Bosch TSG28 ICME10

Bosch TSG28 ICME10 - TSG 28 ICME 10 Copenhagen July 2004...

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1 Mathematical Cognition and Mathematical Cognition and the Anthropological Approach to Didactics the Anthropological Approach to Didactics the institutional relativity of knowledge the institutional relativity of knowledge Marianna Bosch Marianna Bosch Universitat Ramon Llull (Barcelona) Universitat Ramon Llull (Barcelona) TSG 28 - ICME 10 Copenhagen, July 2004
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2 [A]ny scientific activity (including mathematics) is made up (through its language) by means of metaphors . Thought develops basing itself on metaphors; more generally, ‘ rhetoric ’ is a component of scientific activity. […] However, the greatest problem here lies in the choice of ‘ good ’ metaphors, of genuinely fecund metaphors which will not get out of hand. The Greek mathematicians, thus, were unable to consider the ration of integers as numbers . They lacked the audacity to adopt this metaphor, and this excessive respect for cultural convention raised an obstacle to the development of the science they had created. Yves Chevallard (1992) Fundamental concepts of didactics: perspectives given by an anthropological approach
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3 1. Epistemology and didactics: how to 1. Epistemology and didactics: how to interpretate mathematical knowledge interpretate mathematical knowledge 2. Embodied concepts 2. Embodied concepts VS VS praxeologies: praxeologies: the case of the ‘continuity of functions’ the case of the ‘continuity of functions’ 3. Concluding remarks: what is 3. Concluding remarks: what is mathematical knowledge made of? mathematical knowledge made of?
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1.1. Epistemology and Didactics of Mathematics: 1.1. Epistemology and Didactics of Mathematics: the ‘Brousseaunian Revolution’ the ‘Brousseaunian Revolution’ Theory of Didactic Situations (1972) The ‘metaphor’ of Brousseau GENERAL MODEL OF MATHEMATICS What is Mathematics? modelled by SITUATIONS : games against a milieu under given institutional constraints SPECIFIC MODEL OF A MATHEMATICAL ‘PIECE OF KNOWLEDGE’: What are decimals numbers? What is Counting? Geometry? modelled by
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This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.

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Bosch TSG28 ICME10 - TSG 28 ICME 10 Copenhagen July 2004...

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