A transição do aritmético para o algébrico no ensino da matemática no Colégio Terceira parte: Vias de abordagem e problemas didáticos.

In this third part on the "Transition from arithmetic to algebraic in the teaching of mathematics in high school" we reflect on the term modeling: modeling, in the sense that we use this word, can be based on a non-mathematical system as well as on a mathematical system. The didactic analysis of the curricular perspectives we have outlined reveals problems in the didactics of mathematics that underline the need for very close links, for a tenacious dialectic, which should be everyone's concern, between fundamental research in didactics and the development activities of the teaching system. In contrast, the present situation reveals the great superficiality of which the empirical and dogmatic tradition has made us unfortunate heirs. It is not enough to weaken, decide, and act to solve the problems we are and continue to be faced with. As in other fields, research is no longer that part of the dream in which high-growth societies could offer themselves as a bonus. It is up to it to explore on behalf of all, the avenues of the possible. [ABSTRACT FROM AUTHOR]