[coryrc]

You're absolutely correct on your second point.

But for the first point, as poor as research in education is, there have been improvements in educational methods. I read some examples about the Common Core mathematics pedagogy, prepared to be as angry as Feynman, but they were actually teaching kids how to do arithmetic the way I do (which is way better than New Math or brute force methods): 99x5 is 500-5 not 5+(4+5)*10+400. Are their changes more likely to be improvements rather than demerits? I do not know.

[WalterBright]

There have certainly been changes in educational methods, but I doubt there are improvements. Math achievement has been flat for the last 50 years. The "new math" and "look-say" methods were largely invented to drive new textbook sales.

[coryrc]

I think you should look into the complaints about common core; I think, if you're good at arithmetic (like I assume most of us programmers are), that you'll find the current methods an improvement over those and about as good as can be done by our grade-segregated, "no-child-left-behind", Prussian educational system.

[WalterBright]

Like I said, no measurable aggregate improvement in the last 50 years.

[coryrc]

So many other factors have gone down, that might actually be an achievement.

[kwhitefoot]

I learnt arithmetic in the early sixties. 99x5 would be 9x5x10+9x5 = 450+45 = 495

Perhaps it helped that we all knew the 12 times tables.

Is there some new magical way of doing long multiplication that is more effective and easier to understand?

[coryrc]

999999*5 is far easier as 5000000-5 than 45+450+4500+...

Are you really arguing that the latter is faster and more effective to do in your head?

[kwhitefoot]

Not at all. I didn't know we were discussing mental arithmetic.

[coryrc]

Even on paper it's far simpler

(1000000-1)*5 => 5000000-5 => 4999995

Learning to find these patterns early sets up students for having an easier time with algebra later. Algebra is just rearranging equations. I don't understand, but students do struggle with going from "12/3=?" to "3*X=12 solve for X". We can't keep failing so many students every year and expect our country to hold together.