Educational forms of initiation in mathematical culture

A review of literature shows that during the history of mathematics education at school the answer of what counts as ‘real mathematics’ varies. An argument will be given here that defines as ‘real mathematics’ any activity of participating in a mathematical practice. The acknowledgement of the discursive nature of school practices requires an in-depth analysis of the notion of classroom discourse. For a further analysis of this problem Bakhtin’s notion of speech genre is used. The genre particularly functions as a means for the interlocutors for evaluating utterances as a legitimate part of an ongoing mathematical discourse. The notion of speech genre brings a cultural historical dimension in the discourse that is supposed to be acted out by the teacher who demonstrates the tools, rules, and norms that are passed on by a mathematical community. This has several consequences for the role of the teacher. His or her mathematical attitude acts out tendencies emerging from the history of the mathematical community (like systemacy, non-contradiction etc.) that subsequently can be imitated and appropriated by pupils in a discourse. Mathematical attitude is the link between the cultural historical dimension of mathematical practices and individual mathematical thinking.