Ateliers de fabrication et d'étude d'objets mathématiques, le cas des instruments à calculer

Abstract : For this research in mathematics education, the observations took place in a centre which develops scientific and technological culture, and works with students finishing primary school. The objective of this centre is to make and study scientific objects. To study the case of mathematics – that is to say the making and the studying of mathematical objects – we chose the calculating instruments (the Chinese abacus, the bones to multiply: Napier and Genaille-Lucas ones, and the slide rule). We show that the making of the instruments with the monitors of the Centre is an important phase as each child makes a material output. We also propose the studying of the instruments with teachers asking directly to children the question of the instructions for use. We analyze this kind of activity like a situation of research which necessitates the mobilization of notional knowledge (relative to a notion) and transversal knowledge in mathematics. So, the studying of instruments creates knowledge outputs. This way – by creating outputs – we built the partnership between the centre and school. Notional knowledge covers the place-value system, the algorithms for calculating and in particular the notion of carried-number that is undistinguished from place-value system. In fact, the comprehension of the carried-number is a necessary condition to mechanize calculating instruments. Finally, we show that defining the carried-number is a mathematical question, rich in sense for both students and teachers training.
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Caroline Poisard. Ateliers de fabrication et d'étude d'objets mathématiques, le cas des instruments à calculer. Education. Université de Provence - Aix-Marseille I, 2005. Français. ⟨tel-00011850⟩

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