Entre primos e compostos: Um estudo sobre abordagem do teorema fundamental da aritmética no 6º ano do Ensino Fundamental

Abstract

In this work, we present discussions on the main definitions and properties related to some basic arithmetic concepts, such as prime and composite numbers, which lead us to the Fundamental Theorem of Arithmetic (TFA): multiple, divisor, prime and composite numbers and decomposition into factors cousins. Our objective was to approach the study of TFA and the key concepts associated with it, with a group of students in the 6th year of Elementary School. The research used as a theoretical basis Vergnaud’s Theory of Conceptual Fields (1983, 2001) and the ideas of Barbosa (2015), Carvalho (2015), Costa (2015), Alencar Filho (1981), Hefez (2016), Krerley and Adán (2012), França (2019) and Santos (2009), furthermore, the National Common Curricular Base (BNCC) will be considered for learning concepts related to Elementary Number Theory, with TFA being a fundamental part of this process. We seek to present prime numbers, analyze their history and the results obtained by mathematicians over time, in addition to exploring curiosities and applications in different contexts. The work will consist of qualitative research on the teaching of prime numbers in Basic Education. During the development of the course conclusion work, we will analyze the approaches to this topic through research and studies available on the subject. At the end of the study, final considerations are presented whose focus shows that the importance of studying TFA and its applications throughout Basic Education.