Abstract
The purpose of this paper is to discuss rational numbers in Academic Mathematics - in the sense of equivalence classes of integers ordered pairs and as elements of a domain field of fractions of integrity ℤ - in order to favor the debate about teachers’ mathematical training. To this end, we investigate more recent historical aspects (from the eighteenth century) on rational numbers, as well as conceptual discussions based on approaches brought by textbooks aimed at Higher Education. In the analysis, we highlight, mainly, dissonances between rational numbers in Academic Mathematics and in School Mathematics, and we highlight the intentionality as a characteristic of the mathematical way of doing Academic Mathematics. Finally, we question to what extent the rational numbers in Academic Mathematics serve the purposes of middle and high school teachers’ mathematics training.
Keywords:
Teachers’ Mathematical Training; Rational Numbers; Academic Mathematics; Equivalence Class; Field of Fractions