Reflexões sobre o princípio fundamental da contagem e suas consequências

Abstract

Combinatorial Analysis is a Mathematics topic that is still considered difficult by most teachers and students. This makes this area of Mathematics feared and, sometimes, avoided by educators themselves. Because usually there is no adequate understanding of this subject, we even find books and websites presenting concepts with inconsistencies or limitations, which further deepens the difficulties in understanding the topic. Therefore, this work aims to contribute to improving the understanding of Combinatorics Analysis through a study focused on the Fundamental Counting Principle, a part considered essential for a good understanding of this area. We seek to explain this principle in detail, aiming to make clear what it produces and in which situations it can be used. In addition to its version regarding the making of two decisions, we present its iterated version and formalizations for each of them using set language. We analyze the statements of this principle in books and websites, in order to verify whether its presentation is being done correctly or adequately. Futhermore, using it, we developed the counting techniques covered in Basic Education and explained the importance of adequate modeling for solving problems and creating other techniques apart those previously discussed. After that, we address some ways of facing Combinatorial Analysis problems in order to contribute to a good application of known methods, as well as presenting a script that can help in facing these problems with greater security. Finally, we propose activities that can be applied and worked on in the classroom to promote the correct and most complete learning possible of the Fundamental Principle of Counting in Basic Education.