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[quote=Anonymous][quote=Anonymous]

It works for some kids, and is an abysmal failure for many others, who need the concrete before the abstract. [/quote]

But they DO teach it in a concrete way first.  The kids work with manipulatives and physical objects for years.  It starts in preschool and kindergarten.

For example, taking a set of 10 jelly beans and working with a partner to divide them in half to they each have the same amount and then counting to discover what that number is.

Or each kid bringing in 100 of something (M&Ms or jolly ranchers etc.) to kindergarten so they can each spread them out on their desk and group them into various piles per the teacher's instruction (I happened to be a volunteer in DC's kindergarten class one of the days they did this.  I think the unit lasted a week.)

Or the class sorting themselves into groups each morning based on a question (Again, a real-life example from my DC's kindergarten class:  Who had a hot breakfast this morning?  Who had a cold breakfast this morning?  Sometimes the kids sorted themselves physically on the rug.  Sometimes they did it by moving their name magnets into one of two columns.  Either way, they then tallyed it up together as a class and and talked about it as an addition equation (8 "Yes" plus 12 "no" equals 20)).

To me, this is a concrete as it gets.  This is experiential learning to help the kids both understand and practice math facts.  Again and again and again.

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