O ensino de combinatória e o método da contagem dupla.

Abstract

This work aims to explore the teaching of Combinatorial Analysis within the context of the National Common Curricular Base (BNCC), which emphasizes the importance of developing combinatorial thinking from elementary school onwards. The dissertation begins with a review of traditional approaches that cover classical concepts such as arrangements, combinations, and permutations. However, the primary focus is on proposing a new teaching methodology centered on double counting, replacing the direct use of conventional formulas. This proposal is grounded in the analysis of the Binomial Coefficient in connection with Set Theory and the Fundamental Counting Principle, aiming to foster a more profound and intuitive grasp of combinatorial concepts. This approach seeks to facilitate meaningful learning, making the teaching of Combinatorial Analysis more accessible to high school students and contributing to a solid foundation in mathematical reasoning. Keywords: Combinatorial Analysis, Double Counting, Mathematics Teaching, BNCC, Teaching Methodology.