Wednesday, February 2, 2011

Education Continued

Miss Self-Important asks:
why assume that our inability to know what skills will be lucrative in the future gives us a basis for cutting anything currently in use out of the curriculum? Is saying that since Stata or R can run regressions for you, we must teach Stata and R instead of long division really that different from saying, in the context of literature, that since the publishing on the internet is really popular, we should start teaching blogging instead of novels?

The long division thing isn't about lucrative, but what is relevant. Computers are very, very good at arithmetic. Far better than human beings. Saying "Teach Stata instead of long division" isn't akin to blog instead of novels; it's more like saying we should teach kids to repair and drive cars instead of how to ride and shoe horses. Yes, riding a horse still works, but cars are better.

Well, that's not quite fair. In a very important way, Stata is built on long division in a way that a car isn't built on horses.

Nevertheless, nobody is going to do long division. If FLG sees two large numbers he does one of two things 1) round so that he can do the division in his hand and thus get an estimate or 2), if he needs more precision, plug it into a computer or calculator. He ain't doing long division by hand. Again, nobody is going to do it by hand.

Certainly a student needs to know what division is, but doing stuff like this by hand is ridiculous.

FLG will say, however, that he could be sympathetic to the case that learning how to do long division isn't merely about the mathematical or arithmetic output. That we all know nobody is going to do this stuff by hand, but that learning an algorithm and applying it correctly or some other more general skill is acquired. But there must be a way to teach those without doing something that a computer could do in a trillionth of the time.


Andrew Stevens said...

I routinely do long division by hand.

FLG said...


Hilarius Bookbinder said...

The long division thing actually seems like a bit of a nonsequitir to me, because my memory of statistics/probability is that it has basically nothing to do with arithmetic. I have friends in math and engineering phds who I can regularly outperform in basic math.

However, you absolutely do need to know something about statistics to use stata, which I can attest from experience.

Andrew Stevens said...

All my life I've done basic calculations in my head just to stay sharp. And I frequently find myself with pencil and paper, but no calculator or computer. (Admittedly, I probably do far more calculations per day than the average person.) Plus, it's just a habit I picked up as a kid when nobody had access to computers and even calculators were fairly uncommon.

I absolutely believe that a strong grounding in fundamentals is necessary to enable a person to check calculations for reasonableness (to guard against input errors) and also is a very strong aid toward understanding at more advanced levels. Without a solid understanding of long division, I think you'd have serious problems with manipulating and factoring polynomials. Now is this useful to people who aren't going to learn calculus or linear algebra? Perhaps not, but I think it's foundational for those people and if they don't learn it young, I'm not certain they'll have the maturity with the ability when they will need it. I shudder to think of a student trying to take differential equations in college, only having learned how to do long division a year or two earlier.

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