Requirements
Admission to the Ph.D. program in Mathematics carries with it a commitment of full financial support for five years, subject only to the condition that the student is making satisfactory progress toward the doctoral degree. This position carries a fixed stipend (the same for all students) for nine months plus tuition and fees. In fulfillment of the requirements for the M.Phil. degree, all students must gain teaching experience as part of their graduate training.
The Mathematics Department believes that training in teaching is an integral part of the training of graduate students as future scientists. Moreover, a large percentage of students will look for jobs in academia. Universities now ask for proof that their prospective faculty members are effective teachers, and hence look for some teaching experience as well as teaching letters from the faculty and copies of student evaluations. Thus, all graduate students are given the opportunity to teach undergraduate courses. As part of the policy of the Graduate School of Art and Sciences, the department has created the position of Director of Graduate Student Teaching, who will usually be the Calculus Director. The following guidelines set parameters for graduate student teaching in the Mathematics Department.
Teaching Responsibilities
In general, students in their first year do not teach, but, in order to provide them with useful exposure to the scope of their future educational role, they typically assist in the Mathematics Help Room. All other students are required to fulfill additional teaching duties every semester. The teaching opportunities in the department are as follows:
1. Calculus III courses or College Algebra
2. Teaching assistantships
3. Supervision of sections of the Undergraduate Seminar
(1) Graduate students listed as the instructor of record teach a section of Calculus I, Calculus II, or College Algebra. Student instructors are solely responsible for their section: grading homework, making and grading exams, holding office hours. Section enrollment is normally limited to 30 students. Every PhD student is required to be the instructor of record during a regular semester one time during the course of their program. This shall be a section of Calculus I, Calculus II, or College Algebra. We encourage students to do this in their 3rd or 4th year. Students who are interested may be the instructor of record more than once, but this is not a requirement. Students who are interested may also teach during the summer, but this does not count towards the requirement.
(2) During semesters in which a student is not an instructor of Calculus or College Algebra, students are assigned to assist a specific instructor in an assistantship role. This requires grading homework and exams, holding regular office hours, and scheduling three hours a week in one of the math Help Rooms.
(3) Students teaching in the Undergraduate Seminar supervise the work and the lectures of undergraduate students. The subject of each individual Undergraduate Seminar is often proposed by the graduate students. The Undergraduate Seminar is supervised by a faculty member.
Selection
Teaching assignments are made by the Director of Undergraduate Studies, who takes into consideration both the teaching obligations of the department and the needs of each Teaching Fellow. With the exception of first year students, all students are assigned teaching duties. Preferences expressed by the students and competence, in particular an adequate command of English, are all taken into account. However, students supported by a nonUniversity fellowship (such as the NSF grants) are exempt if this is a condition of the fellowship. Finally, all teaching assignments are contingent upon a studentâ€™s satisfactory academic progress.
Guidance and Training
The Director of Graduate Student Teaching is responsible for training and advising Teaching Fellows.
The Teaching Seminar
Firstyear students are required to participate in a semesterlong course on the teaching of mathematics. In this seminar they practice:

 Creating a web page for a course
 Writing a syllabus
 Writing and grading exams
 Lecturing on a Calculus topic
Usually the students will be asked to prepare an hourlong lecture and will deliver about half of it. The presentation is then discussed by the class and the instructor. Other means of instruction might include giving a lecture in an actual Calculus section, with feedback from the instructor and the class.
General advice on the philosophy and practice of teaching in an American University is available in the form of a lecture in the Teaching Seminar, the department’s Faculty Teaching Guide, and discussions held at the beginning of each semester under the auspices of the Director of Graduate Student Teaching. There is also a manual prepared by the Graduate School of Arts and Sciences, which students may consult.
The American Language Program
All graduate students who are from countries whose native language is other than English must demonstrate oral and written proficiency in English or pass the International Teaching Fellows Course offered by the American Language Program (ALP). The ALP requirement should be completed in the graduate student’s first year of study, to ensure communication problems are identified and improved before students begin their teaching requirement in year 2.
Specific Training Requirements
1. Teaching Fellows assigned to Faculty
The faculty member is responsible for the training and guidance of the students who are assigned to help him/her teach a course.
2. Calculus sections
Syllabi are available on the web for Calculus IIV courses. Meetings are held at the beginning of the semester under the auspices of the Director of Graduate Student Teaching, or a faculty member designated as course head, to discuss the syllabus and other issues pertaining to the course, such as exams and grading policies. At least once a semester, the Director of Graduate Student Teaching or another faculty member delegated by him will visit each class taught by a graduate student for the purposes of evaluation and feedback.
3. College Algebra
The Director of Graduate Student Teaching is responsible for advising the Teaching Fellows who teach College Algebra.
4. Summer session
The Director of Graduate Student Teaching will designate a representative for the summer session, usually a faculty member, who is responsible for (among other tasks) advising graduate students teaching summer courses.
Evaluation
Student evaluation forms (or an electronic equivalent) are distributed at the end of every course taught by graduate students. The evaluations are kept in the department. The evaluations are one of the elements taken into account in writing letters of recommendation. Needless to say, the evaluations are subject to interpretation. Comments from faculty members supervising a TA or supervising the undergraduate seminars are also taken into account. The Calculus Director will also evaluate the students teaching Calculus sections by visiting their classes.
Fairness Issues
Insofar as is possible, the duties of the various Teaching Fellows are roughly comparable. A point of reference is the amount of time spent by graduate students teaching a section of Calculus.
The level of teaching must be satisfactory, both in fairness to the undergraduates who take the courses and as part of the training. It is of course not possible to write a good teaching letter for a student who is not an adequate or dedicated teacher. Likewise, the department cannot appoint graduate students as instructors in the summer session if they do not have an adequate teaching record.
Complaints from undergraduate students taught by graduate students come to the attention of the Director of Graduate Student Teaching or the Director of Undergraduate Studies. They assess the validity of the complaints, and find remedies as appropriate. In the past, some instructors have found it useful to distribute an informal questionnaire in the middle of the semester to see if the pace of the course is appropriate and asking for suggestions.
Graduate students’ grievances should be resolved first by bringing them to the attention of the Director of Graduate Student Teaching or the Director of Undergraduate Studies. If they cannot be resolved at this stage they can be appealed first to the Director of Graduate Study, next to the Chair of the Mathematics Department, and then to the Assistant Dean for Graduate Teaching at GSAS.
Policy on Graduate Research Assistants (GRAs)
1) A student who receives a graduate research fellowship will in general continue with his or her normal teaching responsibilities. However, at the request of the Principal Investigator on the grant supporting the GRA (who will usually be the student’s adviser), the student may get relief up to one and a half years from teaching.
2) It is understood that all students will have some kind of teaching experience as part of their graduate training, which will include at least one course of actual classroom experience (i.e., teaching Calculus or College Algebra). Moreover, it is understood that they will have sufficient prior experience as a Teaching Fellow to prepare them for this. However, students holding an outside fellowship which expressly forbids them to teach are exempt from this rule.
3) The stipend for a GRA will be no less than that for other students.
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