Alex and Dan discussed some of the basic ideas and concerns involved with teaching math at Notre Dame. The discussion can be broken down into responses to several questions, as follows:
Grad students are generally asked to teach calculus, linear algebra, finite math, basic logic, and a few other specialty courses. First year students do not teach, and second year students only TA, so the earliest that a grad student at ND may teach is the summer following the second year.
At Notre Dame, multisection courses are expected to proceed at the same rate so that the same material is covered in each section. Exams are department-wide (not section-specific), which can be tricky if one instructor falls behind or if each instructor chooses what to emphasize what they see fit. Thus, communication between the various instructors is essential!
Traditionally, tutorials were glorified Q\&A sessions. It was the duty of the TA to answer homework questions and perhaps administer quizzes during the tutorial. There were other duties, such as grading quizzes and helping to grade exams, as well. The new type of tutorial involves active learning by means of group work. The class is split into small groups and given an activity to work on together. The duties of the teaching assistants for this type of tutorial include the creation of the activities and actively helping the groups work through their activities (in addition to grading, as before). Most calculus classes have been switched to the new style of tutorial. There are mixed feelings about the benefits of the new tutorials, but the students do appear to be learning more as a result of the switch.
Just check out the math department's lists of tradition fall and spring courses - all courses appear on at least one of those lists, with both the old three-digit and the new five-digit numbering schemes. Alex pointed out that there was some logic behind the choice of the new five-digit scheme. For example courses ending in 50 and 60 form sequences, more basic courses have lower numbers, and various sorts of courses have certain ending numbers (e.g., algebraic courses end with a 5).
Alex assigns the courses, but he does rely on the input from a specific grad student. Currently, that grad student in Heather Hannah. They try very hard to match courses with instructors without causing schedule conflicts or violating preferences. If you are unhappy with your assignment, or if you have a conflict, make sure that you mention it to one of them - they will do what they can to accomodate you.
Generally, every course looks about the same from year to year. The exams fall at about the same times each semester, and the syllabi also remain about the same. The University has a strict set of guidelines for determining grades (e.g., the final exam must account for at least some certain percentage but no more than than another certain percentage of the final grade). Alex sends around a sheet detailing these things at the beginning of each semester, so keep your eyes open in case you find yourself teaching a course.
Yes, there are, and they are generally good. Their job is to grade the homework and keep track of the homework grades. If you are lucky, the grader will return the homework to you promptly. Some graders are even good enough to write up a couple brief notes about how the class is doing as a whole, from time to time. No matter what, make sure you keep track of the homework grades as well, either by asking the grader to send you an electronic copy of the grades from time to time or by keeping your own records. Computers don't fail terribly often, but the homework grades for an entire course have been lost in the past because the instructor failed to keep a backup.
Note: If you remember anything else from this discussion that you found useful, please mention it to Dan Bates.
(reported by Dan Bates)