Why Johnny can’t calculate
THE LOS ANGELES Unified School District deserves praise for ongoing improvements in student achievement in math, especially in the elementary grades. Less encouraging is that LAUSD math scores for middle and high school are poor and lag far behind the rest of the state.
Only 11% of L.A. Unified’s eighth-graders scored “proficient” or “advanced” in algebra I on the 2005 state standards exam, compared to 34% statewide. The corresponding percentages within the LAUSD for 10th-grade geometry and 11th-grade algebra II are 5% and 4%, respectively, about one-third the pass rates statewide.
What accounts for the low achievement in middle and high school mathematics in the district? A standard explanation is lack of funds. Certainly more money could -- if spent wisely -- improve education in the LAUSD, but unfortunately the district uses scarce resources in ways that undermine student achievement.
Take professional development. The district requires math teachers to attend in-service meetings to learn more math and better ways to teach it. No one would quarrel with those goals, but the quality of professional development programs is often so poor that they are likely to cause more harm than good.
LAUSD teachers and math coaches are wrongly instructed not to use time-tested, standard methods of arithmetic. High school teachers are steered away from conventional and powerful techniques in algebra and directed to use unreliable “guess and check” methods and physical objects instead. Even elementary school teachers are discouraged from following their high-quality state-approved math books and from teaching the best methods of calculation, the standard algorithms of arithmetic.
Confirming our own observations, the head of one of the stronger LAUSD high school math departments lamented: “The mandatory 40-hour algebra training was worthless. We had to teach the trainers how to do algebra ... the people in charge of making final decisions on math [in the LAUSD] don’t know math!”
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.
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.
Adding to teacher’s problems is that the district administers the state exams well before the end of the spring semester, leaving students little time to master the standards. Couple this with the district’s insistence that all students take algebra I -- even those who failed middle school math courses -- and it is not surprising that math teachers are frustrated. (The California math framework identifies as a long-term goal taking algebra I in the eighth grade as the default choice, but it also cautions against enrolling unprepared students.)
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.
The root cause of the LAUSD’s shortcomings in math is its failure to place its best math teachers in charge of math policies. Cronyism substitutes for knowledge of subject matter. The district should systematically require those in authority over math policies to pass rigorous math tests and interviews at the chalkboard before a panel of university mathematicians and veteran math teachers.