Elementary dissertations on combinatorial theory: towards an inculturation of mathematics

Abstract

In this work, we focused on the teaching of combinatorial theory with two types of problems: those which the results can be verified by direct counting and those that cannot be verified, because the number of events do not allow verifying one by one all the arrangements obtained due to time issues. Besides, we determined the didactic and academic utility of both types of problems. Another aspect that was included is the attention to singularities, as part of the attention to diversity: meaning the particular attention that must be given to advanced students.

A series of examples on commensurable problems and its didactic use were incorporated, which don’t pretend –due to time- to give a definitive answer on the teaching of counting techniques, but rather to show slightly the possible ways to address this exciting theme in a didactic manner. Examples of incommensurable problems and its academic utility were also visualized in order to attend the singularities of students who love mathematics.