The fact that the classroom you have been examining is a mathematics class
reminds me of something revealed by the business of Clever Hans, the
counting horse.
For those of you who do not know him this wonder animal of the turn of the
century was able to give the solution to most any arithmetic problem by
tapping the appropriate number of times with his hoof. His trainer, who was
both a horse trainer and a mathematics instructor, was evidently convinced
that Hans had genuine computational abilities, and when Hans was tested by
experts it was impossible to detect any form of deliberate cuing from the
trainer -- in fact he did not have to be present. However, Hans could not
give correct answers to problems which the questioner did not know. And
what was finally established as the truth about Hans' cleverness was that
his training had attuned him very finely to those little signs of building
tension (turning into relief) that humans inevitably exhibit as the horse
approaches the correct number of taps.
The sensmorale of this can be that "horses cannot count" or that "horses
are awfully good at sensing the fine mimetics of another species." To me it
shows how deeply ingrained our adherence to mathematical correctness is --
even after Oskar Pfungst had "revealed the trick" he could not suppress the
inadvertent signals in himself. Which is, I suspect, what happens also what
is at work in the situation that you describe:
>a reform mathematics classroom in which the teacher believes
>that she is supporting multiple solutions to problems--in line with the
>new standards. However, the multiple speakers that do provide multiple
>solutions are responded to in a way that is distincty monologic. In so
>doing she indicates (by overlapping speech, among other things) the
>dominant values in her classroom--which end up being at odds with her
>espoused values.
Talk about "supporting multiple solutions" serves many useful functions --
it does not just convince oneself and others that this is what I do in my
classroom (and that all thus is well), but also (this is what _I_ believe)
potentially guides my development of forms of action that agree with what I
say. Even so, once we have acquired the habit of knowing with correctness
we are "Pfungsted". We reveal the values dominating us. So. What can we do
but feed some new and reflective talk back into the circus?
Also, Ellice, the phrase "espoused values" associates to me with some
pretty "innocently", unknowingly normative reasoning from "some educational
researchers". I would not like to place you in that group, so (asking as a
non-native English speaker) is there an expression with a more neutral
flavour?
respectfully
Eva
* Davis, Hank. 1993. Numerical competence in animals: Life beyond Clever
Hans. In: S. T. Boysen, E. J. Capaldi. (eds) The Development of Numerical
Competence. Animal and Human Models. Hillsdale, NJ: Lawrence Erlbaum
Associates.
* Sebeok, Thomas A., and Robert Rosenthal. 1981. The Clever Hans
phenomenon: communication with horses, whales, apes & people. New York: New
York Academy of sciences.