One can learn mathematics by investigating particular cases?

Abstract

The discussion about the possibility of construction of mathematical objects in schools – constructions that have to do with subsidies provided by mathematical modeling activities – is the core of this article, which is marked (methodologically) by qualitative perquisition of theoretical and bibliographic nature. The deduction, although not exclusive of mathematical thinking, is its most significant atribute, differentiating this thinking of the cognitive actions that are initiated by the approach of particular cases. The particular cases usually are characteristic of the world that is understood as real. This gives rise to favorable reviews – in teaching and learning – to the idea of failure of the mathematical modeling when she (the mathematical modeling) aims at elaboration of mathematical objects, because the activity of modeling (aside from the bond that she keeps with the deduction) can not succeed without the so-called real situations. These (real) situations require (and are demanded by) cognitive processes that are opposing when walking deductive because they (the situations) contain singularities, though the deduction is necessary for the cognitive subject when he not only connect with the mathematical field, but also with several situations that are called real. The directive question of this article is the same as his title: “on can learn Mathematics by investigating particular cases?”. This article – by emphasizing the ties involving the matters “disorder, order, induction and deduction” – presents arguments that lead to results or conclusions in favor of the effectiveness of “learning (and/or construction) of Mathematics with the help of the act of modeling”, without disrespect, in turn, the use of mathematical modeling in order also to improve math skills previously internalized and assimilated by the student.