Teaching is required of all graduate students, typically one semester per year (exceptions include students with external funding who might teach less, and students beyond their fifth year who may need to teach in both terms for funding reasons).
Generally, first-year students work as coaches for calculus classes. As coaches, they run optional problem solving sessions and meet with small discussion sections of undergraduates.
Second-year students often work as teaching assistants for intermediate level courses, such as linear algebra (Math 222, 225, 226), real analysis (Math 255, 256), or discrete mathematics (Math 244). Duties may include holding office hours, leading discussion sections, and grading assessments.
In the Spring of their second-year, graduate students attend the Lang teaching seminar, which is listed as Math 827. In this seminar, experienced faculty help graduate students understand the challenges of teaching and prepare for leading their calculus class in the following year.
Students in their third-year or above typically teach a section of a coordinated calculus course (differential, integral or multivariable).