BACK TO WEB VERSION

FALL 2005
Building a Better Math Teacher
by Frank Stephenson

UGA leads a joint effort to produce more and better-qualified teachers armed with a deeper understanding of mathematics.

A 2004 international study of math performance among school children in 11 industrialized countries showed that U.S. students not only are still lagging behind their foreign counterparts, but also may be losing ground.

The study, the third of its kind done since 1995, showed that out of three grade levels — the 4th, 8th and 12th grades — American students ranked no higher than 8th place among their peers in countries that included Australia, Hungary, Japan, Norway and the Russian Federation.

The new findings raise again the plight of U.S. math educators and school districts that have borne increasing criticism in recent years for the dismal math scores posted by their students. In their defense, school officials typically cite a lack of money and other resources necessary to attract and hold onto good math teachers.

But increasingly, fingers are pointing to a long-running and highly divisive feud over the best way to teach math. These so-called “math wars” — essentially a battle between those who value teaching the process of math over content — is a decades-long dispute that critics say is wrecking math education and producing bad teachers.

Noted math educator William H. Schmidt of Michigan State University is typical of critics who blame the nation’s critical shortage in qualified math teachers on a philosophical-turned-political debate that no other country in the world seems the least bit troubled by. Schmidt argues that the debate has created a watered-down curriculum in math education classes throughout colleges of education, leading to graduates who often have weak computational skills and only a shallow understanding of mathematics concepts.

“We must address this issue of teacher quality, and one important way is to begin by including mathematical knowledge as a key component in the definition of teacher quality,” Schmidt wrote. To produce more high-quality teachers, math educators must stop pushing “reform that is not based on scientific evidence but rather on opinion and someone’s ideology,” he said.

Policymakers say that U.S. students’ poor grasp of mathematics has serious implications for the nation’s capacity in science and technology and thus for its global competitiveness.

In a report to a Senate Education Committee in April 2005, Brian K. Fitzgerald, executive director of the Business-Higher Education Forum (a Washington, D.C., lobbyist group that represents U.S. corporations and universities), described a number of “disturbing trends” that his group’s research had identified. While demands for American workers with mathematics and science skills are at an all-time high, the performance levels of American students on comparative international math and science tests may charitably be described as “disappointing,” Fitzgerald said, as are the numbers of science and engineering degrees awarded to Americans. Fundamental to these problems, he noted, is that the nation faces “a critical shortage of qualified mathematics and science teachers.”

This aspect of the forum’s report came as no surprise to experienced K-12 educators, who’ve bemoaned the teacher-shortage crisis for decades. A 1981 study showed that 43 of 45 states surveyed had fewer math teachers than they needed. Two years later, A Nation at Risk, a hard-hitting report commissioned by the U.S. Department of Education, cited critical shortages in qualified math and science teachers nationwide. The report criticized widespread teacher-training curricula that the authors described as being “weighted heavily with courses in ‘educational methods’ at the expense of courses in subjects to be taught.”

Since that dismal assessment 25 years ago, the situation hasn’t improved much, if at all. A 2004 survey done by the Brookings Institution’s Brown Center on Education Policy showed that only 22 percent of the nation’s 16,000 middle-school math teachers majored in mathematics in college. Only 41 percent possessed specific teaching credentials or certificates in math.

The findings reinforce critical assessments of how and what the nation’s math teachers are being taught. The result is that too many teachers are walking into math classrooms ill equipped to teach the subject, simply because there aren’t enough qualified teachers to meet the demand.

“School districts have to use people who aren’t certified in math, who have not had math training and aren’t prepared to be math teachers,” said Jeremy Kilpatrick, a Regents Professor at the University of Georgia who is among the country’s foremost researchers on K-12 mathematics education. “But what’s a principal to do? You’ve got a class full of kids who need to be taught algebra and you don’t have any more algebra teachers, so you hire somebody — anybody — to teach those kids algebra, and that person may not know a thing about algebra. It’s a scandal.”

Kilpatrick is now part of a national effort, based at UGA and the University of Michigan, aimed specifically at improving the mathematics knowledge and skills of math teachers. His colleague, Pat Wilson, also a professor in UGA’s Department of Mathematics and Science Education, is team leader and principal investigator of a five-year, $10.3 million, National Science Foundation initiative with this as its principal goal. Wilson, Kilpatrick, and professor of mathematics and science education James Wilson (no relation) are the UGA contingent of leadership for the project run jointly by the two universities.

The NSF and other federal agencies are tackling this enormously complex dilemma — poor math performance among the nation’s school kids — from many varied perspectives. However, the UGA-Michigan project is focused exclusively on “finding out how to create the most proficient teachers possible,” Pat Wilson said. Because of the project’s unique focus, the NSF has made UGA’s Center for Proficiency in Teaching Mathematics (CPTM) part of their Centers for Learning and Teaching program, which established CPTM as a national endeavor.

For years, critics of the preparation of math teachers have been quick to single out the nation’s colleges of education as the chief culprit. The 1983 At Risk report fired its own salvo at these schools, citing a survey of 1,350 teacher-training institutions where elementary-school teacher candidates spent more than 40 percent of their time taking required courses in things other than mathematics.

Wilson said that her center, by contrast, isn’t singling out education colleges. “Our focus is much broader than that. The people who teach mathematics to students who are preparing to be mathematics teachers are a varied group. We have to pay attention to all of the people who teach the teachers.”

Typically, graduates of programs in colleges of education who intend to teach in a particular subject area — mathematics and science in particular — get instruction not only from within their education departments but also from mathematicians and scientists in colleges of arts and sciences. Oftentimes, these teachers of would-be math teachers don’t have a good grasp of the kinds of mathematics their students really need to be effective instructors in K-12 classrooms, Wilson said.

Another important group, often overlooked, is the practicing teachers themselves. “We have studies that say that some teachers are learning the mathematics they need for teaching on the job. That may not be all bad,” she said, “especially if by so doing you’re developing broader and more mature insights into the subject. But school district leaders need to do all they can to provide these teachers with an opportunity for continuing education and professional development.”

In June 2004, the center held its second week-long institute (the first one took place during the preceding summer) that brought together teachers from colleges of education, academic mathematicians, practicing math teachers, principals and school district leaders from across the country for an intensive study of mathematics used in teaching grades K-8. The central idea behind the institutes is to assess the deficiencies in critical mathematics knowledge among teachers and to develop the best strategies for filling those gaps.

Meanwhile, the center is operating year-round on both campuses to help revise their respective Ph.D. programs in math education. It has catalyzed apprenticeships for doctoral students who regularly visit practicing teachers in their classrooms and soak up the real-world challenges of teaching math to young people coming from a variety of socioeconomic backgrounds. The center also has established groups of math teachers within schools who come together specifically to gain a broader, more in-depth appreciation of mathematics.

“Knowing mathematics is absolutely essential to becoming a good [math] teacher, but it’s not sufficient. There’s much more that’s needed,” Pat Wilson said. “What we’re especially interested in is defining what we mean by a deeper understanding of mathematics — which is what we see missing in the classrooms. Research mathematicians and engineers, for example, need a different kind of knowledge of mathematics than most teachers do. They don’t need as broad a knowledge as someone who is going to teach.”

In reaching toward a “deeper understanding” of math, Wilson said she believes that teachers need to look past what mathematics has come to be seen as — a highly compartmentalized discipline whereby labels such as “algebra,” “geometry,” “trigonometry” and “calculus” imply little or no connection with each other. In truth they are all branches of the same tree, nourished by the same underlying concepts.

The center-sponsored visits from doctoral students and regular meetings of math-teacher support groups help address the fact that acquisition of a deeper understanding often falls between the cracks. Too often math teachers don’t acquire it in college, Wilson said, and once on the job, it is even harder to achieve given the day-to-day demands on teachers’ time and the rare opportunities for continued education or professional development.

Essential to that deeper understanding is to move away from rote memorization — the bread-and-butter of standard math instruction since colonial days (and the bane of math-education reformers for decades). “What’s so dangerous is trying to memorize mathematics, because if you forget, you’re lost,” she said. “We want people to have a variety of ways to figure something out and have it make sense.”

New approaches for producing more qualified teachers can’t come soon enough for the nation’s 15,000 public school districts. The federal No Child Left Behind Act of 2002 requires all states to have certifiably qualified teachers in their classrooms by the end of the 2005-2006 school year. Teachers will be required to hold either an undergraduate degree in their subject areas or pass a rigorous national test. Given the woeful level of K-12 math training documented by repeated national surveys, however, meeting this requirement remains a supreme challenge.

Beyond the continuing noise from the “math wars” over how best to teach math not just to students but to would-be math teachers as well, Kilpatrick, an outspoken advocate of teacher preparedness, sees the whole dilemma as boiling down to a question of dollars and “sense.”

“Yes, we don’t have enough qualified teachers,” he said, “but you can get them if you have enough money. The widespread inequity in funding underlies the education problems we face as a country.

“Researchers have shown again and again that kids in the poor schools don’t do as well as those in the richer schools, which often are practically next-door. They don’t have the qualified teachers or the other resources they need. So it’s just another case of the rich getting richer and the poor getting poorer.”

For more information access http://www.cptm.us or e-mail Pat Wilson at pswilson@uga.edu, Jeremy Kilpatrick at jkilpat@uga.edu or Jim Wilson at jwilson@uga.edu.

Frank Stephenson, a Florida-based freelance writer, has won national awards for his writing.