# Up the Opportunity Ladder With Algebra. For inner-city pupils, Project Algebra bridges the gap between arithmetic and career-expanding, college-track courses

EDUCATION: INNOVATIVE MATH PROGRAM

BOSTON — LIKE a lot of young black sixth-graders, Chad wears a carefully razored Afro and sports a set of foot-smothering, high-top sneakers that make him appear to walk on air. But unlike most others in his peer group, Chad is already learning the concepts of algebra. What's more, he loves it. ``It isn't simple like 2 times 3 equals 6,'' he says. ``It's a different approach to math - it's really cool.''

Chad is part of Robert Moses' vision that the cutting edge of civil rights in America is not in the glitzy area of electoral politics, but in a much humbler place - public school classrooms.

Specifically, that means getting to the hearts and minds of disadvantaged blacks kids early enough, and with the right kind of teaching, to give them confidence in handling algebra - the key to higher, college-track math.

Without algebra, the door is locked to geometry, trigonometry, and calculus - the basis for science and engineering. The overwhelming number of blacks never get to or through algebra, Mr. Moses says. In 1986, for example, only one half of 1 percent of American PhDs in science and engineering were black.

That's why Moses, a Harvard philosophy major, a saint of the civil rights movement, and a MacArthur fellow, has been quietly working for eight years with a group of devoted teachers on something called the ``Algebra Project'' here at the Martin Luther King (K-8) School.

Starting in sixth grade, students are introduced to three foundational concepts in algebra: how much, how many, and which way?

Constantly using references from real life - such as incoming and outgoing trips on the local subway (trips classes actually take) - they learn concepts such as displacement, frequency, and equivalence.

Teaching algebra through what is familiar makes students less afraid of it, teachers say. ``Math terms can be pretty scary'' for students,'' says teacher-aide Sae Ghose. ``Like they might be scared about the idea of `relative frequency.' But we make them see they have a power over the definitions, and the numbers.''

Today, about 15 out of 25 King school students a year pass the test that takes them out of high school algebra - and into geometry. Before the Algebra Project, none passed.

Even students who don't pass go into honors algebra. ``That surrounds them with other kids interested in learning,'' says math teacher Mary Lou Mehrling, who first invited Moses into her classroom six years ago. ``It'll be a good peer group, and that's really important.''

Recent national headlines about poor math teaching in American classrooms were not news to Moses. He has already developed a new approach, based on classroom experience.

The nub of the idea is simple: There's a huge gap between the simple arithmetic of elementary school, which stresses counting, and algebra, which stresses symbolic and conceptual relationships among numbers. But there's no real curriculum or teaching to help students bridge that gap - make the switch in language and meaning to algebra.

Sixth-graders, for example, think of subtraction or a minus sign as meaning ``take away,'' Moses says. Yet in algebra, subtraction and the minus sign take on very different meanings. Textbooks have little to say about this change, he contends.

So instead of digging in and learning the underlying conceptual framework of algebra, students simply learn to memorize rules and manipulate numbers.

``Rather than learn the important questions of `What is a number?' and `How does it behave?' they just become good at manipulating symbols. Why numbers behave this way ceases to become a question.''

It's bad math teaching, Moses says. Students from supportive, educated families may get through algebra. But not most inner-city black kids. ``They just give up,'' Moses says. ``They don't understand it and they don't see the reason for it.''

Moses blames the problem on the math research community, which he says has promoted increasingly abstract math in schools.

In the Algebra Project, students start with the concrete and break it down into the basics - how much, how many, which way?

The breakdown process follows a hierarchy along these lines:

1.Describe a physical event or scene that can be translated into an algebra problem (the subway line, for example).

2.Draw a picture of the event.

3.Describe the problem in ordinary English.

4.Refine the ordinary English into more precise language.

5.Translate the precise language into math symbols or equations.

Students think through every aspect of a problem: If you take 64 subway trips and 15 of them start at the Alewife Station, what is the percentage frequency of Alewife starts? 15/64, or 23 percent.

Moses remembers in 1958 going from graduate work at Harvard into the public schools of New York City. ``There was a sense of excitement. You were teaching what was in line with current math research. It was abstract. We did set theory. Students wrote proofs for algebraic equations, because that's what you did in geometry. The problem was, it wasn't working. And it didn't work. And it's nowhere to be found now. It's not in textbooks. It didn't take.''

Then, in something of a momentous move, Moses went south from New York to work for civil rights. As head of the Student Non-Violent Coordinating Committee, he defined the soft-spoken antihero of the era - more interested in grass-roots voter education than the media glare.

Taylor Branch, speaking of his recent Pulitzer Prize-winning civil rights history, ``Parting the Waters,'' says Moses is ``the second deepest character'' in the 900-page book, after Martin Luther King.

In 1975, after a 10-year odyssey in Tanzania (see sidebar), Moses started tutoring his first-grade daughter, Maisha, in math to make sure she kept up. By the eighth grade, Maisha (now a Harvard undergrad) was one of only two blacks at the Martin Luther King School headed for higher math. Her teacher, Ms. Mehrling, asked Moses to help. He organized the community: He convinced recalcitrant black parents of the importance of early math training, met with teachers, and picked up students at 7:30 in the morning for early math classes.

Currently, he's finishing a sixth grade ``transition curriculum.''

Teachers at the Algebra Project say the open classroom environment is important. Students work at their own pace - in groups and individually. Three teachers are present who often reteach fractions and decimals. ``There's lots of repetition, low pressure, and lots of teacher support,'' says Mehrling.

An important part of the class has nothing to do with math at all. It's an atmosphere of seriousness established by teachers - often for an entire period before algebra - through an ``efficacy curriculum.'' It's a time in which teacher and class frankly discuss things like acting up to hide a lack of skills, the problems of peer-group values, and what it means to be worthy.

``When you start taking yourself seriously, you start taking what you do seriously,'' says teacher Lynn Ward.

Students participate more after such discussions. In Ms. Ward's class, 10 of 14 hands were raised on most math questions.

It's the spirit of ``access'' that's most important in the Algebra Project, teachers feel. ``We don't teach only to select children who are `ready,''' says Yolanda Rodriguez, an algebra teacher for 14 years. ``We include all children - regardless of their success.''