality is much more complex The use of technology favours conceptual reasoning Computer technologies desqualify teaching pratices orientated towards skill acquisition, and support constructivist approaches In fact, our first observations of students In fact, our first observations of students working with DERIVE clearly showed: working with DERIVE clearly showed: 1. The existence of two opposite tendencies : One favouring reflexive and strategic work One tending to save reflection or reduce the global coherence of action 2. The fact that technical work changes but does not disappear at all 3. The essential role played by the didactic situations at stake and by the teachers management of these This was the starting point of a...
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1-Artigue-powerpoint - Learning mathematics in a CAS...

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