The New York Times article “Building a Better Teacher”* describes two different studies of exceptional teachers and what they do that makes them great. One study is by Deborah Ball, Dean of the School of Education at Michigan State University, who created Mathematical Knowledge for Teaching (MKT). The second is by Doug Lemov, an educational consultant and author of Lemov’s Taxonomy. What makes excellent teachers is a paradoxical combination: Both MKT and Lemov’s Taxonomy identify a repertoire of standard practices that teachers engage in constantly. But at the same time, both Ball and Lemov have observed that expert teachers improvise constantly. After describing how Deborah Ball, in a math class she was teaching, spent ten minutes entertaining a student’s incorrect idea about odd and even numbers–ultimately, to guide the class to an important fact that was not on the day’s lesson plan–the NYT article notes “Dropping a lesson plan and fruitfully improvising requires a certain kind of knowledge.”