Teaching math

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For those of you interested in math, here is a first/second grade word problem.

You buy a ice cream cone that cost $1.74 and give the ice cream lady $2.00. How much do you get back?

Here is the answer and work submitted by the child:

     - 200

The important thing to be able to observe is what the child did right, and why they made the mistakes that they did.

Many people think arithmetic is easy because they learned it so young, but in fact it is quite difficult. Most people have trouble dealing with amounts larger than 7 and resort to memorized facts and learned algorithms to do even simple arithmetic.

If you don't believe me try to do the problem above without using Arabic numerals.

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Eh, teach them Calculus first- they get it better. This constant drilling of "arithmetic first, memorize meaningless formulas for seemingly no reason" crap is what is wrong with the whole damn system in the first place.
Are you seriously suggesting I teach my (almost) five year old calculus before arithmetic?
I think arithmetic has more day-to-day uses than calculus by a long shot.

Do you have kids? Have you attempted this?
I cant see a way to explain 2x + 4 if he doesn't understand addition or multiplication.
If you read the article, you'd see that it isn't a matter of teaching them things like 2x + 4, but rather the whole concept of... well, all of it. Integration is, after all, just the area beneath something- that can be pretty easy to teach kids with things like Legos.

Hell, most of math could use more Legos.

My issue is the fact that, the way that we teach math robs the actual "math" from it. It isn't memorizing facts and applying them to problems to demonstrate that, yes, Riemann is correct and what he demonstrated so many years ago is still right. There are stories to math- stories that are completely ignored. There's discovery in math- but be warned, if you do anything in math against how your teacher taught it, you will fail the test.

How do we nurture a love for math when we don't even let kids discover things without punishment for doing so?
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