Combinatorics, Probability, and their articulations in Middle School Mathematics textbooks

Abstract

We analysed if, and how, relations between Combinatorics and Probability are presented to teachers and students in Middle School Mathematics textbooks. The eleven collections approved by the National Textbook Program (PNLD 2017) for the mentioned educational level were analysed, representing a total of 44 textbooks. In light of the Theory of Conceptual Fields and of specific theoretical contributions regarding Combinatorics and Probability, the 298 combinatorial problems and the 874 probabilistic problems identified were classified according to the type of situation addressed and the symbolic representations presented, as well as those requested in these problems. In addition, the focus of the paper was to analyse the possible articulations between Combinatorics and Probability in the problems identified, supported by existing relationships between these two areas of Mathematics. In this sense, approximately 15% of the problems had the potential to explore articulations of such nature, which were related to the use of common symbolic representations (9% of the problems) or based in typical contexts or a deeper examination of problems (6% of the problems). The results discussed here also raise reflections on expectations regarding the collections of textbooks that take place after the approval of the National Common Curricular Base (BNCC), that is, materials constructed based on the new current curricular prescriptions. The analysis in this sense, of collections of Middle School Mathematics textbooks approved by PNLD 2020, is in progress, consisting in another stage of the thesis research of which the present paper presents an approach.

Combinatorics; Probability; Articulation of areas; Textbooks; Middle School