Análise combinatória: uma proposta de classificação de problemas de contagem indireta simples

Abstract

It is well-known that a significant portion of students face considerable challenges in the context of the Mathematics discipline. Given this reality, it becomes imperative for educators to adopt strategies and pedagogical approaches aimed at facilitating the teaching and understanding of mathematical content. In this perspective, the present work aimed to present a proposal for the classification of simple indirect counting problems that could contribute to facilitating the teaching and learning of Combinatorial Analysis, in addition to analyzing its application by students in a third-year class of the New High School at a state school in the Municipality of Quixaba, Pernambuco. To carry out the work, we conducted qualitative research of the field study type. We used a questionnaire that was applied in two stages, each consisting of seven problems, in which students were instructed to classify them according to their characteristics. In the first stage, the questionnaire was applied without the proposal being presented, while in the second stage, it was applied after the presentation and discussion of the proposal. The theoretical foundations of this work emerged from the discussions of Núñez (2018), Handaya (2017), Pessoa and Borba (2010), Oliveira (2017), Rêgo (2023), and other authors who base their research on teaching and learning processes and problem classification. Additionally, the documents that guide the definition of the Basic Education curricula in Brazil were also important in providing theoretical support for this study. The results obtained demonstrated the potential of the proposal, with a considerable increase in the number of correct answers after its presentation and positive comments from students, highlighting that the proposal helped in classifying problems.