Fraction Division

FRACTION DIVISION….In the LA Times today, math gurus David Klein and Jennifer Marple tell us that one of the reasons high school kids in Los Angeles aren’t learning math is because the teachers themselves get rotten training. This particular anecdote struck me as especially bizarre:

Too often, the math that teachers are taught at district training sessions is just plain wrong. For instance, middle school teachers are erroneously taught that fraction division is repeated subtraction. This makes sense only for special examples such as 3/4 divided by 1/4 . In this case, 3/4 may be decreased by 1/4 a total of three times, until nothing is left, and the quotient is indeed 3. Understanding division as repeated subtraction, however, is nonsensical for a problem like 1/4 divided by 2/3 because 2/3 cannot be subtracted from 1/4 even once. No wonder students have trouble with fractions in high school.

“Fraction division is repeated subtraction”? I don’t even get that. Even in the example that “works,” how does getting nothing somehow translate into 3?

And what’s the point, anyway? It’s one thing to try some weird new technique when the old one is difficult to understand, but fraction division is simple. Why would anyone spend any time trying to come up with some new way of teaching it?

UPDATE: I guess I read too quickly. Division as repeated subtraction makes sense for whole numbers, but I missed how it works for fractions. My mistake. It just never occurred to me to think of it that way.

It’s still a pretty dumb idea, though.