The Logical-Historical Movement of Arithmetic Progression: a contribution to math teaching

Abstract

This article describes aspects of the logical-historical movement of the concept of Arithmetic Progression (AP), identifying conceptual links (internal and external) with Algebra, which is taught in secondary school. The methodology is a bibliographical review of Brazilian sources in Portuguese and Spanish. The analysis of the results shows that the logical-historical movement of AP, didactically, enables students to develop mental actions linked to theoretical thinking through access to conceptual links. Thus, the teaching of AP is not just an operative technique, but an opportunity to develop a concept as a cognitive tool, developed from human needs. Some of the internal links in the concept of AP are common to other algebraic concepts, such as fluency, magnitude, variable, field of variation and interdependence, but we can add our own links, such as order (position), whose field of variation is the set of natural numbers, and the existence of a constant variation (difference) between the terms of the sequence.