Proceedings CIEAEM 58 –SRNI, Czech Republic, July 9-15, 2006 “Quaderni di Ricerca in Didattica (Matematica)”, Supplemento n. 2, 2009.
G.R.I.M. (Department of Mathematics, University of Palermo, Italy)
Concept theory provides a wide model for the understanding of concept acquisition, conceptual change – including paradigm shift – and conceptual dynamic in general. For example the conceptic model (Aberkane
2004) suggests that ideas are formed in a generative manner, much like sentences in Chomskian grammars, and that the universe of all possible ideas is in a sense “algebraically” closed under mental operations, that is, any idea can be transformed into any other, however distant, after a finite number of mental operations. Mental operations are not Turing operations, essentially because they are not Russeltyped, when notably any concept of concept is another concept, and any set of ideas or meta-idea is still an idea. Here we apply the conceptic model to maths pedagogy, with the aim of increasing the bandwidth of knowledge transfer. We propose that any background can be efficiently diverted to learn mathematics or conversely, that any knowledge of any field being organized into a conceptual structure can be recruited to facilitate the appropriation of mathematical theories. We introduce the notion of conceptic filter (later filter), i.e. any combination of concepts that are linked to each other so that they form a usable theory to describe the fact that the filter of mathematics can be efficiently constructed by using any background as a priming filter.
Idriss J. Aberkane, Cédric Saule
Ecole Normale Supérieure (Paris), département de Biologie. 46 Rue d’Ulm 75005 Paris Cedex 05
Université Paris-Sud XI (Orsay), département d’Informatique
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