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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