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[Xmca-l] Davydov mathematics

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 "scientific concept.")

Can anyone help?
*Andy Blunden*

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.