Perceptual semiosis and the microgenesis of algebraic generalizations

This paper deals with the problem of algebraic generalizations of elementary geometric-numeric patterns. It focuses on understanding the role played by the various semiotic systems mobilized by students in the progressive process of perceptual apprehension of a pattern and its generalization. The microgenetic analysis of the mathematical activity of two small groups of students in a Grade 9 class shows how making recourse to semiotic resources, such as gestures, language, and rhythm, allows the students to objectify different aspects of their spatial-temporal mathematical experience. The analysis also shows some 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 expressions.