CHALLENGES AND TECHNIQUES OF COUNTING IN COMPETITIONS FOR MATHEMATICS TEACHERS AT FEDERAL INSTITUTES
Mathematics; Public Selection Exams; Teachers; Federal Institutes; Counting Techniques.
The present work, titled “Challenges and Counting Techniques in Mathematics Teacher Selection Exams for Federal Institutes,” explores the importance and usage of counting problems in public selection exams for teaching positions at Federal Institutes (IFs). The research investigates recent exams from these competitions, highlighting the frequency and types of counting problems, such as permutations and combinations, that are commonly addressed. The study also covers Pascal’s Triangle and Newton’s Binomial, fundamental tools in high school mathematics, analyzing their properties and applications. Additionally, it includes combinatorial and algebraic demonstrations of some properties of Pascal’s Triangle and presents practical applications of these properties in the classroom. Moreover, the work proposes solutions to counting problems that have been featured in exams for mathematics teaching positions at IFs. The dissertation is structured into five chapters, ranging from basic concepts of counting methods to more in-depth discussions on the use of these concepts in educational contexts. The ultimate goal is to provide useful study material for candidates preparing for these exams, emphasizing the relevance and complexity of counting problems in teacher selection. Thus, the work not only contributes to the technical knowledge of the field but also offers practical support for the development of teaching and learning strategies focused on combinatorics.