By Del Stover
9/28/04 -- As the nation moves to boost the academic rigor of its public schools, educators and policymakers are putting the spotlight on a 4,000-year-old branch of mathematics: algebra.
At least 20 states have toughened the algebra requirements demanded of students in recent years -- and made algebra a more important part of the state exit exams that students must pass to earn a high school diploma.
This, in turn, has prompted local school officials to re-examine their own commitment to algebra instruction. Some school districts are introducing pre-algebra concepts into the lower grades; others are making algebra courses mandatory for the first time. Yet others are establishing tutoring programs and two-year courses in introductory algebra to help low-performing students make the grade.
The attention being given to algebra is largely due to recognition that tomorrow's work force will need to be math savvy and skilled in problem solving, says Joan Leitzel, program director of Ohio's Mathematics and Science Initiative.
Leitzel says her state "is making the transition to a knowledge-based economy, so we expect Ohio students will need to be well prepared for [high-tech] jobs that depend quite heavily on math that is built on algebra."
Algebra is a branch of mathematics that, by the simplest definition, uses letters and symbols to represent numbers, as in the equation 2(x)+1=9. Usually taught in middle or early high school, algebra is a stepping stone to more advanced coursework in high school.
But what really has caught the attention of educators and policymakers is research showing the value of algebra in helping students develop the abstract reasoning and problem-solving skills that make for success in school and career.
Threshold for success
"If you had to pick a threshold -- somewhere in the high school curriculum -- that pretty much guarantees students will go on to college, graduate from college, and land a good job -- it's Algebra II," says Anthony Carnevale, a senior fellow at the National Center on Education and the Economy.
Although the trend has gone largely unnoticed, the number of students taking algebra has been steadily growing. In 1982, the federal government reported that only 35.6 percent of high school graduates had studied two years of algebra; in 2000, the percentage was 64.3 percent. State standards have almost assuredly pushed up this figure in recent years.
"We are expanding the population that gets the opportunity to study algebra, whereas in the past it might only have been some students -- particularly those who were going on to college," says Cathy Seeley, president of the National Council of Teachers of Mathematics (NCTM). Today, educators realize "all students can benefit from this particular kind of math."
That positive trend is offset by a familiar problem: As so often is the case in education, minority and poor students are being left behind.
Too many are taught by less-qualified teachers than those found in affluent school systems. Others attend elementary schools that lack the rigorous math instruction necessary to prepare them for advanced math coursework.
That reality recently was evident in California, where local schools sought waivers for thousands of high school students, some of whom were not adequately prepared for the algebra questions on the state's exit exam. The waiver applications were "a reaction in some places where students were tracked . . . somehow they were taking some kind of remedial math or taking algebra and not passing," says Kay Garcia, an education program consultant with the California Department of Education.
An early start
This achievement gap will prove tough to close, but many school systems are accepting the challenge. In California's Atascadero Unified School District, where nearly 90 percent of students passed the state's math exam last year -- but where 72 percent of disadvantaged students failed -- officials have introduced a two-year introductory algebra course to give low-performing students more time to master the course demands.
In Baltimore, every ninth grader now must take algebra in preparation for Maryland's high school exit exam. School officials are confronting the reality that, for some low-achieving students, "their math problem-solving and thinking skills are not necessarily adequate to confront the challenges of algebra," says Frank DeStefano, high school district officer for the Baltimore City Public Schools.
As a consequence, school officials have been revising the math curriculum to ensure that elementary and middle school students are better prepared in advance of their first algebra class, he says. Also, student tutoring and teacher training programs are being implemented to improve student academic performance.
The district also is hoping to boost student performance in 18 schools by piloting Math Connections, an innovative, commercial math curriculum developed with funds from the National Science Foundation.
"We're going to double the amount of [instructional] time for students who need it," DeStefano says. "We're in the midst of our own high school reform, and we're really putting an emphasis on student success in algebra."
Within the math community, there is still some debate about what grade introductory algebra should be introduced and what specifics should be taught. But Seeley advises school board members to not let such debate distract them from the central policy issue they should be concerned about: The overall K-12 curriculum should move children forward in math in a logical, consistent manner.
Leitzel agrees. There's no reason, for example, not to teach pre-algebraic concepts in the elementary school and gradually build up student knowledge of the subject.
"The ideas of algebra should become a part of a student's math education quite early," she says. "It's not that you do arithmetic, then one day you start algebra. Algebra is a generalization of arithmetic. If you do it right, students scarcely know when they start algebra."
Debate over standards
Educators also suggest it wise not to jump the gun if they hear of debate about the quality of state and NCTM standards regarding algebra. Some mathematicians and policymakers complain the standards are vague and not rigorous enough and rely too much on word problems, make too much use of calculators, and fail to teach key concepts.
Such concerns are prompting some reflection. The National Center for Education Statistics recently announced plans to study the content and teaching of introductory algebra in the nation's schools.
Meanwhile, NCTM intends to focus its professional development efforts this year on algebra.
As to the criticism, however, Seeley says it's not the standards that are failing students; it's that not enough schools are following them faithfully. Implemented properly, she says, the standards lay the foundation for a solid education in algebra.
"As you look at some of the more recent math programs, the richer, more innovative programs for middle schools and high schools, you'll find they make interesting use of algebra," she says. "Algebra includes much more than solving equations and doing lots of rote kinds of symbolic procedures. The standards address the real issues of what math is most useful to people in a technological society."