Sobre a boa docência matemática e o conceito de número: de um olhar natural para uma perspectiva real, com vislumbres de transcendência.

Abstract

The present work begins proposing a reflection about the characteristics of a good mathematical teaching. Thus, considering fundamentally the thought of Elon Lages Lima and Ubiratan D ’Ambrosio, technical aspects - of epistemic nature - are secured in a dialectic integration with metaepistemic aspects. Then, on the optics of the component one of the “Conceituação”, we develop a digression about the concept of number. So, we start from natural numbers and some of its important theorems and structural results are signed. Then, and always in a spirit of continuous progressive gain of dialectical complexity, we talk about the integers. Therefore, the path of commensurability, or incommensurability, between line segments is the conceptual key used to visualize the real numbers: the Fundamental Theorem of Arithmetic being an engine for such key and, in this way, it fosters a spirit of cohesion between the concepts of numbers. The work provides infinite examples of irrational numbers. Two famous irrationals, e and π, are analytically considered. Finally, we briefly discuss algebraic and transcendent numbers and mention the powerful Theorem on Geometric Constructions.