A construção do conceito de número natural e o uso das operações fundamentais nas séries iniciais do ensino fundamental: uma análise conceitual

Abstract

This research addresses the conceptual analysis of the construction of natural number and use of fundamental operations which are worked in the early grades. The history of counting comes to help the understand the emergence of the natural numbers along with considerations made from the theory of numbers, specifically the Peano’s axioms. The activities performed had the objective to verify in practice how the positional decimal system and the fundamental operations of addition, subtraction, multiplication and division work, and also how the algorithms are developed by professionals who teach these contents. These activities constitute a guidance manual on the content mentioned above, worked from the manipulation of the golden material. This material was used as a tool. it is an important teaching resource, and provided an overview of some concrete ideas that needed to be abstracted. The math workshop was taught from the mediation of the Sequence Fedathi, providing discussions that formed the basis for our analyzes. Besides the teaching resource, teachers-students involved in this research had the opportunity to, work with other ways of calculating the arithmetic of natural numbers. They could also relish the exchange of experiences. We seek a kind of mathematics that is beyond the algorithms that were explored in order to identify the understanding of the participants regarding the calculation techniques as well as the concepts of each of them. Epistemology of teachers-students was one of the issues discussed during the workshop. The results of this work showed how relevant is the mastering of the mathematical knowledge by the professionals who teach mathematics in the early grades. Results also proved that it is necessary to improve teaching practice through continuing education.