ABSTRACT
This chapter focuses on an attempt to take multiple theoretical lenses for examining two pieces of data, the first, a fully transcribed event in a Grade 11 mathematics classroom, in a South African school of low socio-economic status, focused on quadratic inequalities. The second piece is made up of two interviews with two pairs of learners that were held a few months after the event. Sfard's chapter introduces her commognitive framework to analyze closely a few vignettes from Mr. T's classroom, supplementing it by an analysis of the students' talk in the interviews. Relying on Vygotsky's socio-cultural theory of learning and on Wittgenstein's late philosophy, Sfard dissolves the historical dichotomy between thinking and communicating, claiming the former is actually just an intrapersonal version of the latter. Sfard's view conceptualizes learning as participation in collectively established forms of practice or discourse. This view leads one to assume that learning mathematics is the process of becoming a participant in the community of mathematicians.
