Reflective Discourse and Collective Reflection

The analysis in this paper focuses on the relationship between classroom discourse and mathematical development. We give particular attention to reflective discourse, in which mathematical activity is objectified and becomes an explicit topic of conversation. We differentiate between students' development of particular mathematical concepts and their development of a general orientation to mathematical activity. Specific issues addressed include both the teacher's role and the role of symbolization in supporting reflective shifts in the discourse. We subsequently contrast our analysis of reflective discourse with Vygotskian accounts of learning that also stress the importance of social interaction and semiotic mediation. We then relate the discussion to characterizations of classroom discourse derived from Lakatos' philosophical analysis.