Algebraic Balance Invariants present in the strategies of third grade of elementary school students

Abstract

In several countries, there have been recurrent reports of difficulties in understanding of algebraic concepts. The solution to this problem, proposed by much of the mathematical educators' community around the world, was to promote the introduction of algebraic concepts since the early school years. The aim of this work was to describe and analyze the operational invariants used by third grade students elementary school in situations involving the notion of algebraic balance. The methodology of data production and data analysis used was the handling-formalization clinical method. The subjects were 24 third grade students of elementary school, which were submitted to an activity involving four weights and two scales. The participants should balance the weights twoby-two, without knowing the extent of one of the unknown weights the algebraic problem. Clinical interviews were held with all participants to investigate the operational invariants used by them to solve the problem. The theoretical research framework is the theory of conceptual fields. It was noted the possibility of using four operational invariants: the theorems-in-action "complete the missing amount" and "find the unknown from the balance"; and related concepts-in-action "sequence without numbers that repeat" and "balance weights on the scale". The knowledge of how the child develops the initial algebraic balance notion, which is the beginning of the process of understanding the formal equation concept, can help early years teachers to create activities that stimulate the development of this algebraic ability.

Keywords:
Algebraic Balance; Algebraic Thinking; Literacy Cycle