Next message: Dennis McCowan: "[Channel-talkpupmath] Notes from weston's fourth session"
Weston watched session three on November 1 and ate pizza while we
watched! Significant issues raised by the readings for the session
included:
1. A student needs time to "see it on her own" regardless of attempts by
teachers to prompt her.
2. Discomfort arises when trying to reconcile a new idea with prior
knowledge.
3. Heterogeneous grouping aided students in looking at different
approaches to a problem.
4. Students can hold tenaciously to an idea.
5. Once a technique works, students may apply it universally without
thought, especially if being pushed beyond their current level of
understanding.
6. To explain your thinking you need personal ownership of the idea.
7. We have learned that student writing needs a intended audience to be
productive; this appears to also be true when developing a "proof."
Just as the audience for a piece of writing influences your approach and
choice of vocabulary, a proof is significantly influenced by the
identity of your listeners.
We enjoyed the diversity of our members solutions to the first
half-pizza problem and were blown away by Barndon's isomorphism. We
paused te tape just at the end of Brandon's work and discussed him
briefly; when the tape resumed and we learned he was in the "low" math
group the silence in our room was very powerful!
We were disappointed with Prof Maher's comment that "we have on tape
times when you all agreed but were wrong." the Monday morning
quarterback in us would have preferred to have picked up on Jeff's
comment "yea, but some other class might not all agree with us."
(Would a refernece to the universally held belief that the universe
rotates around the earth have been a possible response here too?)
Certainly the last homework problem challenged us all and we may need to
spend some time in session 4 looking at it.
We continue to be enthusiastic about the opportunities provided by this
series!
Dennis McCowan
Weston
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