Teacher resources and professional development across the curriculum

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Private Universe Project in Mathematics



From: Dennis McCowan (mccowan@massed.net)
Date: Mon Oct 30 2000 - 09:55:57 EST

  • Next message: Ruth Sargent: "[Channel-talkpupmath] pupmath"

    The first two sessions were so rich we could probably spend the rest of
    the workshop discussing them. With the help of the readings, it became
    clear to me that there was some significant shifting of the question
    being worked on by the students. The first shift was from "make as many
    towers as you can" to "how many different towers can you make?" It
    seemed that students were initially responding to the query "how do you
    know you have them all?" by trying to determining how many there were.
    After all, for many people (thankfully not all!)mathematics is just an
    attempt to answer "how many"- especially in the early years. It is
    interesting to consider how students would have responded if the
    researchers had repeatedly asked instead "how can we make all the
    different towers?" Both this question are answered by the "doubling"
    rule, but they are significantly different questions to me. For qyite a
    while, Stephanie seemed to be saying "I make them all by first figuring
    out how many there can be, then trying and trying until I get that
    many." Isn't that how we often respond to open-ended questions-
    essentially trying to determine "how will I know when I am 'done' ?"

    The other interesting observation concerns the role of conversation in
    learning. initailly I reacted to stephanie by remarking that her
    "learning style" - her personality "type" if you will- was one who
    needed to talk before she could decide what she was thinking. as the
    serioes progressed, I saw the conversations as a useful tool to peek
    inside student's minds , to find out what their current level of concept
    aquisition was. But now it's clear that these talks are not just
    recordings of a "current state" but are rather a crusial part of the
    process of revising that state. It's in the midst of these
    conversations that students are doing some of their most important
    mathematics! in "How Children learn Mathematics" Pamela Liebeck talks
    about the E-L-P-S process used by students to acquire math concepts:
    E=experience the concept, L=use language to express the concept P= draw
    a picture of the concept S= represent the concept symboliccally.
    Before this series I saw the "L" phase as an indicator- when you name a
    concept you begin to own it- but ow it appears as a much more dynamic
    stage. Many thanks to those researchers who put this series together-
    can't wait for session three!

    Dennis McCowan
    Weston High

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