Today's *LA Times* rightly laments that LA Unified is home to quite a few teachers, supervisors, and program directors who're totally incompetent at teaching math:

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.

District "pacing plans" are another example. These tell teachers the order in which they should teach topics for each math class. Some of the plans hinder rather than promote understanding. One draft plan called for 10th-grade geometry teachers to teach the so-called distance formula before the Pythagorean theorem, but the distance formula needs the Pythagorean theorem for its explanation, and should be taught first.

[...]

Still another problem is the LAUSD's history of selecting poorly written math textbooks. In 2000, the district ignored the textbook recommendations of Caltech, UC and Cal State mathematicians and the legendary teacher Jaime Escalante, portrayed in the movie "Stand and Deliver." The most widely used current algebra I textbook was heavily criticized by a panel of mathematicians appointed by the California Board of Education. To supplement this weak textbook, the district uses expensive computer programs that are not state approved.

This sort of thing rarely goes down at middle class schools as parents catch it, PTA's don't stand for it, and community pressure stops it. So how can we bring upper-income standards to lower-income schools? Easy. Mix them:

Since 2000, school officials [in Raleigh] have used income as a prime factor in assigning students to schools, with the goal of limiting the proportion of low-income students in any school to no more than 40 percent.

[...]

In Wake County, only 40 percent of black students in grades three through eight scored at grade level on state tests a decade ago. Last spring, 80 percent did. Hispanic students have made similar strides. Overall, 91 percent of students in those grades scored at grade level in the spring, up from 79 percent 10 years ago.

This is one of those big, but broadly unpopular policies (too resonant of busing) that'd actually do great things if widely enacted. The politics of it suck, but if we want an even *close* to fair society that gives those born in the wrong areas the right chances, this is the direction we'll have to go.