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*To*: <xmca@weber.ucsd.edu>*Subject*: Re: education, technology & chat (The Mathematics of it)*From*: "Peg Griffin" <Peg.Griffin@worldnet.att.net>*Date*: Wed, 10 Nov 2004 15:36:47 -0600*Delivered-to*: xmca@weber.ucsd.edu*Old-return-path*: <owner-xmca@weber.ucsd.edu>*References*: <s19233c3.051@MORPHEUS.PPS> <55B5D5E0-335A-11D9-8216-000A957B2E66@portlandschools.org>*Reply-to*: xmca@weber.ucsd.edu*Resent-date*: Wed, 10 Nov 2004 13:29:55 -0800 (PST)*Resent-from*: xmca@weber.ucsd.edu*Resent-message-id*: <hpnZ-B.A.PlB.ShokBB@weber>*Resent-sender*: xmca-request@weber.ucsd.edu

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. Peg ----- Original Message ----- From: "Peter Moxhay" <moxhap@portlandschools.org> To: <xmca@weber.ucsd.edu> 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 > open... > > 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 > the > math (or other) content of the software? > > Peter > > > > > > > >

**References**:**Re: education, technology & chat (The Mathematics of it)***From:*Peter Moxhay <moxhap@portlandschools.org>

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