Number theory in training of Mathematics teachers: (mis)understandings about primality and fundamental theorem of Arithmetic

Abstract: This article discusses the ways in which a group of undergraduates in Mathematics understand concepts related to number theory, including "prime numbers" and "fundamental theorem of arithmetic". Through a qualitative approach, the answers for two questions were collected from ten subjects, which were analyzed in the light of the concept of transparency/opacity of numerical representations, in order to verify whether there was consistency between the concepts set out in one answer in comparison to the problem that should be solved in the other. The text highlights strategies used by research participants related to issues involving the primality of natural numbers, and the importance of formal knowledge of number theory by the mathematics teachers in training. In addition, there were elements that allowed us to conclude that the appeal to intuition, though not always correct, and too prescriptive often occurred, both in the context researched and in the works used as theoretical references.