Números inteiros nos ensinos fundamental e médio - Rama, Aguinaldo José (2005)
We present an analysis of three collections of mathematics text books for primary school. The choice of the collections is oriented by the synthesis presented in the guidebook of the Plano Nacional do Livro Didático. The goal of the analysis is to investigate the way the authors approach the integers, mainly the concept of divisibility. Our main focus concerns proof strategies and the use of challenging problem situations. Two other aspects are considered: relations between integers and other mathematical subjects, particularly álgebra and geometry; articulations between old and new contents, and the resulting review of subjects, during which it is expectec that the learners growing maturity is taken into consideration. We verify that one of the collections presents good informal proofs, suitable for this learning level, using a variety of methods; it also properly explores the potencial of problems related to integers. The second collection presents some convincing proofs together with unsuitable ones, while the third one states several properties without exibiting explanation concerns. The last ones provide few problems demanding a greater sophistication of reasoning. The three collections present the subject in 5th and 6th grades, in the context of natural numbers, and no overview is provided after the introduction of negative numbers. The second part of the work is dedicated to middle school. We examine the eleven collections recomended by the guidebook of the Plano Nacional do Livro do Ensino Médio. We analyse the review of the integers at the beggining of the first books of the collections. Generally speaking, the review is superficial; divisibility concepts including negatives is explored only in the context of exercises. Few more elaborated problems are proposed Finally, we suggest actitities for middle scholl relating integers to a variety of themes, as geometry, complex number, polynomials, combinatorial analysis