• They may meet before the quarter to discuss the outline/goals for the course.
• They may continue to meet regularly during the quarter to discuss and evaluate the teaching of the course.
• They may jointly prepare homework, quizzes, and exams, or review and comment on each other's materials.  Furthermore, the Intern may be able to examine course materials prepared previously by the Adviser and use them as a source of ideas.
• They may observe and discuss each other's classes.
• They may choose to develop a new approach to a part of the course, and work together to implement and evaluate the new ideas.

Graduate students are expected to enroll in Math 597 the first two times they teach their own sections of courses they have not taught before; they may optionally enroll a third time as well.  Among the possible advantages to the Intern:

• The Advisor has experience with the course in question, and can field questions, help with class preparations, and suggest or critique materials.
• If the Intern has not TA'ed the course, tapping the Advisor's experience may be essential.  If the Advisor is teaching the same course the preceeding quarter, the Intern may wish to visit the Advisor's class during that preceeding quarter.
• The Intern gets practice discussing issues of pedagogy, an important skill for the job interview process.
• The Advisor gains a wide exposure to the Intern's teaching skills and ideas.  This provides a basis for a substantial teaching letter of recommendation, if the Intern requests it.