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Re: education, technology & chat (The Mathematics of it)
I really like the Davydov work, especially rising from the abstract to the
concrete. I think that knowing a bit about Davydov's work on measurement
helps me to see when classes are getting into epigenetic byways, or off
topic, or missing opportunities for laying a foundation.
The following is a little section from a draft of a piece that I am working
on with Catherine King. We make a plea for measurement to be a part of
early mathematics curricula. As you know, I bet, just about everyone
nowadays accepts a need to consider numbers/counting/operations and geometry
but measurement is often just taken as a silly willy-nilly sort of thing or
a procedural thing, not a serious foundation for mathematics development.
(If we see another preschool class laying different size carrots end to end
to so-called measure something in a Thanksgiving theme activity, we will
scream. Talk about needing to transform the content!) Anyhow here's a bit
from our section on measurement; what do you think?
Measuring sets a precedent that units can be ever further partitioned,
breaking ground in which rational numbers can be planted in later school
years. Measurement lessons provide a foil to developing misconceptions that
all numbers are whole and that number itself is a countable entity. Later
lessons on fractions may take advantage of a measurement curriculum
essentially about a whole and its partitioned equal sized units. Children
with such an introduction to measurement may encounter fractions in fourth
grade more prepared to grapple with the idea that 2/3 is 1/3 plus 1/3 or
that 3/4 is the same amount as 6/8 or that four halves is the same as two.
It is, after all, a matter of picking your unit and partitioning the whole.
A measurement curriculum can enrich children's mathematics development.
A useful curriculum goes beyond direct object comparisons and seriation
activities. It does more than provide opportunities to cover space with
non-conventional units. It does not stop at teaching techniques for
mechanically applying rulers or balance scales and reading numbers from
them. The curriculum gives value to measurement activities by mathematizing
them: engaging students to focus on whole-part relations, thinking about
what they are counting, recognizing what makes a unit sensible to count,
improving specific skills that serve the essential ideas. The curriculum
provides a context for cultural tools like rulers and scales to be welcomed
as ways to take a shortcut through the iteration of measurement units and
the counting of them. It provides a context for estimated measurements as a
part of checking to see when a measurement result should be doubted and the
procedures should be executed again so that the goal of measurement is met:
The quantity is described with precision.
Now that I look at it out of context, maybe that doesn't make too much
sense. Oh well, maybe it will to some of us.
----- Original Message -----
From: "Peter Moxhay" <firstname.lastname@example.org>
Sent: Wednesday, November 10, 2004 2:51 PM
Subject: Re: education, technology & chat (The Mathematics of it)
> > Clarification, please, for a phrase I think I don't understand: "in a
> > chat-like way."
> I guess I used a deliberately sloppy phrase to leave the interpretation
> Even though Davydov's approach may not appeal to all, his work did have
> a clear emphasis
> on the need to transform the *content* of instruction as well as the
> form. In his case,
> it was the ascent from the abstract to the concrete as a principle for
> organizing the content.
> Others on the list (the topic was "education, technology & CHAT) no
> doubt have other
> approaches to curriculum content.
> I'd just be interested to hear from others working on technology &
> education & chat
> what their approach to the content is. Does one just grab at a specific
> topic in
> math, say "polygons," and create software around this topic that enables
> good peer interaction, for example? Or does one's interest and
> knowledge of chat
> guide, in some way or other (not necessarily Davydov's!) the choice of
> math (or other) content of the software?