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Re: [xmca] a minus times a plus

Up to a point, that sounds good FK.

But a couple of instant reactions,

1. I find that people's workings differ enormously, and hearing someone else's inner speech could just be confusing.

2. Talking it aloud is something that needs to be sublated. That's the whole point. So we only really need to hear the workings that are central to the lesson.

3. But the point is (I think) that M. may have missed something and can't catch up because she doesn't share with her teacher what her problem is. I suspect that if M. attended your lesson and did participate, her problems would be over.

4. I suspect that Eric has a point. She lacks confidence in her own ability and we suspect she is too shy to speak up and her whole learning process may be obstructed by this tension.


Ng Foo Keong wrote:

i am teaching some math tuition classes in Singapore, and i am
trying to apply the current academic discourse on mathematical
discourse i.e. moving away from essentialist beliefs about fixed
cognitive abilities to looking at _how_ students and teachers
communicate and make intersubjective meaning.  i model by
making all my cognitive as well as metacognitive processes obvious
by talking out loud, and using different colours to mark pertinent
points to note.  i also intentionally (and sometimes unintentionally)
make mistakes, so pupils could apply a critical mind and build their
identities as active mathematical thinkers instead of being passive
listeners.  i get students to explain their working to the class and to
each other.

seems to be working nicely.   ;-)


2009/6/29  <ERIC.RAMBERG@spps.org>:

Perhaps this is helpful, perhaps not.  The military conducts exercises
with recruits that place them in extremely stressful situations.  Swimming
in frigid water,high altitudes, etc. and then asks them to do mundane
exercises (sort cards, say the alphabet, multiplication tables, etc.).
Those who fail these mundane exercises do not suffer deficits but rather
have a profundity for their brains to resort to basic survival mode and
abort any attempt of higher psychological functioning.  Anxiety has a huge
influence on how people's higher psychological functions work and as any
CHATer would know anxiety is tied to the socio-cultural-history of a given
activity.  Steve is on the right track to bring up Davidov's notion of
backward tracking but yes I find the explanation to be Piaget in nature
but not piaget in concept.  Perhaps it is piaget in nature because
intellectuals at a certain level of development speak in very scope and
sequence methodology regardless of their philosophical underpinnings.

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