REFLECTIVE DISCOURSE AND COLLECTIVE REFLECTION

The analysis in this paper focuses on the relationship between classro om discourse and mathematical development. We give particular attentio n to reflective discourse, in which mathematical activity is objectifi ed and becomes an explicit topic of conversation. We differentiate bet ween students' development of particular mathematical concepts and the ir development of a general orientation to mathematical activity. Spec ific issues addressed include both the teacher's role and the role of symbolization in supporting reflective shifts in the discourse. We sub sequently contrast our analysis of reflective discourse with Vygotskia n accounts of learning that also stress the importance of social inter action and semiotic mediation. We then relate the discussion to charac terizations of classroom discourse derived from Lakatos' philosophical analysis.