Math educators, with good reasons, have long recommended that students be required to study algebra. Many districts mandate algebra in the ninth grade. California, one-upping everyone else, currently requires eighth graders to take algebra. Japanese children begin studying algebra in the fifth grade. So How's it working out?
Findings from a study involving 160,000 Chicago high school students offer a cautionary tale of what can happen, in practice, when school systems require students to take algebra at a particular grade level.
160,000 is a lot of students, and normally the bigger the sample from the population, the more reliable the conclusions. Researchers studied eleven “waves” of students entering ninth grade from 1994 to 2005.
(Researchers) compared changes within schools from cohort to cohort during a period before the policy took effect with a period several years afterward. They also compared schools that underwent the changes with those that already had an “algebra for all” policy in place.
What did the researchers find?
The policy change may have yielded unintended effects, according to researchers from the Consortium on Chicago School Research, based at the University of Chicago. While algebra enrollment increased across the district, the percentages of students failing math in 9th grade also rose after the new policy took effect.
By the same token, the researchers say, the change did not seem to lead to any significant test-score gains for students in math or in sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school.
Not much upside. More students failed, test scores were flat, and the percentage of students motivated to take advanced math course did not rise, but, gee, “algebra enrollment increased.” The district says more students will fail when required to take harder courses without supports in place. Yet the district made attempts include supports over the last seven or eight years.
Steps include developing curricular materials introducing students to algebra concepts in grades K-8, requiring struggling 9th graders to take double periods of algebra, and providing more professional development in math to middle and high school teachers..
One of the researchers thinks that test scores did not improve because teachers may have “watered down” the content because “math classes included children with a wider range of ability levels following the change.”
But Japanese elementary schools are not tracked. All children study exactly the same material with such predictability that some observers have quipped that every child in Japan is on the same page of the textbook on any given day. I have successfully taught Algebra 1 to high school special education students, or to give due credit, special education students have successfully learned Algebra 1 under my guidance.
The problem is with issuing mandates without a coherent, integrated societal commitment to the foundations of education, mathematics in particular. I have seen Montessori preschool students exploring algebra with manipulatives. I have often said that lots of profound math can be learned without any resort to pencil and paper. Children do not necessarily need numerals to understand number.
There is one other thing. Japanese children from kindergarten age regularly take abacus lessons the way American children take piano or ballet. Generating a sum with the abacus is different than generating a sum using the written algorithm. The activity of thinking about number and computation in more than one way leads to greater mathematical flexibility. Japanese students can therefore more readily absorb and manifest algebraic thinking. That's my hypothesis anyway and maybe the Gates Foundation or somebody else will provide me a grant to test it.
(P.S. You may enjoy reading the comments at the end of the link.)
Other links from the cited story:
“Calif. Judge Blocks Requirement For 8th Graders to Take Algebra,” January 7, 2009.
“Experts Question Calif.’s Algebra Edict,” July 30, 2008.
“Chat: California's Algebra 1 Mandate for 8th Graders,” July 30, 2008.