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Section 6 The final three years

Subsection 6.1 Courses

There is a breadth requirement manifested as a classroom course requirement for all graduate students; it is present to encourage students to enhance their mathematical background. It is the breadth of mathematical knowledge which allows students to better see connections between different areas of mathematics, and often spawns the most interesting research.

There is also a practical side to this requirement. Teaching a course for the first time requires significantly more preparation time than one for which you already have a good perspective and source materials. Taking good notes in classroom courses provides a wealth of resources.

For first-year students the breadth requirement is six classroom courses; for second-years it is four. Over the course of the last three years, students are required to take a total of eight classroom courses. A student whose accumulated total falls below three courses per year must petition the GPC for an exception which is granted only if the student has a viable plan to make up the deficit in the following year.

Since full-time students are required to register for three courses each term, once you have advanced to candidacy, you should make up the difference between the 3 course load and classroom courses from among Math 156 (Graduate Research), Math 157 (Thesis Research), and/or Math 158 (Independent Research).

Finally, remember that neither the teaching seminar (Math 147) nor your own teaching assignments count towards this total. Please remember to register for Math 149 each time you teach for the department; this tracks the teaching requirement for graduation.

Subsection 6.2 Teaching

Graduate students typically teach one course in each of their final three years of study, and these experiences can be quite varied depending upon the level of the course as well as whether it is a multi-sectioned course or not. Students should register for Math 149 in the terms that they teach; Math 149 does not count towards the classroom course requirement.

Graduate student teaching assignments are made after faculty teaching schedules have been settled. Generally what remains is a large pool of courses. Specific teaching assignments are informed by a number of sources: feedback about the student in the teaching seminar and practica, previous TA or teaching evaluations, as well as graduate student requests. The department chair asks for teaching preferences of the graduate students from among the pool of available courses, and just as with faculty, those requests are honored as best they can; assignments of students to courses must satisfy many constraints. However, if you have a specific request, e.g., if you prefer not to co-teach with your advisor, make that request known to to chair. It may not be possible to honor it, but it never hurts to ask.

Subsubsection 6.2.1 Course Supervisor

A course supervisor is a faculty member who oversees a course taught by postdocs, junior faculty or graduate students, but is not actually teaching the course. The course supervisor reviews the syllabus (in its broadest sense), previews all exams, and advises on assignment of final grades.

Subsubsection 6.2.2 Course Chairs

A course chair is a faculty member who oversees a multi-sectioned course. The course chair sets the syllabus (in its broadest sense). Of course in lower-level courses, the topics syllabus is essentially fixed by department consensus, but there can be some variation in how what type of homework is done (e.g., WeBWorK or written homework) and how the course is evaluated.

There is not always agreement among all faculty teaching a multi-sectioned course about how a course should be constructed and run, but by department policy all sections are subject to common evaluation, so the course chair sets the procedures and syllabus to be followed in that offering of the course.

Subsubsection 6.2.3 Teaching Mentors

A teaching mentor is assigned to all graduate students who teach. The role of the mentor is especially critical in the first teaching experience, and can vary with subsequent teaching opportunities based upon evaluations of previous teaching.

Graduate students are often fond of thinking they should be in full control of the courses they teach. That is more than a little like someone getting a driver's license and feeling they are an accomplished driver having only passed a road test. There is always more to learn about your profession.

Teaching mentors have many duties which dovetail with that of course supervisors and course chairs. The syllabus is set by the course supervisor or chair. In a multi-sectioned course, exams are drafted in consultation with the teaching faculty, and final decisions left to the course chair. In a single-section course, the faculty member drafts the exam which is then reviewed by the teaching mentor who gives feedback to the instructor. The teaching mentor also reviews final grades to make sure they align with department guidelines and to help the instructor resolve borderline cases. All these roles of the teaching mentor apply uniformly to any graduate student who is teaching.

The role of the teaching mentor can vary depending upon the needs of the instructor as perceived either by the instructor or the mentor. In particular, a teaching mentor is expected to be highly involved with those teaching for the first time, with the degree of involvement negotiable for those who have taught previously and have strong teaching evaluations. To be an effective mentor, they should visit the class two to three times during the term. The ideal schedule is for a first visit to occur within the second week of term. This has provided time for the instructor to set the tone of the class and develop some rapport. A class is observed and the mentor takes notes. Following the class, the student and mentor meet and discuss the class. Ideally, a mentor starts by asking what were the goals of that day's class and how effective the instructor felt they were in accomplishing those goals. Ideas of things that they thought went well or not are mentioned. Then in that context, the mentor can review how they felt the class went, and make suggestions for different ways to accomplish certain goals. A followup visit should occur in another couple of weeks. If things are going well, there may be no other visits unless requested. If problems still seem apparent, more visits and brainstorming sessions may be needed.

Yes; it is a bit unsettling to have someone in your classroom observing you, but evaluation is a part of life and certainly part of your career. The goal of the mentor is to help you become a better communicator, something from which all parties benefit.

Subsubsection 6.2.4 Teaching Evaluation

The department has a teaching evaluation committee whose job it is to visit the classroom of all graduate students, postdocs, and junior faculty members. Their role is to visit a typical class, and following a discussion with the instructor, write a review which often forms a core piece of a teaching letter.

There are often a large number of classes for the committee to visit, and you are best served by getting feedback in the first half of the term, so if a member of the teaching evaluation committee does not contact you about setting up a visit within the first two weeks of the term, contact the chair of the committee to help move things along.

Subsubsection 6.2.5 Outline of responsibilities and expected time commitments

The amount of time one commits to teaching varies among instructors, and any faculty member will freely admit that the first time they teach a course, it requires far more time and energy than subsequently. Typically, most graduate students are teaching courses for the first time, and so the preparation will be more demanding than for someone having taught the course before. But the key here is the effort is demanding, but not all-consuming.

Students should place their efforts in perspective. For those who will choose an academic path, their normal responsibilities each term include teaching one or more classes, doing research, advising students, as well as other department duties. Learning to balance those responsibilities is also an essential part of becoming a professional mathematician. Starting now is a good idea.

All this is to say that you cannot make teaching your one class a 40 hour per week job. That kind of time commitment is unrealistic, and not remotely proportional to your responsibilities. Of course you want to do a good job with your class and you should. But you cannot (and should not try to) do everything and try every technique. It takes a long time for someone to develop fully into a good teacher, and some lessons are learned only upon reflection of hobbled previous efforts.


What are the demands of teaching a course?

  • Preparing lectures and handouts
  • Writing homework problems, solutions, grading
  • Office hours
  • Website maintenance, exam writing and grading

In a multi-sectioned course, some of the labor is distributed: one person writes homework problems, another the solutions, still another updates the web pages. If you are on your own, you need to learn to balance. Not everything needs to be TeXed or a Beamer presentation. Handwriting notes, handouts, solutions etc saves an enormous amount of time.

Subsubsection 6.2.6 The Honor Principle and your course

The last thing you want to think about when teaching is the possibility of an honor code violation, but be very clear such violations do occur and many are the result of a lack of clarity in how the honor principle applies to your course.

First, you should make a point to read the academic honor principle. Then you should decide how it applies to your course. Can students collaborate on homework? projects? exams? How should credit be attributed? What resources are allowed?

Once you decide how the honor principle should apply to your course, make this very explicit on your course syllabus. Then make sure you talk about it in class. All this reduces the chances that a potential violation is a result of lack of clarity.

Still on occasion, things do occur. Virtually identical [incorrect] answers on exam problems, homework/exam solutions too sophisticated for the student of using notation not seen in the text. For cases in which you think a student's answer was informed by information on the internet (presuming it was not allowed), you can probably find the source online. Still what do you do?

Having read the honor principle, you know you are not to resolve the matter on your own, though asking students for clarification is allowed. Your first action is to bring the matter to your course chair or supervisor who will advise you further. If need be, the department chair can give further opinion.

If it is decided that this is a likely violation of the honor principle, contact the office of Community Standards and Accountability which will give you information for how to submit your materials.

Subsection 6.3 Travel: Conferences, Invited Talks, Interviews

Travel for whatever purpose requires booking flights, making hotel reservations, and planning for local transportation costs and meals. In many instances funding is available to graduate students, but such funding is generally in the form of reimbursement, meaning you need to carry the load in the short term.

While there are times you can arrange for the College to pick up some of the interim costs, there can be trade offs, and certainly hotel, local transportation and meals are all expenses you will have to carry until reimbursed. So it makes good sense to start building a travel fund of your own to help smooth out the bumps.

The largest expense generally is travel to and from a conference. If you are taking an authorized professional trip, one option available to you is to book your flight through the College travel office. With Tracy's authorization, the cost in the short term is carried by the department, which you then reimburse when you receive funding from the outside entity.

Note that since this is a corporate booking, it may not be the cheapest option for air travel, which means while the College is carrying the short-term load, more of your reimbursement will go to travel costs. On the other hand, if you want to book your own flight through wing-and-a-prayer air, you are free to do so, but then it is your credit card which is carrying the debt until you receive reimbursement.

Subsubsection 6.3.1 Conferences

Conferences are wonderful opportunities to make new and meet old colleagues, learn about the work of others and present your own work. Some of the people you meet eventually may write letters for you, either for jobs or for when you come up for tenure, so keep in mind that conferences are a professional activity.

When you find a conference of interest and want to attend, the first question is whether you are allowed to be away from campus? Is your advisor aware and in agreement that this is a valuable activity? Are you teaching, TAing? How will those responsibilities be handled?

If you are going to a conference, the following sources of funding should be investigated, pretty much in this order:

  • Graduate student support obtained from the conference organizers: More and more conferences offer graduate student support, but you have to apply for it and often obtain a letter recommending you as a viable participant. Such funding can supplement travel, housing and meals, or just some subset of those.
  • Sometimes there is money to help defray costs available from the department. Application is made by contacting the graduate representative, and funding is limited.
  • At least once during your Dartmouth career, the graduate office provides some funding to defray the costs of a professional conference. Most graduate students use this attend a national meeting of their professional society.

Subsubsection 6.3.2 Invited Talks (colloquia/seminars)

You may be invited to give a seminar or colloquium talk. In this situation, most if not all of your expenses will be reimbursed, but you must carry the short-term load, so between booking a flight and waiting for the University to reimburse you, certainly two to three months will elapse. Generally hotel and meals are covered locally and not borne by you.

Subsubsection 6.3.3 Interviews

Eventually, you will interviewing for jobs. Sometimes perspective employers will have you book flights through their travel agents saving you the costs, but not always, so again your credit card could be carrying the load for 2-3 months. And if you are lucky enough to have many interviews, these costs can be significant, so some advanced planning is worth your while. Again meals and hotel are generally handled by the local host, so do not add to your interim costs.

Subsection 6.4 Language Exam

The formal requirement for a reading knowledge of a foreign language exam has been eliminated.

It should be understood that mathematics is written in many languages, and the need to be able to read papers in languages other than English remains an important tool. Some Advancement Committees may expect students to demonstrate some level of proficiency in reading mathematics written in languages other than English.