Historical Creativities for the Teaching of Functions and Infinitesimal Calculus

This article presents reflections on a research that investigated processes operationalized by mathematical thoughts and practices which sought explanations for the ways of being of mathematical objects in their correlations in the socio-cultural context throughout our human history and how these ways of being they were captured, and still are, by the mind of those who exercised creativity in all the dimensions of mathematical creation both in the past and in the present, in order to produce knowledge to be disseminated in the school and scientific context. The research is a historical-epistemological study on mathematical creation, aimed at characterizing modes of stages of this creation focusing on the development of infinitesimal calculus and on the concept of function. At the end of the article, we propose educational guidelines for the teaching of these mathematical themes, based on the creation processes announced throughout the text.