Analysing the notion of algebraic thinking based on empirical evidence / Un análisis del concepto de pensamiento algebraico basado en evidencia empírica

Abstract

The purpose of the present study was to examine the structure and development of algebraic thinking across multiple dimensions. An algebraic thinking test was administered to 803 students aged 10–13 years old. One hundred and one students of different performance outcomes in the algebraic thinking test participated in semi-structured clinical interviews in order to develop further insights into students’ strategies and difficulties. The results confirmed the multifaceted nature of algebraic thinking and showed that algebraic thinking consists of three aspects: reasoning about covariation, generalization of arithmetic properties and abilities directly related to algebraic syntax. Each one of these aspects is composed of specific algebraic thinking abilities, such as modelling relations using algebraic symbols. Four groups of students of different algebraic thinking profiles were identified: ‘pre-algebraic’, ‘protoalgebraic-procedural’, ‘relational-symbolic algebraic thinking’ and ‘structural-global algebraic thinking’. The results also supported the presence of a consistent trend in the difficulty level across the algebraic thinking abilities, which suggests a specific developmental trend from a more procedural perspective of algebraic thinking to a more structural one.