“Arithmetical Complement of a Number”: A Mathematics Knowledge to Teach

Resumo

This article aims to present a theoretical-methodological discussion about mathematics to teach, a theoretical category developed by Valente (2017). This concept is mobilised from studies in the perspective of the History of Mathematics Education that intends to search the history of the professional knowledge of teaching and training of teachers, in the scope of mathematics teaching. These studies have used the conceptual categories of knowledge to teach and knowledge for teaching, developed by the Research Team on Social History of Education, as a theoretical-methodological tool for their investigations, which are the basis for the theoretical construction of the concept mathematic to teach. To achieve our objective, we tried to perform an articulation between the conceptions of Charlot (2000) and Hofstetter e Schneuwly (2017) regarding the presentation of the knowledge in the form of an object. Lastly, we applied the concept of mathematics to teach, in our perspective, to point the movement that has turned the arithmetical complement in knowledge in the form of an object, that is, in a mathematics to teach.