The mediating role of a teacher’s use of semiotic resources in pupils’ early algebraic reasoning

The final publication is available at Springer via http://dx.doi.org/10.1007/s11858-012-0421-2.This paper focuses on the semiotic resources used by an experienced sixth-grade teacher when her pupils are working on a mathematical task involving written text and the two inscriptions of figure and diagram. Socio-cultural analytical constructs such as semiotic bundle, space of joint action and togethering are applied in order to enable and frame the collective activity of the teacher and pupils. Four extracts from different situations in the classroom illustrate the important role of both teacher gestures and pupil gestures, interacting with other modalities such as speech and inscription, in the process of making sense of pupils’ appropriation of coordinating two dimensions in a diagram. It is argued that the nature of the mathematical task is an important entry point into early algebraic reasoning. The study emphasises the mediating role of the dynamics of semiotic bundles produced in teacher–pupil dialogues as a promising way to address the fundamental relationships between mathematics, pupil and teacher in a classroom context in order to provoke pupil involvement and engagement when experiencing mathematics