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Re: education, technology & chat (The Mathematics of it)
I've been known to describe people as characters in Rembrandt drawings so I
guess the Tolstoy interpretation is fair play.
Here're some pointers that might be okay:
There's a piece by Davydov that was translated into English long ago by the
US mathematics teaching Association that gives a nice intro into the little
one's mathematics issues. Davydov, V. V. 1990. Types of generalization in
instruction: Logical and psychological problems in the structuring of school
curricula (J. Teller, Trans.). Reston, VA: NCTM.
Mike Cole, I bet there's no rights on that anymore -- can that be scanned
and posted? Each copy I go to great lengths to get gets stolen.
For language but for older ones, I've gotten a lot from thinking through the
A. K. Markova book "The Teaching and Mastery of Language" from M. E. Sharpe
publishers in 1979. That's first language. (and there's Galperin and
Elkonin on language arts sorts of things, too.)
And a wonderful piece about learning and development is Mescheryakov's
"Awakening to Life" (Progress Publishers in English also 1979) with an
Ilyenkov afterword introducing essays by the former students of
Mescheryakov's school described in the book.
As for the originally English stuff that is more contemporary-- do you want
it? The Gelman and Gallistel and the Siegler? and so on?
Is this okay for a start?
Maybe it wouldn't be a bad idea to have a topical biblio of sorts with
things that we've all written, too -- besides e-mail.
I want to thank xmca for helping me have a good week of thinking.
It has been great to keep my head on as I (a) figure out how to stop going
to Florida for election work a couple of days every week, (b) determine to
keep myself in the game of the many issues being done in my name as a US
citizen, and (c) try to be careful enough about nitpicky details of two work
projects that have entered that awful phase at about the same time.
----- Original Message -----
From: "David Preiss" <firstname.lastname@example.org>
Sent: Friday, November 12, 2004 3:06 PM
Subject: RE: education, technology & chat (The Mathematics of it)
> Hi Peg and others,
> I have loved this discussion but I may confess that is not in my ZPD.
> So, I guess I may have missed lots of things because speakers here are
> like the Tolstoian characters at the end of Thought & Language
> communicating a lot without enough speech. I also assume that some of
> you know each other personally, which makes thing easier to understand
> because it looks like there are lots of thing that are follow ups of
> other discussions. (Coming back at the issue of Stalkers at XMCA...) May
> be you want to recommend some reading for starters? Also, are there
> similar discussions concerning the teaching of language?
> David Preiss, M.Phil.
> Pontificia Universidad Catolica de Chile www.puc.cl
> PACE Center at Yale University www.yale.edu/pace
> Homepage: http://pantheon.yale.edu/~ddp6/
> Phone: 56-2-3547174
> E-mail: email@example.com or firstname.lastname@example.org
> -----Mensaje original-----
> De: Peg Griffin [mailto:Peg.Griffin@worldnet.att.net]
> Enviado el: Friday, November 12, 2004 4:22 PM
> Para: email@example.com
> Asunto: Re: education, technology & chat (The Mathematics of it)
> Wow in the portland schools, huh? Terrific.
> Can you get operations and their models with their strategy variants
> into the stream as problems of equality of measured continuous quantity
> (free of numbers)? A > B (Jenny's amount of clay is greater than
> Sasha's and it isn't fair) so how do you get A=B but by getting some C
> so that A-C and
> B+C. From clay models to drawings of it to lines about it to letters
> it -- and you can model all the different operations situations that
> Siegler and his folks get into. There is no doubt that numbers will
> creep in too soon because non-continuous quantity entities will, but at
> least there is some escape from a put-aside unit for measurement, maybe?
> --- Original Message -----
> From: "Peter Moxhay" <firstname.lastname@example.org>
> To: <email@example.com>
> Sent: Thursday, November 11, 2004 1:55 PM
> Subject: Re: education, technology & chat (The Mathematics of it)
> > Peg, you wrote:
> > > he portlandschools in your e-mil address. I want
> > > to know more about it.
> > It's the Portland, Maine, public school system.
> > > So, no, I haven't gotten it central, but I get measurement and
> > > modeling of operations in by whatever means necessary. Number
> > > words, count lists of
> > > them, the Gelman and Gallistel and following stuff, and the info
> > > number word structuring in other languages -- it can be a useful
> > > complication for numbers curricula, don't you think?
> > Of course! There are many ways to go about it. Getting the points you
> > mentioned added into a traditional introduction of number is a really
> > good start.
> > The challenge for me has been, though, to keep the measurement-based
> > approach from being pushed off to the side as a "unit" -- a nice way
> > to do "measurement " for a couple of weeks and then we move on to
> > another, unrelated topic. AT-based approaches have such potential for
> > a qualitative change in how concepts are
> > developed in children -- engaging teachers and administrators in a
> > dialogue on this
> > is a task of a different order of magnitude, I've found.
> > Peter