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**But wouldn't you say that number crunching (learning how to

manipulate the numbers) would provide a framework within which a

person could grasp math? I'm certainly not advocating sitting a kid

down and making him do it...been there done that hated it...but I'm

thinking, an ability to grasp the concepts depends upon the knowledge

of the numbers. Not the numbers on paper NECESSARILY, but the numbers.**
AND
**Yea..... Don't you need to know **how** to do the math with a calculator so
you can push the right buttons? Memorizing numbers is not the same as
***how*** to do it.
Lara......... who still does NOT know her times-tables (and loves her
calculator), but knows **what** multiplication is!! (Hey!!! I went to pub
school for
12 years and graduated with high honors, AND had a dad who stood over me a
hit me on the head when I said the wrong answer to the times-table flash
cards
he was holding; shouldn't I know all of them then? hehehe)**

At least one of my children learned an incredible amount about arithmetic and
the symbols used for the operations by playing around with a calculator. She
asked for a calculator of her own when she was five or thereabouts, so I gave
her one. She would sit and mess around with it for long stretches of time,
over a period of many months. Eventually she started showing me stuff. One of the
things she had discovered was the concept of multiplication. She showed me
how if she pushed the * button in between two numbers, she got the same result
as if she had added the first number to itself as many times as her second
number. (I wish I had written down the words she used to explain this to me,
they've flown the coop I'm afraid). She had discovered patterns from repeated
adding of numbers. (for instance, that multiples of 5 always end in 5 or 0.) She
had figured out division. She had discovered negative numbers. She had
recognized relationships between odd and even numbers, and discovered the power of zero.

Deborah in IL