Yess4Conf_JBL

# Yess4Conf_JBL - Research about technology in mathematics...

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http://jb.lagrange.free.fr/site Research about technology in mathematics education: an evolution Jean-baptiste Lagrange Equipe de didactique des mathématiques, université Paris 7

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http://jb.lagrange.free.fr/site These themes are not independant. They differ by a specific entry into our general questionning, but they are convergent. We adopt different theoretical orientations (TSD, TA, activity theory …). Our specificity is to cross these approaches and to analyse the implications of theoretical choices.
http://jb.lagrange.free.fr/site An example Vandebrouk (1999) L’utilisation du tableau noir par des enseignants de mathématiques An Emergent Inquiring Field: the Introduction in the Classroom of Online Exercises Set

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http://jb.lagrange.free.fr/site A lecture about research in technologies. For what purpose ? The role of artefacts in human Knowledge Cognition Social activity An Artefact Is a product of art or industry, Expresses a fundamental property of a living being: to have a project and to inscribe this project in a production. (Monod)
http://jb.lagrange.free.fr/site Artefacts influence conceptualisation Multiplication is not an operation It does not commute Artefacts 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36 Task: The table and the calculator are two artefacts that can play specific roles in the conceptualisation of multiplication. - as an operation, as a commutative operation. Please specify these roles.

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http://jb.lagrange.free.fr/site Table Calculator Operation Commutativity T1: the role of artefacts in conceptualisation
http://jb.lagrange.free.fr/site Technologies Frameworks 1. Programming and visualizing Reification theories 2. Microworlds Constructionism Situated cognition 3. Spreadsheets and Computer Symbolic Systems Instrumental and Anthropological approaches 4. Quickly progessing uses of the Internet, Uses by ‘ordinary’ teachers New challenges and a need for new approaches

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http://jb.lagrange.free.fr/site Reification « Many theoretical and empirical arguments may be employed to show that in mathematics, operational conception precedes the structural. What is conceived as a process at one level becomes an object at a higher level. » Sfard and Linchevski The gains and the pitfalls of reification
http://jb.lagrange.free.fr/site Programming Important feature of computer technology Specific languages proposed as means to manipulate mathematical entities. A central assumption : programming Helps learners to reflect on actions Favours conceptualisation (reification).

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http://jb.lagrange.free.fr/site ISETL and APOS A programming language associated with a specific theory “An individual's mathematical knowledge is her or his tendency to respond to mathematical
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## This note was uploaded on 11/11/2011 for the course MATH 220 taught by Professor Kearn during the Fall '11 term at BYU.

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Yess4Conf_JBL - Research about technology in mathematics...

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