Important questions, of course, and nice that you have some data
that bears on them. Did you, or could you still, interview these
teachers and ask them, first, why they did or did not do the
things that place them in your two categories, and then, more
explicitly ask them about their view of how one _should_ teach
math, and whether the _other_ strategy is desirable, useful and
under what circumstances?
I think that teachers very often do have theories about such
matters, or at least reasons why they make these choices. Very
often in science, and probably also in math, teachers believe
that the 'abstract-authoritative' approach is what they should
be using and only switch over to the 'personal-conversational'
mode if they feel they have to to get anywhere. Some teachers,
I think, themselves rebel against the abstract-authoritative
model and try to use it as little as possible (though they
may feel a bit guilty about not doing what they still may
think they are supposed to do).
I would be interested to know if the more personal teachers
are also ones who feel more at home with and comfortable
with math, even if they reject its ideology about how it
should be taught. I have noted this anecdotally in science
teaching. My experience however is mainly with secondary
science education, and biased toward new teachers.
As to more formal theory about such matters, I don't
know that there is much. Some might identify the abstract
approach with a middle-class disposition, but the
authoritative by-the-book side of this same approach is
favored by the working class disposition. On the difference
between language arts and math, that fits of course with
models of the ideologies these disciplines have about
themselves: humanistic vs technical. Regarding the type of
relationship with students, as in 'parental-guide' vs.
'professional-initiator', that lies in the area of
teacher's theories about teaching, on which various people
have worked (in science and math mainly about their
epistemological theories, but since the theories tend to
be holistic teachers do not separate beliefs about
knowledge from beliefs about students).
Perhaps it would be useful to try to infer from the data
something about the teachers general sense of what their
students need as learners. Do they in fact construct their
students differently in language arts vs. math lessons?
It would be quite fascinating to know whether teacher
student interactions create distinctly different identities,
notions of student ability and needs, and approaches to
teaching as a function of subject area. This is pretty well
only possible in elementary education. I do not know this
literature well. Are there studies that compare how
teachers can be different kinds of teacher, producing
different kinds of students, from one subject area to another? JAY.
JAY LEMKE.
City University of New York.
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