You can't teach what you don't know—and when it comes to math, some teachers just don't know enough. Why? 

Michigan State University professor William H. Schmidt and his colleagues look at the mathematics that American middle school teachers took during their teacher preparation and produce some hard evidence of prevailing substandard preparation. 

First though, recall some earlier work in which Schmidt examined how teachers were prepared in 16 countries. There, he unearthed the essential knowledge for middle school teachers based on the relationship between coursework and teachers' strong performance on an international assessment of math content knowledge and math pedagogical content knowledge. The top performing teachers had all studied nine topics, including linear algebra, calculus, probability, differential equations, functions/equations and also had opportunities to analyze math instruction. 

This latest study looks more closely at US preparation, examining how many US programs deliver this essential content. Even on this basic question, Schmidt finds enormous, inexplicable variations among institutions in what they consider to be essential content. Schmidt estimates that only about a third of America's middle school teachers took coursework addressing this content. For the rest of teachers, a sizeable portion of the content never gets covered. Compare that to some of our international counterparts which include a number of countries where 80 percent of all teachers learned essential content.

Percentage of Middle School Teachers Who Completed at Least Eight of Nine Essential Math Courses