True or false: “The primary task of a mathematics graduate student is to learn, and ultimately to create, mathematics.” Most graduate school faculty, including this author, would heartily agree. But such an individual, upon graduation[26], will be asked to teach his or her own course in the academy or to work as part of a group in industry. It is natural[27] to expect such a student to develop the skills necessary to do so while in graduate school. In this article I focus on some novel ways for mathematics departments to promote the development of teaching (and communication) skills, consistent[28] with the primary focus on subject matter mastery noted above.