I have no reservations about early childhood development including the learning of geometric shapes that adults know as "alphabet letters" or as "Arabic digits" ... if only by exploring keyboards of computers and calculators and cellphones.
As the child evolves, there comes a time when it is easy and "natural" (in today's world) for children to learn that such geometric shapes are commonly used to represent things ... "A is for apples." Not far behind is beginning to learn how such characters are (can be) strung together by using successive *places * ... with the strings having meanings of their own. Down the line comes learning how to *pronounce* some such strings [scrabble & digit-tiles] ... and learning how such strings are alphabetically ordered. Although all of such learning can be nurtured at pre-school levels, it does not become imperative until children formally encounter "spelling" and multi-place Arabic numerals.
However, it is not until children reach a "conservation" level ... roughly, grade 3 ... when they can internalize the notions that the *places* can be assigned numeric values ... as "place values." That is why Grade-2 teachers always have had trouble teaching "place values." It is beyond the comprehension of children who have not yet reached the "conservation" stage.
It is bad enough that the Achieve Corporation's mathematics "standards" for American schools start the teaching of "place values" at primary-school levels ... so prompting under-informed schools to inundate the very young with mathematical meanderings that are beyond their abilities to comprehend.
But now, some mathematically confused researchers are thinking that age-3 children perceive "place values", merely because some children know how to alphabetically order some multi-place numerals. The danger from researchers' mistakes of that kind is that ill-informed teacher educators, curriculum designers, authors, education officers, and researchers might use such mistakes as grounds for trying to press the teaching of place values even into pre-school levels.
Nationwide under-education and mis-education of mathematics-educators, in the mathematics of "place values", has always hurt most children, and "CCSS" threatens to worsen that plight. So, what we don't need is for mathematically under-educated researchers to lead us deeper into that swamp.
- -------------------------------------------------- From: "GS Chandy" <email@example.com> Sent: Tuesday, December 24, 2013 1:01 AM To: <firstname.lastname@example.org> Subject: [SPAM]Re: Kids understand multi-digit numbers as early as age 3
> To me it appears that Clyde Greeno is entirely correct in his assessment > that the claim in the article appears to be just "Poppycock!" - as > implied in Domenico Rosa's comment as well ("It seems that the solution to > U.S. pseudo-education in arithmetic may lie with three-year-olds" - dt. > Dec 23, 2013 10:23 PM, > http://mathforum.org/kb/thread.jspa?threadID=2612288). > > I believe that children at the age of three have plenty of things to learn > about themselves (about their own bodies and intellects) AND about the > world around them rather than studying multi-digit numbers and their > formal representation, etc. > > The article leads to the fear that - if its conclusions are accepted by > the powers-that-be in education - primary schools will now force children > at age three to study place-valued digits and stuff like that whether or > not they are interested in these things that some adults have decreed they > are ready to learn! > > May I suggest that these 'experts' should seriously look at the way > mothers teach their infant children from birth onwards, before they come > out with these poppycock suggestions about how they should be exposed to > math ideas. If they do not have the imagination to do that, they might do > well to absorb the wisdom that Maria Montessori brought to 'child > learning'. > > GSC