A similar pattern of difference between M and T as primary objects is visible in the ‘how’
of the pedagogic discourse. Where M is the primary object, framing is relatively weak in
terms of sequence and pacing—but overall selection and evaluative criteria are controlled
quite firmly by the lecturer. For example, while what gets to be put up on the board is
generated by the class discussion and the productions that students come up with, the
lecturer selects this from what has been generated (she does not for example, ask for a
volunteer). The lecturer steers the conversation through the way in which evaluation takes
place in the classroom, and in such a way that there is no question about what is legitimate.
What is incorrect is clearly negated and replaced by a correct production. Criteria are fairly
strongly framed; grounding is clear and to be authorised from within mathematics itself.
However, the pacing and the sequencing are relatively weak, with students' input being a
critical factor in how the focus moves from event to event. Social relations are flattened and
students and the lecturer interact within the context as knowledgeable participants. An
invisible pedagogy operates in which it appears that the students' have considerable control,however, the context is closely managed by the lecturer. When T is in focus, a similar
pedagogy is implemented. However, the framing of evaluative rules now appears to be
weak: the grounding is not firm; things may or may not be accepted and the grounds upon
which this is to be decided are not clear. The knowledge base for acquisition is opaque, but at
the same time is taken for granted. Experience belongs to all and all experience is valid.
While at face value, the practice appears unitary and smooth across M and T events, what the
methodology makes visible is that what is constituted as knowledge across them is substantively
different.