Algebra Focus of Trend To Raise Academic Stakes
Although efforts by New York City and other school systems to require students to take algebra and other advanced courses to graduate are a step forward, they could fail without adequate staff development, supports for students and families, and a rethinking of the entire K-12 curriculum, experts warned last week.
The announcement this month by Schools Chancellor Ramon C. Cortines that New York City students will have to take three courses each of academic mathematics and science is the most recent and dramatic evidence of a national trend. (See Education Week, May 11, 1994.)
New York's new standards, which are among the toughest in the country, are only one example of the steps taken by urban districts to stiffen their academic expectations for students, with a particular emphasis on algebra. Other districts that are raising their sights include:
- The six urban sites in the College Board's Equity 2000 project--Fort Worth; Milwaukee; Nashville; Prince George's County, Md.; Providence, R.I.; and San Jose, Calif.--which require all students to take algebra in the 9th grade and geometry in the 10th. The pilot program is trying to close gaps in the rates at which rich and poor, and minority and nonminority, students attend and complete college.
- The nine districts awarded grants last week under the National Science Foundation's Urban Systemic Initiative, which have promised that all their students will take algebra by the end of 9th grade. (See story, page 8.)
- Baltimore, where this year's 9th graders are required to take a three-year sequence of math courses to graduate that includes algebra, geometry, and one additional class to get them ready for calculus. They also have to pass biology, chemistry, and physics.
- The Cambridge, Mass., schools, which this year for the first time are requiring all 8th graders to take algebra. Boston, which already requires students to pass algebra to graduate, is considering mandating it by the 8th grade.
'Setup for Failure'
Such increased graduation requirements reflect a national movement for higher expectations for students. Algebra has been singled out because it is widely viewed as a "gatekeeper'' to the entire college-preparatory curriculum.
A recent study by the College Board found that high school graduates who had taken one or more years of algebra were 2 times more likely to go to college than those who had not.
In addition, among those who completed algebra in high school, the gap in college-going rates between minority and nonminority students virtually disappeared.
"The essential message is that, unless kids are brain-damaged, all kids can learn at very high levels,'' said Vinetta C. Jones, the national director of Equity 2000.
But Ms. Jones also warned that requiring algebra for everyone without changing the rest of the system "is a setup for failure.''
Equity 2000 sites provide summer institutes and ongoing workshops for teachers, guidance counselors, and principals; supplemental classes on Saturdays and during the summer for students; tutors and mentors; and "Family Math'' and other activities to get students and parents working together.
"Algebra for everyone has been a dream that for some has turned into a nightmare,'' argued Jack Price, the president of the National Council of Teachers of Mathematics.
"Many school boards ... have interpreted this to mean that every child should be placed in what we might call a traditional first-year algebra class,'' Mr. Price said. "As a result, some students have simply experienced failure at a higher level.''
"We need to begin to think of algebraic thinking as a strand throughout the K-12 curriculum,'' he added, "not simply as a course in high school that is currently a filter for higher mathematics.''
Critics say first-year algebra typically has been taught in isolation and has stressed rules and procedures over real-world applications. In contrast, some urban districts are trying to teach algebra through an emphasis on problem-solving, cooperative learning, and hands-on activities.
Success and Failure
New approaches to teaching algebra, combined with additional supports for students and teachers, appear to be paying off.
The average Equity 2000 site now has more than 80 percent of its 9th graders enrolled in algebra or a more advanced course.
The failure rate among those enrolled in algebra is substantial. But Ms. Jones noted that at its current level of about 50 percent, the failure rate is no higher than it was before enrollment increased, meaning that in absolute terms many more students are passing the course.
"Part of it is attitude,'' Ms. Jones said. "Failing a lot of kids, some feel, makes them a better teacher.''
The best strategy, most agree, is to introduce algebraic thinking earlier in the curriculum.
One example is the Algebra Project, founded in 1982 by Robert Moses, a prominent civil-rights leader. The initiative, which now reaches more than 10,000 children in schools across the country, provides a transitional curriculum that introduces 6th graders to concepts that will be needed later in algebra.
Through the Algebra Project, students learn to think, speak, and write mathematically by tackling problems in their daily lives.
"If you open up the Algebra Project book, there's lots of blank space for kids to write and draw pictures and create symbols,'' observed Lynne Godfrey, a math-staff developer in Cambridge, where the project first got its start. "There's lots of work that's generated by the students and by their peers.''
"In a standard math book, the problems are already written,'' she added. "The expected solutions are usually at the back of the book.''
Both the Algebra Project and Equity 2000 also emphasize parent and community involvement.
"Parents are not aware of what's happening with this whole tracking issue,'' Ms. Jones pointed out. "They don't know that their kids are in these dead-end courses that are preparing them for the permanent underclass.''
But the major problem facing the urban districts is finding enough teachers qualified to teach higher-level mathematics, particularly to diverse groups of students.
'The Biggest Challenge'
"Probably the biggest challenge that we've had across our schools is staffing added sections of algebra and geometry with adequately prepared teachers,'' said Donald Horrigan, the Prince George's County coordinator for Equity 2000.
"It's kind of a medium success,'' said Paul Lyons, the coordinator of mathematics for the Cambridge school system. "We've got a lot of kids studying better mathematics than they've studied in the past.''
"On the other hand, I think teachers have had a difficult time trying to manage all these different levels of kids in the same classroom,'' Mr. Lyons added.
Moreover, just requiring algebra does not open the gates to advanced studies. Dorothy Strong, the manager of mathematics support for the Chicago schools, said the district has for at least five years required students to pass algebra in order to graduate.
"But ... by the time those kids got to the senior year, they could take algebra and quit mathematics,'' she observed.
In 1990-91, for example, Chicago reported that 61.4 percent of its 10th graders had passed first-year algebra. But only 1.4 percent had successfully completed an Advanced Placement or International Baccalaureate math class. "What New York City is saying,'' Ms. Strong added, "is that you're going to take a full sequence of courses.''
Both Milwaukee and Providence are eliminating all low-level, non-college-preparatory English classes for this year's 9th graders. Their goal is to eliminate tracking across the curriculum.