The Theory of Subconstructs and the Rational Number as Operator: from algebraic to cognitive structures

Abstract

We present a literature review on the role of the operator subconstruct in the learning of rational numbers. We chose to focus on this subconstruct because it is related to the operation of multiplication, which places it in a position of importance when one considers the development of so-called multiplicative reasoning. We reviewed the literature seeking to make explicit perspectives in which the role of this interpretation of rational number is considered important in the school curriculum, and to describe empirical research findings and theoretical reflections related to work with this subconstruct in school. We finish by presenting some issues that we believe deserve additional attention. The objective is to present a synthesis of the literature on this specific topic, offering support that may contribute to teachers’ construction of a professional view regarding rational numbers. Key-words: Mathematics Education. Rational Numbers. Subconstructs. Operator.