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*To*: xmca@weber.ucsd.edu*Subject*: Re: education, technology & chat (The Mathematics of it)*From*: Peter Moxhay <moxhap@portlandschools.org>*Date*: Thu, 11 Nov 2004 12:06:16 -0500*Delivered-to*: xmca@weber.ucsd.edu*In-reply-to*: <s192430f.007@MORPHEUS.PPS>*Old-return-path*: <owner-xmca@weber.ucsd.edu>*References*: <s192430f.007@MORPHEUS.PPS>*Reply-to*: xmca@weber.ucsd.edu*Resent-date*: Thu, 11 Nov 2004 09:06:23 -0800 (PST)*Resent-from*: xmca@weber.ucsd.edu*Resent-message-id*: <LujRdB.A.m5B.Ow5kBB@weber>*Resent-sender*: xmca-request@weber.ucsd.edu

Peg, What you write here makes perfect sense to me and resonates with my experience of the Davydov math curriculum. But are you arguing for adding measurement to a curriculum that develops the concept of number in the traditional way (through the counting up of discrete objects)? Or for placing measurement at the center of the curriculum (as Davydov does) -- as the genetic source of the theoretical concept of number?

argues that it is only via the model that a generalization is formed. Peter

Measuring sets a precedent that units can be ever furtherpartitioned,breaking ground in which rational numbers can be planted in laterschoolyears. Measurement lessons provide a foil to developingmisconceptions thatall numbers are whole and that number itself is a countable entity.Laterlessons on fractions may take advantage of a measurement curriculumessentially about a whole and its partitioned equal sized units.Childrenwith such an introduction to measurement may encounter fractions infourthgrade more prepared to grapple with the idea that 2/3 is 1/3 plus 1/3orthat 3/4 is the same amount as 6/8 or that four halves is the same astwo.It is, after all, a matter of picking your unit and partitioning thewhole.A measurement curriculum can enrich children's mathematicsdevelopment.A useful curriculum goes beyond direct object comparisons and seriationactivities. It does more than provide opportunities to cover spacewithnon-conventional units. It does not stop at teaching techniques for mechanically applying rulers or balance scales and reading numbers fromthem. The curriculum gives value to measurement activities bymathematizingthem: engaging students to focus on whole-part relations, thinkingaboutwhat they are counting, recognizing what makes a unit sensible tocount,improving specific skills that serve the essential ideas. Thecurriculumprovides a context for cultural tools like rulers and scales to bewelcomedas ways to take a shortcut through the iteration of measurement unitsandthe counting of them. It provides a context for estimatedmeasurements as apart of checking to see when a measurement result should be doubtedand theprocedures should be executed again so that the goal of measurement ismet:The quantity is described with precision.

**Follow-Ups**:**Re: education, technology & chat (The Mathematics of it)***From:*"Peg Griffin" <Peg.Griffin@worldnet.att.net>

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