Los Angeles Times
September 26, 2005
Why Johnny can't calculate
By David Klein and Jennifer Marple
September 26, 2005
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
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
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.
DAVID KLEIN is a professor of mathematics at Cal State Northridge
and the lead author of "The State of State Math Standards 2005,"
published by the Thomas B. Fordham Foundation. JENNIFER MARPLE teaches
at Monroe High School and is an LAUSD math coach. E-mail: