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Where's the Math?

At the center of the current debate about math instruction is the question of what basic mathematics students really need. Is there a difference between the math everyone needs and the math needed by those who go into math intensive fields?

These are questions Reed Stevens, associate professor in the UW College of Education, has been considering for some time. “As a student, I heard, ‘Oh, you’ll learn all this stuff and then you’ll apply it some time later,’” says Stevens. “I took it for granted that was true.”

Was it? Stevens, who has an undergraduate degree in mathematics and a Ph.D. in cognition and development, decided to investigate by examining the evidence for such claims.
He spent months inside the offices of professionals, following their daily work and projects. The professions he has studied include architecture, engineering, and science and are among those where we conventionally expect the most clear applications of school math. The architects, he discovered, worked problems out with visuals, not textbook algorithms. Engineers use mathematics, but much of that is embedded in their computational tools, and they too use forms of quantitative reasoning that looked very different from the activities of school math. It turned out that school math was a fairly rare species of activity outside of school.
“If you spend a month with architects, you’ll never once see them write an equation,” says Stevens.

The story was the same when he studied roadway engineers. “All the calculations were done on the computer,” says Stevens.

The professionals who actually do use school mathematical forms in daily practice are professional mathematicians. “They really do represent things mathematically in everyday life,” says Stevens, who taught higher mathematics at both high school and college levels. “They’re like poets who can hear poetry in everything.”

That poetry is apparently lost on the American Everyman and Everywoman. In a recent ethnographic study, Stevens and three UW graduate students spent months inside private households, documenting how families dealt with bills, mortgage refinances, kids’ college saving accounts, credit card debt. If there is one set of experiences where we’d expect to see school math in everyday life, it is in these consequential financial situations, but again, they saw little school-like math in action. “Almost to a person none of these people would take the school math, put it on a piece of paper and translate their situation through it,” says Stevens.

His team also collected all the financial offers that came through household mailboxes in a month: credit card offers, life insurance offers. “This deal, that deal. How do they choose?” says Stevens. “Mathematics education has not armed people to make those decisions. It could, and it should.”
Contrasts are stark between the real world and the traditional mathematics classroom. The school math routine is familiar: Mass-marketed textbooks progress topic by topic. Students are asked to solve problems under each topic: linear equations, quadratic equations, factoring. Teachers illustrate how to do it, then have all their students repeat the algorithm. Finally, there is the test, the mandated grade. Some students pass, some fail. Then it’s onto the next unit.
The outside world doesn’t operate that way, Stevens points out. There are no scores, just practical demands. Everyone does different tasks. There are divisions of labor. And, as unskilled jobs continue to disappear from the U.S. economy, there are increasing demands for problem-solving and critical-thinking skills in employees.

Is it practical to try to bring this outside world inside the classroom? One approach — hotly debated among mathematical reformists and traditionalists — is project-based math. Under this model, students might be tasked with restoring a Northwest salmon stream to health or designing a livable building for scientists in the Antarctic.

Ideally, working in groups, students pore over geometric forms on blueprints or design comparative salinity studies of river water. Guided by teachers, they debate mathematical ideas over weeks or months, then come up with original solutions for practical real-world problems.

Stevens weighed the pros and cons of project-based math after an in-depth look at one middle-school classroom. On the positive side, the projects engaged a wide range of students — not just the high-achievers on college math tracks. The projects also proved to even reluctant students that mathematics could be a useful tool.

But Stevens also witnessed how genuine opportunities for recognizing mathematical moments can get lost if teachers aren’t there to catch and guide them, and how difficult it is for even the most well-intended instructors to tear away from traditional methods, such as worksheets and tests.

“It’s important to ask ‘Is this a real problem — or is it a cover story for [school] math as usual?’” says Stevens. “If students don’t have the sense that it’s real, if they think it’s pretend, then it’s just theater.”

For reform practices such as project-based math to work, he argues, educators will have to accept wholesale, consistent, school-wide change, real change, not “theater.” That’s difficult, despite the fact that old methods have failed so many students on so many levels.

Even high achieving students are falling below international standards. In 2004, students in 11 out of 15 countries in the developed world scored higher than U.S. students in advanced mathematics. No country scored significantly lower.
At the same time, demand for real-world mathematical skills is increasing. Stevens wants to understand just what those demands are. Science and engineering occupations are expected to increase 70 percent by 2012, while others increase by only 15 percent. Will these high-skill jobs be outsourced to other countries? Can our math catch up in time?
“It’s important to ask,” says Stevens, “how much of the mathematics learned in school can be applied in the real world? Not the real world of astrophysics — the real world in which we all live, where every day we face decisions that mathematical tools and ideas might inform.” It may be that the math we require in schools, or at least the way we often present it, is not the math we actually need.

For more information on Stevens’ school and workplace comparisons see:

Stevens, R. (2000). Who counts what as math: Emergent and
assigned mathematical problems in a project-based classroom.
In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching
and Learning. Elsivier.
Stevens, R. (2000). Divisions of labor in school and in the workplace: Comparing computer and paper-supported activities across settings. Journal of the Learning Sciences, 9, 373-401