A long train of links starting with Belle gets you to the assertion that children in L.A. schools are having trouble learning fractional division because they are being taught that fraction division is repeated subtraction (in the same way that division of natural numbers is repeated subtraction).
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.
Leave aside the odd use of 'erroneously' to describe a working algorithm, but does anyone really think that it's easier to teach kids this complicated method of subtracting fractions instead of the normal "invert and multiply" method? The subtraction method is going to take more computation except in the rare cases where the two fractions have the form a/b and ca/b. I guess that's the point of all the hubub. But maybe I'm out of touch with exactly how the average kid learns math.