Initial training of mathematics teachers: a concept study on the fundamental theorem of arithmetics

Abstract

This article focuses on the approach of the Fundamental Theorem of Arithmetic in the initial training of mathematics teachers in public university of Rio de Janeiro. It is a case study, which uses a concept study model (concept study). According to this model, teachers share experiences and learn collaboratively in order to question and rebuild their personal knowledge of mathematical concepts and their teaching. We conducted the concept study in four workshops that preceded the beginning of classes in a discipline dedicated to Elementary Theory of Numbers with the students enrolled to attend it. Among the results, we highlight the licensees' understanding of the multiple and factor concepts and their characteristics, we request divisibility, prime numbers and decomposition into prime factors. In the end, they considered the recommended properties of the multiple and factor concepts to justify the divisibility requirements and use the prime factor decomposition to simplify calculations. Reflecting on teaching, conclude that the fact of decomposing a number into prime factors is not a guarantee that basic education students will use this decomposition to obtain their factors, simplify calculations, find or m.m.c. or the m.d.c. between numbers. If you guarantee a conscious and non-mechanized performance of the students in these actions, he will develop a work in the classroom that progressively explores as multiplicative structures, that is, a multiplication of natural numbers, their properties and representations.