[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Xmca-l] Davydov mathematics
- To: "eXtended Mind, Culture, Activity" <email@example.com>
- Subject: [Xmca-l] Davydov mathematics
- From: Andy Blunden <firstname.lastname@example.org>
- Date: Mon, 3 Nov 2014 14:47:46 +1100
- In-reply-to: <CAHCnM0Dsnfu94PT=HUxiyKXqT-LsVXTjviYmz+E-mw0Waj83EQ@mail.gmail.com>
- List-archive: <https://mailman.ucsd.edu/mailman/private/xmca-l>
- List-help: <mailto:email@example.com?subject=help>
- List-id: "eXtended Mind, Culture, Activity" <xmca-l.mailman.ucsd.edu>
- List-post: <mailto:firstname.lastname@example.org>
- List-subscribe: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:email@example.com?subject=subscribe>
- List-unsubscribe: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:firstname.lastname@example.org?subject=unsubscribe>
- References: <email@example.com> <15A0050C-24E2-4D3D-A4BD-7C8FBE47F907@umich.edu> <5449F0B6.firstname.lastname@example.org> <6073CDA7-B612-4CC2-AB79-312CE63F78BB@umich.edu> <email@example.com> <700B31E6-4D18-43A1-8357-47B8EAF5D08F@umich.edu> <firstname.lastname@example.org> <66AA7EEB-1F34-485D-9227-5F8EB31A56F8@umich.edu> <ced5ad95d0ae4d14ae2db1df8a8cd26e@SN2PR0601MB798.namprd06.prod.outlook.com> <4E081611-A3BD-46F3-AE79-BB41E08CCF87@umich.edu> <544DAD02.email@example.com> <95546616-8723-4803-A0D9-72ECAF4F5143@umich.edu> <544DCA93.firstname.lastname@example.org> <A20F993F-947D-4800-B5A2-896CAB22007A@umich.edu> <5452D88F.email@example.com> <firstname.lastname@example.org> <email@example.com> <firstname.lastname@example.org> <86D8D1D6-E3A2-4FA2-9F6D-0A55359E31D8@umich.edu> <email@example.com> <4FD6099D-A5CB-4A9B-911D-D4B2E192E724@umich.edu> <CAHCnM0Dsnfu94PT=HUxiyKXqT-LsVXTjviYmz+E-mw0Waj83EQ@mail.gmail.com>
- Reply-to: <firstname.lastname@example.org>, "eXtended Mind, Culture, Activity" <email@example.com>
- Sender: <firstname.lastname@example.org>
- User-agent: Thunderbird 22.214.171.124 (Windows/20090812)
Mike, thank you for the two Schmittau articles on Davydov maths teaching.
The first was very brief, but useful.
The second was very helpful, in that it did put a lot of meat on the
bones of my sketchy understanding of what VVD's maths program meant, but
I have some problems with it, which people on the list could probably
help me with.
(1) The abstract claims that the order of learning (first arithmetic and
then algebra) traditionally used is reversed. I found this an astounding
idea. But when I read, this seems not to be what actually happens. The
children are doing complex arithemetical task like dividing by 3-digit
numbers, and still haven't actually got to algebra. Though
(2) there is talk of a schematic kids are offered to use to structure
problems. It would help to know what this schematic is.
(3) There is a fault in the PDF, causing some mathematical symbols to
not show, which (I think) is making some of the examples incomprehensible,
(4) though I find telling a kid who says 14-4-4=14 is making an error a
bit rich as it seems to me an equally valid answer to an ill-posed problem.
(5) Finally, Schmittau assumes that by "pre-concept" Vygotsky meant
"complex". I thought this at first, until a few years ago David Ke
kindly corrected me, and indeed this is not the case. Although merely a
question of terminology, a rather crucial one, as it is pre-concepts
which are the basis for learning mathematics and "complexes" lead to set
theory only. I note that Paula Towsey in her work, also distinguishes
"preconcepts" as a particular formation, not simply a name for the whole
bunch of concepts arising prior to the formation of theoretical
concepts. (Though I did appreciate Schmittau's rare distinction implied
in the use of the term "theoretical concept" instead of the more usual
Can anyone help?
mike cole wrote:
As a small contribution to this interesting thread, two of Jean Schmittau's
writings. She has done a lot work with Davydov's ideas in math ed that may
give those following the discussion some useful info.