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Contribution to the Topic Group 27, ICM 11, Mexico

The following web address, http://tsg.icme11.org/document/get/391

can download the contribution made by,

John D. Godino, Mauro Rivas, Walter F. Castro and Patricia Konic

to Topic Group 27 of the ICMI 11, "Mathematical Knowledge for Teaching" with the title,

AND epistemic ANALYSIS OF AN ARITHMETIC COGNITIVISM - Algebraic PROBLEM SOLUTION

Abstract:

We analyze the solution of a problem proposed on the context of a mathematics methods course for in-training primary teachers, by applying some notions of the “onto-semiotic approach” to mathematics knowledge. The generalization of the arithmetic statement given to students involves the use of algebraic reasoning, giving way to the study of the relations between arithmetic and algebra, as well as the relations between empirical and deductive argumentation. The solution of elementary problems and the epistemic-cognitive reflection on the objects and meanings used during the solution is proposed as a means to overcome a limited students’ conception on the nature of mathematics, usually reduced to its conceptual and procedural aspects.