Among teacher educators and staff developers in higher education (and
research with this affiliation) there is very often an assumption that when
you _say_ that you teach in a certain way, then an observer in your
classroom should also be able to _see and hear_ you teaching in this way,
or else you have been dishonest in "reporting your intentions" -- basically
(although this is most often only implied) you have presented the
researcher with information that you think is socially appropriate, while
all the time secretly adhering to other values.
In these suspicions there are underlying "objectivist" assumptions about
communication being the exchange of objectively true-or-false information,
in this case concerning subjective states, and also "cognitivist"
assumptions about subjective intentions as causes for observable action.
This is close to the contrast that John Shotter makes (in "Social
accountability and selfhood") between "reporting" and "telling" as
conceptualisations of what people do when expressing their goals. He argues
there against the objectivist conceptualisation of "reports" (treating
oneself as a third-person -- people don't), and for a conceptualisation of
"telling" others about what your commitments are (as first-person to
second-person -- people do).
So I prefer to think (and I think we are coming at this from roughly the
same side) that teachers are reasonably honest in telling us about their
goals in teaching, and that it is by no means surprising that in spite of
this they may be observed doing something with different characteristics.
These discrepancies are interesting as objects of research: how far can we
control our own behavior in complex circumstances by means of consciously
held goals/ /verbal mediation? You point to one important constraint when
you write:
>Some of the "rejected" algorithms are every bit as correct from
>a mathematical stand point as the privileged one. But it is likely that
>the teacher was not prepared to understand alternative but correct
>algorithms. In fact, if I had been the teacher myself I might have
>missed them too.
This is a reflection that I have made, too. About the increased cognitive
load of maintaining a conceptually orchestral discourse in the classroom as
opposed to a conceptually monological one. Arguably, this is something that
one could learn with experience: learning to recognize alternative paths, I
mean.
On the other hand, doing something effectively to make your own classroom
behavior agree closer with your expressed goals at the level of discourse
flow, might also mean finding a way of "slowing down without losing hold"
(practically I would feel totally incompetent at this). The orchestration
you hint at in your elaboration of what goes on in your transcripts sounds
like the pattern and pacing of the teacher's contributions are geared to
multiple purposes: guiding towards correct knowledge (by the means of
neglect or enhancement that you mention) as well as maintaining
concentrated student attention to the topic (by fast pacing and "central
conduction").
Eva