Majoring in Math Not Always a Classroom Plus

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Ask a parent, politician, or school board member to describe the ideal qualifications of a math teacher, and most would probably rank having a college major in that subject high on the list.

Yet when it comes to improving student learning in elementary and middle school, research shows that the value of that academic credential is limited—at best.

On the one hand, recent nationwide test scores show middle school students taught by a teacher with an undergraduate mathematics major scoring better, on average, in that subject than those whose teachers did not have that degree. Yet many observers view those results with caution, saying the weight of evidence does not show a connection between teachers’ having majored in math and higher student math achievement, particularly before high school.

That disconnect might seem counterintuitive, given the broad concern among policymakers about improving math teachers’ credentials, and about how states and school districts can improve educators’ professional training and skills.

But researchers who have studied school and college math instruction say that while math content is obviously essential for teachers, educators also need a more refined set of classroom-ready tools than a college math major, on its own, is likely to offer.

Math teachers need to “know the subject matter well and how to teach it,” said Deborah Loewenberg Ball, a scholar who has studied math teaching extensively. “The problem is that the math major is not a good proxy for that.”

A report released last year by the National Mathematics Advisory Panel—on which Ms. Ball, the dean of the University of Michigan’s school of education, served—found no evidence of a link between teachers’ degree attainment in college and student academic gains in elementary and middle grades. A slightly stronger connection was found between math majors and students’ high school performance, according to the report, which set a high bar for the sorts of scholarly studies that met its standards for evidence.

Qualifications Unknown

The evidence was also weak, the panel found, of a connection between other, presumed measures of teacher knowledge and expertise, such as preservice and professional development training, and certification in math, which teachers can earn without majoring in math. (“Essential Qualities of Math Teaching Remain Unknown,” April 2, 2008.)

Recent results from the National Assessment of Educational Progress present a mixed picture when it comes to the utility of a math major for instruction in pre-high school classrooms.

On average, 8th graders taught by a teacher with an undergraduate major in math scored a 287 on NAEP’s 500-point scale, 9 points higher than their peers taught by nonmajors.

But in individual states, the value of a math major varied widely. In New Jersey, for instance, students taught by majors outperformed peers led by nonmajors by 16 points on NAEP. In other states, however, such as Connecticut and Kansas, students taught by majors and nonmajors scored at roughly the same level.

Some warn of limitations with the data gleaned from the NAEP, noting that it’s unclear what other factors may have influenced the impact of math majors’ teaching. The data also doesn’t show whether students were exposed to teachers with strong professional backgrounds in prior elementary and middle grades, said Julie Greenberg, a senior policy director at the National Council on Teacher Quality, a Washington-based group that advocates policies to improve teacher effectiveness.

Ms. Greenberg’s organization supports high school math teachers obtaining math majors and middle school math educators getting a math major or minor, along with an additional minor that benefits their teaching. Having teachers with that commitment and specialized skill in classrooms benefits students, she said.

“We see larger issues [at work], namely the need to attract the best people into teaching and exit those who aren’t effective,” she explained in an e-mail. “Preparing prospective secondary teachers with both a major (or close to it) and mathematics methods coursework that has proven its value seems to be a prudent course of action.”

Math-certification requirements vary greatly by state and grade level. At the elementary level, where most teachers cover all subjects, educators typically need to take only two or three math courses for certification, said Francis M. Fennell, a former president of the National Council of Teachers of Mathematics. Some middle school teachers become certified after having taken that same math course work and passing a middle school licensing exam; others might take six to eight math content courses, he said. In high schools, it’s more common for teachers to be math majors, meaning they have taken 12 to 15 math courses, he added.

“The landscape is very irregular,” Mr. Fennell said.

A 2007 report by the Council of Chief State School Officers found that 61 percent of grades 7-12 math teachers had majors in their subject. But the percentages varied significantly by state and were not broken down by grade.

Classroom Difference

When the NAEP results for the 2009 math test were released, David P. Driscoll, the chairman of the National Assessment Governing Board, which sets policy for the testing program, pointed to the higher national performance of 8th graders taught by math majors as evidence of the importance of content knowledge. But in a recent interview, Mr. Driscoll said content depth only takes a math teacher so far.“

Just superimposing a math major isn’t going to guarantee anything,” he said. “Teachers need to know their stuff, and they need to know how to apply it.”

The NAEP results also show that teachers who reported having majored in “mathematics education” produced higher scores than teachers who did not. Those results did not surprise Cathy L. Seeley, a senior research associate at the University of Texas at Austin, who said that math education majors are typically required to take several advanced-math classes—as well as coursework on how to explain math in different ways.

Even so, the challenges of K-12 math teaching are often lost on college majors, at least at first, noted Mr. Fennell, a professor of education at McDaniel College, in Westminster, Md.

Majors who switch to a teaching track, Mr. Fennell said, sometimes ask him to allow credits from advanced courses like Calculus 3 to substitute for teaching requirements. He says he explains why he’s turning them down by challenging them to create a basic word problem or number-line representation of a simple fraction or math concept. The majors are usually stumped.“

The kind of algebra that math majors see, the kind of geometry math majors see, is different from what I would refer to as classroom mathematics,” Mr. Fennell said.

Dave Berry, a college math major who teaches that subject at Challenger Middle School in Arizona, says he’s found ways to apply what he learned on campus in the classroom.

The 25-year-old, whose major includes a specialization in education, says he picked up ideas about how to present math by watching the very different approaches used by his math professors at the University of Arizona, in Tucson—even though they were covering college-level material.

At the same time, “none of it really means that much until you get out there and start doing it and you can say, ‘This is going to be effective for me,’ ” Mr. Berry said. “It’s a continual process of self-reflection and examining results.”

Relevant Know-How

The national math panel, in its 2008 report, found a slightly stronger link between teachers math majors and student achievement in high school. That is probably attributable, the University of Michigan’s Ms. Ball said, to a closer link between college content and high school lessons, as opposed to instruction in elementary or middle grades.

In the earlier grades, effective math teachers need a more specific skill set than a college major can typically provide, Ms. Ball argues.

In a 2005 study, she and two colleagues at Michigan, Heather C. Hill and Hyman Bass, developed a series of questions designed to test elementary teachers’ “mathematical knowledge for teaching.” Teachers with that specialized knowledge are more likely to be mathematically adept in a number of key areas, the authors hypothesized. They can “represent” the meaning of problems to students in different ways, figure out where students have gone astray, decide when and how to use math language in class, and make other in-class adjustments—all while covering crucial content, such as numbers and operations, patterns, functions, and geometry.

When they tested the weight of these skills in a study of 700 elementary teachers and nearly 3,000 students, the Michigan researchers found that teachers’ “mathematical knowledge for teaching” was significantly linked to greater student achievement, even when the authors controlled for factors such as child poverty and teachers’ credentials.

States could do more to require greater and more relevant math knowledge, said Mr. Driscoll, the NAGB chairman, by revamping their licensure tests.

Massachusetts, where he used to be state education commissioner, has required elementary teachers to pass a math-specific content section on its exam, as opposed to simply obtaining general passing scores, he noted. Yet many states would be reluctant to fail more aspiring math teachers, Mr. Driscoll acknowledged, given that they are in such short supply.

NCTM President Henry S. Kepner, however, believes a more effective approach would be giving teachers targeted professional development after a year or two in the classroom—when they are acutely aware of what help they need in delivering math content.

“That’s where our bigger growth can occur,” he said.