The decision to introduce algebra to 8th grade students is a beacon of hope in the otherwise bleak K-12 public education system of California. Numerous studies have identified difficulties with algebra as one of the main reasons why high school and even college students were failing to graduate every year. By demanding early mastery in a discipline that Gov. Schwarzenegger called the “key that unlocks the world of science, innovation, engineering and technology,” California has taken a step in the right direction to support the demands of the knowledge-based economy of the 21st century.
Teaching at a community college can give one a sense of how unprepared students generally are in algebra when they graduate from high schools. I began teaching the subject as an adjunct faculty in a community college in northern California this spring. The elementary algebra course included the study of real numbers, linear equations, exponents, polynomials, factorization, quadratic equations, and rational expressions. The first week was revealing. Negative numbers, fractions and divisions, particularly those involving decimals, overwhelmed many students. Calculating something like 54 – (-12) baffled about a quarter of the student who subtracted 12 from 54 to produce a result of 42. Almost half the class was clueless about the order of arithmetic operations, and solved problems like 2 + 4(1/2 + 1/3) as 6(1/2 + 1/3) = 5. Something more complicated like 1/2 + 3/4[-2(1/4 + 5/12) + 3/5] threw almost the entire class off.
It took me an ordinate amount of time to cover the basics and shake off students’ fear of numbers and equations. However, once they sensed the power and beauty of algebra and its relevance, not just to their careers but also to such daily tasks as shopping and driving and lobbying for a cause on campus, they made rapid progress. Convincing them that I would be a patient and sympathetic teacher as long as they made a serious effort at learning algebra also helped.
Frank, floundering in fractions in the beginning, displayed fluency with factorization toward the end. Christina, shaky until spring break, suddenly began solving quadratic equations with ease. Paul, easily the oldest student in the class at 53, exuded confidence that after two attempts, he would pass algebra this time. A college degree that he had to postpone after graduating from high school in the ‘70s now appeared as a distinct possibility. "Everyone gets a second chance in America," was how he summarized his experience.
There was no denying that if the average student had a better foundation in algebra in middle and high schools, I could have made more progress and even delve into some exciting real-world applications before the semester ended.
During spring break, the National Mathematics Advisory Panel released a 120-page report that stated, “Although our students encounter difficulties with many aspects of mathematics, many observers of educational policy see algebra as a central concern. The sharp fall off in mathematics achievement in the U.S. begins when students reach late middle school, where, for more and more students, algebra course work begins …” Three words summarized the panel’s recommendation: “Focus on algebra.”
Yes, funding, teacher training, school resources and myriad other issues pose thorny problems to the vision of California’s State Board of Education. But by testing eighth-graders in algebra within three years and giving them a head-start to flourish in the knowledge-based global economy will more than justify the investments that must be made to the K-12 public education ecosystem of California. As a nation, to cite only one example, we simply cannot afford our fifteen-year-olds to rank 25th among 30 developed nations in math literacy and problem-solving, as the 2006 Program for International Student Assessment (PISA) found.
Besides, lack of qualified teachers may not be as insurmountable a problem as is currently thought. The EnCorps Teacher Initiative in June of last year is attracting retiring baby boomers and other concerned Americans. Their expertise in algebra, geometry, trigonometry, calculus, statistics, physics, chemistry, biology and computer science, honed in the trenches, is precisely what our students need to make these subjects become real for them in classrooms. Certainly the program needs to become more visible, flexible and rewarding but it is a good start.
Californians should support the State Board of Education’s initiative to help our students master the mystery of ‘x’ in algebra. And 8th grade is a great place to start.