Another Layer of Knowing

I know two amazing math brains. They can both do calculus, applied mathematics, and whatever else it is that amazing math brains do. They know their stuff. One of them is an amazing teacher. The other is not. When one sits down with a student to tutor him through a difficult math problem, he prompts and supports and explains and leads his student into understanding. When the other sits down with a student to tutor him through a difficult math problem, he demonstrates how to solve the problem. He gets frustrated and can’t understand why the student can’t do it, too, after the clear procedure he has provided. I know two amazing math brains. One is a teacher. The other is not. It is clear that teaching requires more than simply knowing the content. The skills necessary to support a learner along the path to discovery go beyond content knowledge. Pedagogical knowledge supports good teaching. Similarly, there is more to good coaching than knowing the content. Even being ...