The (homo)morphism concept: didactic transposition, meta-discourse and thematisation

Abstract : This article focuses on the didactic transposition of the homomorphism concept and on the elaboration and evaluation of an activity dedicated to the teaching of this fundamental concept in Abstract Algebra. It does not restrict to Group Theory but on the contrary raises the issue of the teaching and learning of algebraic structuralism, thus bridging Group and Ring Theories and highlighting the phenomenon of thematisation. Emphasis is made on epistemological analysis and its interaction with didactics. The rationale of the isomorphism and homomorphism concepts is discussed, in particular through a textbook analysis focusing on the meta-discourse that mathematicians offer to illuminate the concepts. A piece of didactic engineering, informed by the preceding analysis and using epistemological insight as a meta-lever, is presented. The empirical results of a classroom realisation are discussed in the epistemological framework, through comparison of the a priori and a posteriori analysis. This experiment shows both the potential and the difficulties in connecting the homomorphism formalism to cognitive processes of comparison and identification.
Type de document :
Article dans une revue
International Journal of Research in Undergraduate Mathematics Education, Springer, 2017, à paraître
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https://hal.archives-ouvertes.fr/hal-01408419
Contributeur : Thomas Hausberger <>
Soumis le : dimanche 4 décembre 2016 - 19:44:52
Dernière modification le : jeudi 6 juillet 2017 - 10:47:26

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  • HAL Id : hal-01408419, version 1

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Thomas Hausberger. The (homo)morphism concept: didactic transposition, meta-discourse and thematisation . International Journal of Research in Undergraduate Mathematics Education, Springer, 2017, à paraître. <hal-01408419>

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