Ensino de Análise Combinatória : um estudo das representações de professores de Matemática do Ensino Médio público de São Mateus

Abstract

The Combinatorial Analysis has been considered a difficult subject by both students and teachers of Mathematics, although the resolution of a significant class of counting problems requires only basic knowledge, among which is the Multiplicative Principle. We saw that the main reason for the didactic difficulties with this theme lies in the confluence of two factors: (i) combinatorial problems do not admit a standardization that reduces its resolution to the application of simple algorithms and (ii) the way of teaching Mathematics in Basic Education, which prioritizes a mechanical approach to the content. Ratifying this understanding, we believe that the teaching of Combinatorial Analysis centralized in definitions and formulas, to the detriment of the development of the strategic reasoning, does not favor learning and the ability to solve problems. This is an exploratory-descriptive field study, carried out over the years 2016 and 2017, which, using three instruments of data collection (interview, on-line questionnaire and observation), researched the subject with twenty mathematics teachers from eight State High Schools in São Mateus / ES (Brazil). Specifically, we seek to analyze the representations of teachers related to the Combinatorial Analysis through the assumptions of Cultural History: representation, practice and appropriation, proposed by Roger Chartier; strategies and tactics, by Michel De Certeau; school culture, by Dominique Julia and school subjects, by André Chervel. As a result, we found that most teachers consider that Combinatorial Analysis is one of the most difficult topics to teach in High School and states that the topic was not properly studied in theirs initial or continuing education. In addition, to fill this gap, they use only the textbook and the internet. The researched teachers also do not realize the autonomy that they have in the ambit of the relations of strategy and tactics, in the school context.