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Even as 鈥渞esidency鈥� programs and other hands-on teacher education models flourish, the vexing question of what prospective teachers in the United States should learn in their coursework has gained far less attention in the discourse of international comparisons.

But new evidence suggests that striking the right balance of formal content training with pedagogical methods, particularly in the area of mathematics, is a crucial piece of the training puzzle.

Released in 2010, the , or TEDS-M, examined teacher preparation in 16 countries. It compared how elementary and middle school teachers were trained, including the distribution of time spent on general pedagogy classes; on math pedagogy classes; and on formal math-content training.

More than 80 U.S. universities and 3,000 teachers participated in the study, which was spearheaded by the Institute for Research in Math and Science Education, at Michigan State University. All the teachers took tests of mathematical-content knowledge and pedagogical-content knowledge depending on their certification level.

At the elementary level, the American teachers鈥� performance was neither particularly weak nor strong, and they took roughly the same amount of math coursework as their international counterparts.

But at the middle school level, several countries鈥� teachers significantly outperformed the United States鈥�, with Taiwan鈥檚 more than 1陆 standard deviations higher in math content.

Further, the amount of math coursework in the United States at the lower-secondary level differed markedly from that of the top-performing nations: U.S. middle school teachers took, on average, two fewer advanced-mathematics courses than their international peers.

William H. Schmidt, an education professor at Michigan State University and the interim director of the center, believes the findings help to explain why U.S. students do less well on international math examinations at the lower-secondary level.

鈥淢iddle school teachers are coming out to teach math nowhere near the level of mathematics as those in countries where students perform highly,鈥� he says.

For instance, individuals preparing to be teachers in other countries generally complete linear algebra and a yearlong sequence in calculus; by contrast, U.S. teachers take more general pedagogy at the secondary level.

Boosting Findings

The TEDS-M findings appear to bolster observations about teacher effectiveness in the United States, while raising new questions about teacher-training practices.

Studies have failed to find many characteristics of teachers that seem to predict excellent teaching. But one of the few that does consistently appear to give teachers an edge is knowledge of 鈥攚hether measured by , , or the provision of a degree in the subject.

The implications for teacher education are not easy to tease out. Among other things, the TEDS study found a wide range of performance among aspiring middle school teachers produced by U.S. education schools, with graduates from some institutions performing at the high level of educators trained in Taiwan, and others as poorly as those trained in Botswana, which ranks toward the bottom. (Universities participated with the understanding they would not be identified by name.)

Schmidt and his team at Michigan State continue to probe just what aspects of higher-level math courses seem to help teachers in their ability to convey math concepts to their students.

鈥淒o they need calculus in some narrow sense? That鈥檚 the question, and we鈥檝e had some interesting debates with mathematicians about this,鈥� he says. 鈥淐ould you have more rigorous math that would accomplish the same thing calculus is doing? We don鈥檛 know the answer to that, but it warrants some serious discussions.鈥�

As for elementary teachers, Schmidt believes that many of the countries that exceed the U.S. performance do so because they pull from more academically qualified undergraduates, including those who have had comparatively stronger high school math-content training.

Finland鈥檚 approach to elementary teacher education underscores the point. Its elementary programs are primarily based on general pedagogy and hands-on practice, because the candidates who enter are well trained in math and have all passed the college-matriculation exam, says Jari Lavonen, the director of teacher education at the University of Helsinki.

In addition, those teachers training for secondary positions must take courses in both advanced-content and pedagogical-content knowledge, he noted.

U.S. Examples

Teacher education groups say that more U.S. schools of education are working with arts and sciences faculty to provide content-based courses, as well as to better integrate content and pedagogy training and tap new talent.

鈥淲hen you bring the content experts and pedagogical experts together to leverage their knowledge to improve student experience, you start to illustrate and demonstrate effective teaching, which does inspire people to think about becoming a teacher,鈥� says Sharon P. Robinson, the president of the Washington-based American Association of Colleges for Teacher Education.

Another problem is that middle school teachers in the United States often come with not much more preparation in math than those who want to become elementary teachers. According to the National Council on Teacher Quality, a research and advocacy group also in Washington, , and 14 had no requirements that middle school teachers major or minor in a content area. And in some states, elementary teachers can earn a middle school endorsement on their license without having to learn higher-level mathematics or math pedagogy.

The TEDS-M study also found that those U.S. middle school teachers prepared in secondary programs far outperformed those trained in elementary or middle-school-specific training programs.

鈥淲hen someone needs a middle school math teacher, they typically recruit them from the elementary levels. And too many of them, through no fault of their own, are not as comfortable as they need to be in math to be effective teachers,鈥� says Richard Bisk, the chairman of the math department at Worcester State University, in Massachusetts. 鈥淲e at university have not prepared them.鈥�

Bisk provided assistance to the Massachusetts board of education, which set out in 2007 to ensure that its elementary math teachers had a strong grasp of math content. That year, the board approved for the preparation of K-6 teachers in math requiring them to take nine to 12 semester hours of coursework in mathematics content. And in 2009, it became the first state to institute an independently scored mathematics and math-pedagogy exam for elementary teachers.

The exam is separate from the other content-knowledge test for elementary teachers and has its own cutoff score. It was so challenging that only 27 percent of teachers passed it during its first administration. (About half the test-takers now pass it.)

The 2007 guidelines have gradually filtered down to teacher-training programs, Bisk says. His own university, for instance, now requires elementary candidates to take a sequence of three math courses.

But Schmidt, of Michigan State, believes teachers鈥� colleges鈥攁nd the state bodies that regulate them鈥攕till have a long way to go before all teachers are prepared to teach math at the demanding level called for in the Common Core State Standards Initiative. Those standards had been adopted by all but four states as of late last year.

He contrasts his prior work comparing international academic-content standards, which helped fuel the common-core effort, to the results of TEDS-M, which hasn鈥檛 been as enthusiastically received.

鈥淭he standards study got traction, and things started to happen,鈥� he said. 鈥淏ut that鈥檚 not happened yet in the teacher-preparation world.鈥�