I am not a mathematician and I do not do long division on any regular basis. I certainly haven't written it out in over a year.

But occasionally I have to think about whether a number like 365 is divisible by a number like 7, and I don't have a calculator or computer beside me. I can wait until I'm around electronics, or I can think:

"How many times does 7 go into 36? 5 times." "That makes 35, so now, there's 15 left." "How many times does 7 go into 15? 2 times." "That makes 14, so I'm at 364 -- one day is left over." "7 went into 365 52 times, with one left over."

That is a useful algorithm. You can use that to answer questions about the world. It seems reasonable that if you're not capable of accomplishing that, then you're not going to do well in an environment that requires you to solve problems.

I agree, and of course can do this 'approximation' by hand

(even though I may do it backwards sometimes, like, 365/7 ok, 365 looks like 700/2 so that's a start, or 7x5 = 35 so 7x50 = 350 so there goes)

What I meant to say is that math is not only about juggling numbers

Or to answer that one you can just think "Hey, can I reuse the same calendar two years in a row?" and if the answer is no, then 365 isn't divisible by 7.

I don't see long division as some algorithm to be memorized. It is a fairly simple application of the theorem:

Dividend = Divisor * Quotient + Remainder. and the distributive law.

I was never taught long division as some algorithm to be followed and knowing what it accomplished and how has been enough to perform the operation with ease.

Contrasting that with stuff from later on in my life, I am not so confident with the math I picked up starting high-school. I guess I began following an approach that asked me to commit to memory - focusing on grades as opposed to concrete understanding.

I consider myself pretty decent at math and I would have to look it up if I needed to do long division. It wouldn't take me terribly long to do figure it out, but I don't currently "know" how to do it. Hasn't prevented me from being successful in mid- to upper-level college math yet.

Agreed. I never learned long division, and now I'm getting a PhD in engineering. Computers are good at arithmetic - let them do it! Teach your kids to code instead.

What are they going start with if they don't even know how to write a division algorithm ? real time 3D engines ?

I suppose they'll probably start with something the processor doesn't already do for you in hardware.

What about sorting algorithms? Do you think it's a waist of time to teach them just because it is a solved problem?

I don't think so, I think reinventing the wheel is a great way to learn.

My SAT Math score is 660, ACT Math is 26, I'm in average-level math classes and usually wind up with an A- or B+.

I've done MIT Intro to Computer Science on OCW and am currently working on Stanford Algorithm Design and Analysis on Coursera. MergeSort took maybe 10 minutes to implement in Python. I have little trouble with recursion (now), and am decent at understanding and mentally modeling complex systems (i.e. AP Chemistry).

But The Powers That Be have decided that the rapid and accurate selection and application of procedures to small, contrived "problems" are the best measure of suitability for a STEM education, so I have little to no shot anywhere besides my state's JavaSchool. Maybe they're right.

But from experience, I will say this: when you teach or test sorting algorithms, you're teaching and testing ideas and how students think. When you teach and test fractions, you're teaching a procedure and testing a student's ability to execute it quickly and accurately without getting bored or transposing digits.

IMHO, the relative weights we put on those completely separate abilities are backwards.

(I have never had trouble with the ideas behind fractions, but make me find the common denominator ten times in 5 minutes and I'll probably screw up once or twice.)

I never said you shouldn't try implementing division yourself; everyone should try implementing everything themselves someday. I'm saying that anyone can, if they wish, do a lifetime of useful work (including writing "real-time 3D engines") without ever knowing or implementing a division algorithm. They will start with anything they want.