If demographics were a foolproof predictor, students at Ocala Middle School in San Jose, Calif., could expect to perform dismally in math. Although they live just a few freeway miles from the burnished glass and steel of some of Silicon Valley's most famous corporations, these students and their families -- mostly Latino, with sizable Filipino and smaller Black and White minorities -- have not shared in the wealth and the explosion of knowledge the neighboring computer industry has created.
Almost half of Ocala parents were born outside the United States. Most work at exhausting, poorly paid jobs. The students sometimes have to leave class to translate for a parent at a doctor's office or to care for a sick younger sibling at home. English as a Second Language classes serve one-third of the school's 1,000 students, and many of these have only low-level reading skills in their home languages.
The National Center for Education Statistics reports that in 8th grade, when math tracking typically begins in earnest, 52 percent of White students take pre-algebra or algebra, compared to 36 percent of African American students and 32 percent of Latino students. Urban youngsters from low-income families fare even worse: Just 29 percent will begin high school in a position to take algebra; most will never get beyond basic math.
But at Ocala, and at an increasing number of public schools around the nation, math teachers like Midge Siegfried are out to show that this pattern is not an inevitable outcome but a reversible trend. Siegfried and her colleagues in the math equity movement are focusing on how new approaches to teaching mathematics can best serve low-income and racial-ethnic minority students.
It's no secret that failing at math, or never getting beyond so-called "general math," has serious repercussions in terms of higher education and later employment -- especially for African Americans, Latinos and other minority groups. Study after study has demonstrated that algebra is the "gatekeeper": Students who do not make it through algebra have virtually no chance of attending college or getting well-paying jobs with potential for advancement.
>Siegfried, who has struggled with this predicament at Ocala for eight years, last fall enlisted the resources of the Connected Math Project (CMP). Developed at Michigan State and currently in use in approximately 200 middle schools in 10 states, CMP is one of dozens of math equity programs that have been developed since 1990. The goal of these efforts is to break the cycle of minority under-achievement, getting kids once slated for remedial math onto the "fast track."
CMP, like the other equity programs, operates on the assumption that students learn best in collaborative groups, using mathematical and algebraic concepts to solve problems -- often complex ones -- that people actually encounter in the real world. Gone is the familiar emphasis on applying rote formulas, which do students little good when faced with unfamiliar situations requiring real mathematical understanding.
"Students have to be prepared to take on group work, and not just for solving math problems," Ocala principal Ana Lomas explains. "We know from companies like Apple and Pacific Bell that they'll hire people with a basic education if they know how to work together and think through a situation. So we spend a lot of time teaching the standards and roles required in group settings."
The group work in Midge Siegfried's classes has about it an overarching sense of purpose. The students may share a laugh, but they never forget they are there to do math. Most of the conversations between them are driven by questions: How did you get that answer? Did you check your work? How did you calculate the area?
If a group of students are stuck on a problem, they sometimes ask one another, "Is there another way to find a solution?" Being able to think about math means that students are not lost when a particular procedure for solving a problem fails them; they know there are other approaches that can be attempted. By abandoning the "survival of the fittest" philosophy of traditional math classes, these programs help group members pool their resources, drawing upon each other's strengths to reach a common goal. This interdependence has the added benefit of connecting students whose different backgrounds or experiences might otherwise set them apart.
Connected Math, unlike traditional math, strives to build mathematical literacy. Siegfried's students take polls, figuring out what constitutes a fair random sample. They study probability by rolling dice and flipping coins, the results of which they graph. (Some teachers, observing a propensity for gambling among their students, prefer to explore probability in other ways, such as tallying the colors of cars passing by or of M&M's randomly drawn from a bag.) They calculate the cost of buying and developing a vacant lot, discovering that the fluctuating price of an acre is the crucial variable. In the group problem-solving process, students write out their findings and make presentations before the class. They also undertake long-term, real-life projects such as designing a multipurpose quad for the school grounds.
"Students need to learn how to verbalize what they're thinking about a problem," Siegfried says. "They have to be able to express what they understand and what they need help with. This is particularly important for kids like ours, who often have poor English language skills and whose families can't provide the help they need. But Connected Math helps them talk about mathematical ideas. They work in groups from the very first day of class, and so become accustomed to collaboration early on."
Linda, a 7th grade CMP student, concurs. "This way of doing math was really hard for me because I don't read well. It was hard for me at first to make sense of the problems. But I've been able to get through with the help of others in my group. And this math has helped me with my reading."
The teamwork approach has proven especially popular outside the competitive environment of many suburban, middle-class, predominantly White schools. Those schools, in fact, have been slow to change a system that serves their students well in terms of college admissions and job placement.
"Middle-class students have lots of inherent advantages," explains Karen Mayfield-Ingram of Equals, a math equity program based in Berkeley, Calif. "Their parents have the financial resources to get their kids tutoring help, for instance. And the students know that their parents needed math for college, so they will, too."
Because many middle-class parents routinely use math in their professional lives, their children know intuitively that math has relevance. Further, many of these teenagers have been encouraged to develop sophisticated writing and language skills, so that they're not, as Mayfield-Ingram puts it, "destroyed when they suddenly hit complex word problems."
As Ocala principal Lomas observes, the same math lessons that some students tolerate as a means to an end become for others a dead end. "A lot of kids like ours have traditionally been taught nothing but rote mathematics year after year -- you know, subtraction tests with a timer clicking in the background. But then, when a few of them go on to take the SAT, they find almost nothing but word problems, and all that rote memory does them little good. They don't know how to analyze a problem, how to take it apart."
Midge Siegfried's years of teaching have taught her the same thing. "Some of my students could solve worksheet problems and some could not, but none of it did them much good in the long run. They were still unable to handle word problems, which seemed, after all the drilling, to come at them out of nowhere."
The math equity movement, which gave birth to programs such as CMP, is about a lot more than finding better, hands-on ways to teach mathematical concepts. It's also, more fundamentally, about altering the attitudes of teachers who have come to accept low achievement from certain racial and socioeconomic groups.
"Giving students a lot of worksheets to fill out is indicative of low expectations," Siegfried says. "It suggests that you don't think they're capable of deep thinking about mathematics. Connected Math is built on the belief that it's not only middle-class students who can tackle complex mathematical issues."
Julian Weissglass, director of the Equity in Mathematics Education Leadership Institute at the University of California at Santa Barbara, organizes regular workshops that help teachers recognize and address bias that can result in low expectations. He says that it's not easy for teachers to acknowledge the possibility of racism, the subconscious belief that some students, say African Americans and Latinos, are likely to have a difficult time with math. But it happens frequently, Weissglass asserts, holding himself up as an example.
"A number of years ago," he recalls, "I had an absolutely brilliant, incredible mathematics student in my class. And I remember feeling surprised at the fact that he happened to be Latino. It's very easy for a White teacher, even one who considers himself fair-minded, to think that students of color will not or cannot do intellectually challenging work. So they pass them by or assign them more rudimentary work."
Weissglass believes that bias in the classroom consists of a lot of small things that add up over time. "You have to ask yourself what kind of relationships you're building up with your students from one week to the next, what kind of attention they're getting from you. Who do you call on? What kind of follow-up questions are you asking? Who are you encouraging, discouraging? If teachers really examine themselves, really look at their classroom practices, they'll find there are all kinds of things they can do to improve the performance of students of color. But first, teachers need help with their racism, with learning how to relate to kids who may have very different backgrounds from their own."
These lower expectations for minorities, educators say, are manifested in different ways. Sometimes it's a case of benign neglect -- teachers not taking the time to find out why students may have failed a particular test. Other times it's a case of not demanding enough from "disadvantaged" students on account of misplaced sympathy, argues Karen Mayfield-Ingram of Equals.
"A lot of times teachers want to reach out and help students, but they end up lowering their standards," she says. "They'll say 'This child is one of six kids in the family with a single mother' and end up giving the student a grade that's really for effort rather than for achievement. The challenge is to make achievement possible for students in all kinds of circumstances."
One of the earliest and best-known math equity projects is the Algebra Project, founded in the late 1980s by Robert Moses, a civil rights activist who risked his life in the 1960s to register Black voters in the segregated South. Moses, who is African American, initiated what became the Algebra Project in response to his own daughter's math difficulties in a Cambridge, Mass., middle school.
The problem, Moses thought, was the remote way in which math was taught. He realized that his daughter needed to see math not as a starry abstraction, a series of exercises that had no obvious purpose, but as a representation of the actual world, a language with its own eloquence and power. He believed that students could better understand algebra in terms of symbols that might, for instance, represent stops on a family trip or intervals between musical notes. In Boston, one of the project's sites, familiar subway stops uptown or downtown from the central station provide a concrete way of conceptualizing positive and negative numbers.
Over time Moses turned a personal concern about his daughter's floundering in math into a national effort to help African-American students -- who had traditionally shown low enrollment in algebra, even in high school -- master the subject by the end of the 8th grade. In his own writings, he discusses how the principles behind the Algebra Project were derived from his experiences in the Civil Rights Movement.
Most obvious was the way in which the Algebra Project challenged the status quo -- in this case the subtle but all-too-pervasive belief that Black students could not succeed in higher math. And, like the Civil Rights Movement, the Algebra Project was to be a grass-roots effort; it would draw its curriculum not from some textbook company but from students' everyday lives and surroundings.
"We've got to do something right away to get students into the mainstream of high school math," Moses has said. "It involves a change in the classroom to a more activist, engaged mode of teaching and learning."
Margaret Cozzens, director of elementary and secondary education at the National Science Foundation, which funds 15 math equity programs nationwide, agrees that math bias occurs in subtle but powerful ways.
"Amazingly enough," she says, "hardly anyone worried before 1990 about how to make text materials more relevant to non-White communities. Pick up old textbooks and you'll see lots of White, mostly male, faces. So we only fund materials that are free of gender and racial bias. Instead of boy's names -- boys' and girls' names. Instead of just Anglo-American names -- names like Julio and Tashika."
Julian Weissglass of the Equity in Mathematics Education Leadership Institute is also pressing for the development of mathematics materials that acknowledge the contributions of under-represented cultures. "We don't pay nearly enough attention," he says, "to things like the symmetry designs of Native American pottery or the fact that the Mayans developed the concept of zero long before we did. It's time we address this bias."
A 1995 study published by the National Science Foundation reports positive results from math equity programs: Students in schools with predominantly low-income or racial-ethnic minority populations have scored particularly well on measures such as the SAT, the Iowa Algebra Aptitude Test and a variety of state assessments. African-American high school students in Philadelphia enrolled in the Integrated Mathematics Program (IMP), for instance, are evidencing 20 to 30 percent higher passing rates in major subjects compared to their non-IMP peers. And they're passing math courses at a much higher rate.
But perhaps the best measure of any program's success comes from the students themselves. At Ocala, virtually all the 6th and 7th graders enrolled in CMP -- approximately half of the total number of students -- plan to re-enroll. And many claim that the program has given them a new enthusiasm for mathematics.
"Regular math is boring," says Jasmine, an 8th grader. "It's all 'x2 + 2x + 1,' and so on. The math we're doing now means something in the real world." Martha, a classmate, adds, "We used to just sit in rows and work out of the book. I never saw the point. But the math we're doing here has meaning for me, and I'm planning to stick with it in high school."
Midge Siegfried, for her part, is planning to stick with teaching CMP at Ocala. "I left Ocala for a year to teach math at a suburban high school much closer to my home," Siegfried says. "I had a short commute, five classes a day instead of six, and all the resources you'd ever want. But the instruction was geared to the high achiever; the other kids, usually from the low-income families, were pretty much ignored and tracked into lower-level remedial math. So I came back to Ocala. The kids here -- even those who have no particular affinity for the subject -- have a real chance to succeed in mathematics."