Arithmetic as an essential base for learning algebra: De la aritmética al álgebra, un ejemplo desde la Teoría APOE

Abstract

In this paper we present a very general view of the roll that algebra plays inside mathematics education, as well as the transition process that students go through when they initiate their studies on this subject. To emphasize on the importance of algebra during formal education, we show some statistical data collected from PISA standardized tests. We discuss the connection between the arithmetic knowledge that students possess and the learning of algebraic concepts and procedures, and, based on APOS (actions, processes, objects, schemes) theory we provide an example of the importance of having a solid arithmetic knowledge base for the construction of algebraic concepts. Lastly, we open the door for the generation of didactical proposals to work on that transition from arithmetic towards algebra.