Entre primos e compostos: uma abordagem do teorema fundamental da aritmética no 6° ano do ensino fundamental

Abstract

In this research we present discussions about the main definitions and properties that deal with some concepts of elementary arithmetic such as prime and compound numbers and lead to the Fundamental Theorem of Arithmetic (FTA). For its achievement, the present work aimed to approach the study of the Fundamental Theorem of Arithmetic and the main concepts associated with it with a group of 6th grade students. To reach the proposed objective as an empirical camp of research, as well as its subjects, we conducted a study with students from a philanthropic school located in the southeast region of Teresina. We opted for this school because it was in this space that we taught for over four years. The theoretical foundation of the research relied on the Theory of Conceptual Fields proposed by Gerard Vergnaud. The methodology consisted of a three-stage study. The first referred to the collective application of an initial assessment. The second turned to the intervention stage, which was divided into four groups of activities that addressed the development of appropriate strategies for students to understand and thus differentiate the concept of prime number and compound number, also favoring, within this context, understanding the concept of multiples, dividers and decomposition into prime factors. And finally, the third corresponded to the collective application of a final evaluation, with the same questions as the initial evaluation. At the end of the study, the final considerations are presented whose focus shows that the students developed their own schemes to deal with the concepts about construction. The opened discussions at the end of each activity of the teaching proposal about the definitions and properties involved there created conditions for the conceptual development of the participants of this research, contributing to the advance in the comprehension of a series of mathematical concepts that, although implicit, they were present in each one of your actions.