The development of algebraic thinking in young students: A Vygotskian approach

In this presentation, I draw on Vygotsky’s dialectical concept of development to account for the emergence and growth of algebraic thinking in young students. Inspired by dialectical materialism, I suggest that thinking is not something produced by an isolated or solipsistic mind, nor is it something that solely happens in the head. Thinking is rather a social practice materialized in the body (e.g., through kinaesthetic actions, gestures, perception, visualization), in the use of signs (e.g., mathematical symbols, graphs, written and spoken words), and artifacts of different sorts (rulers, calculators, and so on). Psychologically speaking, thinking is a system: a sensuous dynamic unity of material-ideal units including (inner and outer) speech, gestures, tactility, cultural forms of sensuous imagination, and actual actions with cultural artifacts. Following the late Vygotsky, the development of a system, I suggest, lies in the dialectical organization and reorganization of its units. In this line of thought, the development of thinking is a process of reorganization and expansion through dynamic contradictions, which derive from the manner in which each one of the units of thinking signifies. My empirical investigation of the development of young students’ algebraic thinking draws on longitudinal research in which a cohort of Grade 2 students (aged 7-8 years) was followed during five years. I focus on the following units: perception, gestures, speech, artifact- and symbol-use, and show how a dialectical sublation and reorganization occurred as the students engaged in specific teaching-learning classroom activities with their teachers.