# [ExI] emp again

Ben Zaiboc bbenzai at yahoo.com
Thu May 3 22:23:50 UTC 2012

```"spike" <spike66 at att.net> wrote:

>if we recognize that mastery of arithmetic such as long division takes
>time that can be used on more relevant skills but trains the mind, I can go
>two routes with it: arithmetic either makes children smart or makes them
>stupid.
>

Imo, it's very important to understand what you are doing when you do (for example) long division, but not so important to know how to do it, when there are quicker and more convenient methods available.  Ideally, a person should be able to figure out long division themselves, from first principles, and then discard it in favour of a calculator.  More realistically, a person should know why they want to do long division, then find a quick shortcut to doing it.  Division was one of my (many) big problems in learning maths, and I've recently had the revelation that it's all about reducing things to 1, and related things to proportions (or multiples) of 1.  Now, I may not be able to divide 123456 by 654 in my head, or even with pencil and paper with any speed, but the important thing is knowing why I need to do that, and what it means (if 654 is 1, what is 123456?  Thanks to Excel, I know that it's 188.7706etc...  As for why do I need to know that, I don't.
I'ts just a random example).

For some people, this concept is so blindingly obvious that they would never even think of saying it.  For others, not so much.

There are many such conceptual units in maths, and if a person understands them, it doesn't matter what mechanism they use to calculate the answers.  If they don't grok the concepts, though, then giving them tools to get answers quickly is no real help, it's basically encouraging them to become Cargo Cultists.  As long as the problem remains the same, they'll be fine.  As soon as the problem changes, they'll be utterly lost.

That's my two'pennorth (speaking as someone still trying to wrap their tiny mind around quadratic equations)

Anders wrote:

> I like geometry, but probability/stats help make you more rational.

Yes!  The lottery isn't called a 'stupidity tax' for nothing.

Ben Zaiboc

```