Perceiving the general: The semiotic symphony of students’ algebraic activities

In this article, we deal with students’ algebraic generalizations set in the context of elementary geometric-numeric patterns. Drawing from Vygotsky’s psychology, Leont’ev’s Activity Theory, and Husserl’s phenomenology, we focus on the various semiotic resources mobilized by students in their passage from the particular to the general. Two small groups of Grade 9 students are investigated through a fourdimensional analysis: video, audio, transcripts, and written material. The resulting qualitative analysis shows how discourse, gestures, actions, and rhythms orchestrate one another and how, through a complex and subtle coordination of them, the students objectify different aspects of their spatial-temporal mathematical experience. The analysis also suggests connections between the syntax of the students’ algebraic formulas and the semiotic means of objectification through which the formulas were forged, thereby shedding some light on the meaning of students’ algebraic expression. Some implications for the teaching and learning of mathematics are discussed.