NPR’s All Things Considered: Experts Say Best Instructors Spot Where Students Go Wrong:

Research shows that teachers with degrees in the subjects they teach are more successful. That’s the reason behind teacher-certification requirements in the federal No Child Left Behind education law.
But as Robert Frederick reports, not all mathematicians are successful math teachers. Most could use some help in becoming calculating sleuths. Education experts note that most advanced math programs are geared toward theoretical as opposed to practical instruction.
It’s not enough to know math, says Judith Ramaley of the National Science Foundation. Teachers “also need to understand how the minds of young people work, and how to diagnose� the kinds of tangles kids get into,” she says.