Math Education: An Inconvenient Truth (YouTube)
She complains that students aren't taught and drilled in the algorithms for long multiplication and long division. Her summary was (around 13:40):
- Inability to work alone
- Lack of math fluency
- Lack of basic math skills
- Dependence on calculators
Now, I started watching this expecting I'd agree with her, but the more she went on, the less was I convinced.
In particular, her emphasis on teaching and drilling the most efficient algorithms seems misplaced: we have machines now for following algorithms. This means that most people won't use them often enough to be confident in them — if you don't use them regularly, you'll lose them — so that they'll end up useless. An ability to work through a problem seems much more useful. Even an ability to follow an algorithm from a set of instructions would be more useful than following one by rote.
On the other hand, drilling algorithms seems unconnected to her goals: it gives neither math fluency nor math skills. As far as working alone is concerned, it's completely orthogonal. It may reduce calculator use, but probably won't — multiplication of two- to three-digit numbers just isn't that common.
It's even doubtful whether calculator use is a bad thing. We depend on technology of one sort or another for a lot of things. A pocket calculator is the least of it. Teaching students how to use one effectively is a good thing — not which buttons to press, but when and why, and how to judge whether the answer is meaningful.
Now, there are things that could be improved with math education; emphasis on drilling outdated methods of calculation isn't one of them.
(Putting an atlas in a math textbook is a bad thing, I do agree with her in that. As an atlas, it's bound to be mediocre, and as a math teaching tool, it's likely to be marginally relevant at most. But that's caused more by subject-oriented curricula than any "modern" mathematics: the writers of a math textbook can assume nothing about the atlas, if any, used for the other subjects. An integrated curriculum would solve this; it'd have its own problems.)
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22 May 2007, 1:55 UTCcomment by nifwlseirff
One thing I think is not 'taught' enough, is problem solving. When it is taught, there is only one path to a solution that the teacher will mark as correct. This is not teaching problem solving skills! I had two fantastic maths teachers at high school, who delighted in providing/creating problems that could be solved any number of ways.
Outdated methods of calculation are still useful, especially when trying to figure out in a shop which item makes better economic sense (hmm... sticking to a budget?) It's not feasible to whip out a calculator for every decision.
I find this problem to be similar to music teaching, where some teachers will make students focus on one particular piece of music until the student can play it 'correctly'. This doesn't not teach them much about music, or the difference between subjective/objective evaluation. Allowing students to play by ear, improvisation and encouraging massive amounts of sight reading is more interesting for the students and usually results in a more 'rounded' musician.
22 May 2007, 11:04 UTCcomment by sabik
If it's not feasible to whip out a calculator, long division isn't going to work either :-)
Now, if children were taught approximate mental arithmetic, that would be *very* good. Both in the shops and as a check on the calculator. However, that's not what's being suggested here...
