by Dr. Mark H. Shapiro
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."... ...Albert Einstein.
Commentary of the Day - May 3, 2004: Algebra for All?
The Los Angeles Times recently reported that some 200 school districts in California had been granted waivers from the new graduation requirement that compels every high school student in the "golden state" to pass Algebra 1 before receiving his or her diploma. The school districts that were granted waivers complained that they were unaware of the new law, and that it would be unfair to penalize their students who were about to graduate because of the failings of these districts.
Frankly, the Irascible Professor - a California Resident, didn't know about the law either! It turns out that this requirement was the brainchild of one Charles Poochigian a Republican State Senator from Fresno. According to the April 26, 2004 article in the Times, the "law, passed in 2000, requires all high school students — starting with this year's senior class — to complete Algebra 1 to graduate. The law does not exempt anyone, including students with learning disabilities, English learners or the troubled, at-risk students attending continuation high schools."
The article goes on to say that "Poochigian and his supporters argue that the law is vital to raising the state's educational standards, to closing performance gaps between minority students and their white peers and to preparing students for college and the workplace."
"'Algebra is a gateway skill,' Poochigian said. 'It is important in building higher levels of critical thinking for all students.'"
These are noble thoughts; and, the Irascible Professor would be delighted if all high school students were chafing at the bit to enroll in Algebra 1. However, they also confirm the IP's view that the members of the California State Legislature inhabit some other planet.
Mathematical skills are important, and every high school graduate should be numerate and should possess those mathematical skills that are necessary for everyday life. However, our public high schools enroll students with a very wide range of abilities as well as career interests. While knowledge of algebra is necessary and important for students who plan to go on to a four-year college or university (indeed essentially all four year colleges and universities already require both Algebra I and Algebra II for admission), it is not necessarily the best mathematical preparation for all students.
There are some students who will never master the abstractions of algebra because of learning disabilities and other such problems. Some of these students may pass algebra after great effort by memorization rather than understanding. (The IP is convinced that his junior high school algebra teacher fell into that category. She was clueless about the logical structure of algebra, but she did have the book memorized.) But, there also are many students who are not interested in a four-year college degree. They often head for the community colleges to complete an Associate's degree in any number of vocational areas where the need to solve quadratic equations or to work with polynomials is really quite minimal.
These students do need math, but the math courses they take should emphasize practical numerical skills rather than the abstractions of college prep algebra. What they should study are the bits and pieces of mathematics that are needed by people who work in a wide variety of service occupations and trades, or who operate small businesses. They need to be able to balance books, or to figure simple interest, or to make basic measurements, etc.
Unfortunately, here in California we have developed a "one size fits all" concept of high school education. The concept of multiple tracks or programs in the high school curriculum has become so politically incorrect that anyone suggesting that perhaps not all high school graduates need to go on to a four-year college degree are labeled "reactionary" or worse. Thus, we end up with many high school graduates who have "passed" Algebra 1, but who can't balance their checkbooks.
As a further indication of how far practice deviates from theory and how difficult it is to legislate performance, the California State University system requires all the students it admits to complete three years of high school math including Algebra 1, Geometry, and Algebra 2 with passing grades. Yet close to 50% of our entering students fail the Entry Level Mathematics exam which covers these subjects. Most of our entering students graduated from high school with grades that put them in the top third of their graduating class, and most are of above average intelligence. If they are struggling with the abstractions of algebra and geometry, what does that say about the high school students who don't rank in the top third?
We certainly should improve the preparation of our college-bound high school students; but, we also need to serve the needs of those high school students who are not heading to the four-year colleges and universities.
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© 2004 Dr. Mark H. Shapiro - All rights reserved.