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Deborah Ball: Above the math wars
Quick. Solve this problem:
It's not hard. Anyone with a fourth grade education should find the answer: 875.
But let's say you're the teacher who's supposed to give a kid that fourth-grade education. And let's say that a few of your students answer this way:
Clearly, the answer is wrong. But just saying it's wrong is not much help. If you're going to help your students get it right next time, you should be able to explain where they're going wrong. So, quick: how did your students come up with this answer?
Now figure it out in half a minute, while surrounded by 25 nine-year-olds, and you get an idea of what's required to teach math.
That was the experience of Deborah Ball. While she's now a high-profile figure in education—dean of U-M's School of Education, a member of President Bush's National Mathematics Advisory Panel, and one of the nation's top experts on math education—she started out as a grade-school teacher. For 17 years she taught first- to fifth-graders in East Lansing.
In the beginning, she wasn't very good at teaching math. "I didn't always know enough math to help little kids learn it," she says. "Elementary school teachers are generalists, not specialists." As an education major in college, she'd focused on French and language arts. Her training required her to know math, but it hadn't properly prepared her to teach it. She discovered that "the distinction between just doing math and teaching it is substantial."
It's one thing for, say, an engineer or scientist to know and use math. But teachers have to understand math in a very different way. In fact, when Ball presents professional mathematicians with problems like the one above, many of them can't figure out where students have gone wrong and can't explain how they could get better.
Ball had always been smart and driven. She'd graduated with highest honors from Michigan State. Now, frustrated with her limitations as a math teacher, she turned her passion toward improving. In her spare time, she enrolled in undergraduate math courses, giving herself a solid foundation in the subject. But she didn't stop there: she earned a master's in education, with a focus on mathematics, then went on for a Ph.D.
The whole time, she kept striving to solve the problems she'd encountered as a first-year teacher: what do you need to know in order to teach math? How do you learn it? She has now spent more than 20 years answering those questions.
Ball and her graduate students have spent hundreds of hours observing real students and teachers in real classrooms. She knows the questions students really ask. She knows what those students were probably thinking when they multiplied 25 x 35 and came up with 1055.
(They first multiplied 5 x 5 for 25. They "carried" the 2 over the 3 in 35—but then added it to the 3 before multiplying by 5, rather than after. So instead of getting 5 x 3 + 2 = 17, they got 5 x 5 = 25. Same thing on the next line: 2 x 5 = 10. The students carried the 1, but instead of multiplying 2 x 3, then adding the 1, they added the 1 first, getting 2 x 4 = 8.)
Ball knows students will also find peculiar ways to the correct answer. And she knows that sometimes teachers pick rotten examples to illustrate a point, while other times they give perfect examples that even lay the foundation for later, more advanced work.
This is an academic subject, but Ball's research isn't just "academic." It matters—a lot—in the real world.
Ever since Sputnik, in 1957, the United States has worried about the quality of its math and science education. Decades of effort to improve teaching, raise educational standards, and increase funding have achieved mixed results, at best, and US students still lag on international exams. In an age dominated by science, computer technology and outsourcing, where American workers literally compete against the world for jobs, that's bad news.
Making matters worse are the so-called "math wars," disputes over the best ways to teach mathematics. In a recent front-page story, The New York Times described fights between traditionalists, who call for drilling and memorization of facts, and advocates of "reform math," who try to help kids figure out solutions on their own.
Ball thinks the math wars are "fanned by extremists" on both sides, and "encouraged by the press. It gets in the way of progress."
Ball never settles for easy or partisan answers. Her research rises above the fray. According to Lee Shulman, president of the Carnegie Foundation for the Advancement of Teaching, "Deborah has managed to navigate the middle ground in a field typically decimated by internecine battles between extremists." As a member of President Bush's math panel, Ball says, she's constantly asked, "where do we stand on the math wars. But we aren't taking sides. We're trying to understand what really goes on."
Ball has identified key elements of what she calls "mathematical knowledge for teaching"—the sort of knowledge that makes a teacher great. Teachers who have these skills teach better. Their students learn better. The impact of a teacher with this knowledge is equal to an extra two to three weeks of math class for every 36-week school year.
If that doesn't sound like much, listen to this. Ball notes that the "most significant predictors of school achievement are race and class." A student's personal background, in other words, even trumps attendance as a factor in school success. But teachers with strong math-teaching knowledge can actually neutralize the effects of race and class.
In short, using the skills Deborah Ball has studied, a teacher can have as much influence on a student as enormous personal and social factors have.
Better yet, teachers and education students can learn these skills.
Indeed, as dean, Ball is restructuring the U-M School of Education curriculum around just this sort of teaching. Teaching that works. Teaching that meets the needs of both reformers and traditionalists. Teaching that makes a difference in the lives of children and the life of the nation.
For more information, visit Deborah Ball's website.
John Lofy is editor of Michigan Today