The conception of algebra in Davydov’s proposition for teaching numbers

Abstract

Historically, schooling has established the separation of arithmetic, algebra and geometry, which led movements that culminate in the unification: Mathematics. Nevertheless, curricular propositions do not reflect the interrelationship between these three fields. In this study, it’s been affiliated to Davydov and colleagues, in adopting the assumption that the teaching of mathematics, from the first school year, should bring the idea of the real number, from a study of quantities in the inter-relation between arithmetic, algebraic and geometric meanings. The research problem goes back to the conception of the algebra, in Davydov’s propositions for the introduction of teaching the concept of number. To do so, a dialogue is established with literature concerning the concept of algebra and davydovian proposition. In contemplating the general relationship between quantities, Davydov’s proposal brings components of the conception of algebra as the study of relationships between quantities that vary.