Math Lessons for the Real World

IN an eighth-grade class at Jefferson Middle School in Madison, Wis., students tackle a problem that seems more likely to land on the desk of a city planner.

Here's the dilemma: A reclaimed landfill is being rezoned. One party wants to build high-rise residences on the land, while another group is interested in single-family homes. Which is the best decision, and how should the plans be carried out?

The class is math. But it's not the typical American math class where teachers drill students on arithmetic problems and students must memorize and master abstract concepts from a textbook. In this class, which is serving as a pilot project for math-curricula reform, eighth-graders are using real-life examples to help them learn algebra, linear programming, and how to graph and plot data. During this hour, for instance, students provide examples of feasible and unfeasible building plans and plot the area

of each house or high-rise in a coordinate system.

"Students see how math applies in the real world," says teacher Jane Beebe. "Those who are not good at math can see how to use it."

Making mathematics relate to real life is one of Thomas Romberg's goals for schools across the country. Dr. Romberg is the director of the National Center for Research in Mathematical Sciences Education (NCRMSE) at the University of Wisconsin/Madison. The center is helping to develop new math curricula and materials for grades 5 through 8. Jefferson Middle School and four other area schools are participating in this project.

Why change the way math is taught in United States schools?

Romberg gives several reasons. First, studies over the past 10 years have shown that the US lags behind other countries in math proficiency - a gap experts cite as one of the reasons for its decline in the global marketplace. In order for the US to remain economically competitive, schools need to change how they teach math, he says. Shifts in technology and in how math is used also require that mathematics be taught differently, he says.

Since the mid-1800s the traditional math curriculum in the US has included eight years of arithmetic, a year of algebra, and a year of geometry. But according to Romberg, American schoolchildren are learning math that is hundreds of years out of date.

"The arithmetic we teach through eighth grade is really the arithmetic of the 15th century ... the algebra is from the 17th century, and the geometry? That's pretty much 3rd century BC," Romberg says. Much of what is taught are concepts and procedures that don't always apply to a world that increasingly requires more knowledge in statistics or graphical data, he adds.

The NCRMSE's efforts to restructure math education are part of a large reform movement that is gaining momentum around the country. The movement grew in response to "A Nation at Risk," the National Commission on Excellence in Education's 1983 publication that urged the mathematics community to rethink the teaching and learning of math.

The NCRMSE's purpose is to provide a research base for this national reform movement. The center started five years ago and is funded by the US Department of Education.

Romberg and colleagues developed the project to test new math curricula in local schools after they looked at how other countries teach math. They decided to model the curricula after the Dutch system, because they liked the math materials and examples teachers in The Netherlands use. International studies also show that the European nation ranks among the highest in student math achievement.

So in 1991, the Wisconsin center enlisted the help of Dutch researchers at the Freudenthal Institute at the University of Utrecht, The Netherlands. The Dutch and Americans are developing about 40 curriculum units for grades 5 through 8. The instructional booklets use real-world situations to teach students math. This five-year "Maths in Context" project is funded by the National Science Foundation.

The Dutch and Wisconsin team plan to revise these materials and field-test them on a national scale beginning in 1993. Encyclopedia Britannica will publish the final booklets in 1995.

Romberg emphasizes that shifts in technology make the need for reforms in math education crucial. The development of more sophisticated calculators and computers means that machines now solve problems people once had to calculate by hand. "You no longer have to be a good manipulator at symbols to solve a lot of problems," he says.

But "we're not saying you don't need to know how to add and subtract and so on," Romberg says. "You do, but you need to get familiar with the territory of problem situations that give rise to why you'd want to do addition and subtraction.... It isn't learning the bits and pieces; it's learning the whole territory."

Anton Roodhardt, one of about 25 Dutch researchers working on the project, says his country's emphasis on getting students to think about how to use math in real-life situations is one reason The Netherlands has excelled in the discipline.

"The American way of doing mathematics is that you present the children with mathematics as the finished product. It's already there, and they have to use it," he says. "In our country the children build their own mathematical world, and that means the teacher is busier teaching children to think mathematically. Students are used to the fact that things can be different, so they are not disturbed by unusual questions."

At Jefferson Middle School teachers and parents have been almost overwhelmingly supportive of the project, says Stephanie Smith, who works with Romberg and has helped prepare teachers to teach the units. She attributes part of the positive feedback to efforts to involve the community in the changes. "Parents are concerned about what is happening in math for kids and if kids will be ready for new jobs, technology," she says.

Mrs. Smith, whose daughter attends eighth grade at Jefferson, initiated the project here because she felt the Madison school should reflect the math standards that the National Council of Teachers of Mathematics set up in 1989. The standards gives US schools a guideline for content priorities and emphasis. The "Maths in Context" project is based on these standards.

The project targets grades 5 through 8, because "middle school has been called the black hole of math curriculum," Smith says. "Traditionally the 5-through-8 group has had only about 10 percent of new material, and we think that's appalling."

Many Jefferson students like the new math.

"We've never had to do graphing before. It's fun," says eighth-grader Ramona Lowery.

"Some kids who have finished a unit are saying `use us again as guinea pigs - we don't want to go back to texts,' " Smith says.