Teaching Information For New PhD Students

*Introduction:*

As part of the math PhD program at Yale, graduate students are required to teach one semester of each academic year. The exact teaching duties vary by year, and are described in detail below.

*Teaching Fellow I: Calculus Tutor/Leader for Problem-Solving Sessions:*

This position is assigned to first-year graduate students and requires about 6 hours of student contact per week. In the past, each first-year student was assigned to lead two out of the three calculus tutoring sessions, held Monday-Wednesday, 7-9:30PM. The duties were simple: sit in the assigned room for 2.5 hours and answer any questions that students have. Students were welcome from all calculus courses and, in general, they just came to get help with their homework. Starting with 2011, the Yale math department has replaced these tutoring sessions with course-specific problem-solving sessions, one each for MATH 112, 115, and 120. Rather than the past "office hours" environment of tutoring sessions, these are supplementary practice-and-review sessions (the equivalent of labs for biology students). The duties of the session leader include selecting problems for the students to work on and then discussing the solutions at the board, in addition to answering any questions they might have. Ideally, the exact homework problems would not be discussed, although if students ask about those, similar problems can be substituted instead. The goal is not to help students with their assignments, but to help them understand the necessary concepts and techniques.

Here are some useful tips to keep in mind:

1. You can get your calculus textbooks from Bernadette at the start of the semester. Bring these with you to the tutoring/problem-solving sessions, because the students don't always bring their own.

2. Sometimes the outside door of LOM is locked and students can't get in, so be sure to unlock it before starting the session.

3. Take note of which topics students are having trouble with, as they will be especially honest with you. Since you are not the instructor for their course (nor the grader or TA), they have no reason to pretend to understand something they don't, and hence they will ask you questions anytime they are confused. You won't necessarily see such honesty when you are actually teaching calculus in your third year, so take advantage of it now!

*Teaching Fellow II: Linear Algebra TA*

This position is assigned to second-year graduate students and requires about 5-10 hours of work per week. The exact responsibilities will depend on the instructor of the course you are assigned to and how many graders there are. In general, you will be expected to grade problem sets and input this into a spreadsheet, hold office hours, and answer student questions by email. If you are feeling particularly nice, you might make some review sheets or post solutions to the homework on v2.

Here are some things you'll want to check out before the start of the course:

1. Basic facts: course meeting time/place, instructor, textbook, prerequisites, and syllabus.

2. Homework - how often will problem sets be posted, and when are these due? What is the grading rubric for the problem sets? Will the course have any graders to help you with the workload? What is the lateness policy on homework? Where will you pick up the problem sets (e.g. instructor's mailbox), and where will you drop them off?

3. Exams - how many exams will there be, and when? Will you be asked to help with the grading?

4. Office hours - when are the instructor's office hours? Based on this, class time, and student preference (if known) decide when to hold your own office hours and also ASK BERNADETTE FOR an empty classroom or space to do it.

5. Online - does the instructor make use of v2, or does he/she use a personal website instead? If the former, check that you've been added to the v2 site and have access to the class mailing list and anything else that the instructor deems useful.

*Teaching Fellow III: Calculus Instructor:*

This position is assigned to graduate students from the third year onward. If this includes you, then here's your big chance to teach! As an instructor for MATH 112, 115, or 120, your responsibilities now include giving lectures 2-3 times a week, assigning problem sets, coordinating with your grader to ensure that these are graded, writing the midterms and final (together with the other instructors for this course), and grading the midterms and final (together with other instructors).

*How calculus is taught at Yale:*

Unlike other universities where calculus is taught in one huge lecture hall, Yale breaks up its crop of calculus students into "sections" of about 15-30 students each so that the students can have a more personal, interactive learning experience. Each section is taught by a different instructor (a mix of graduate students and faculty), but the sections have the same exact syllabus, midterms, and finals. At the beginning of each semester, students who sign up for a calculus course, e.g. MATH 115, will then be asked to rank the available sections of MATH 115 in order of preference with respect to their class schedules. Then the online system matches students with sections, attempting to give as many people as possible their first choice.

In order to help ensure that all of the sections are, by and large, doing the same thing, there is a course coordinator. This person (usually a senior faculty member) sets the course syllabus, the grading system, and sends out a suggested outline of topics to be discussed each week. He/She might also suggest a list of specific problems for each homework assignment, which can then be adapted by each instructor as needed. As an instructor, you will meet with the course coordinator 1-2 weeks before the start of classes to ensure that you have all of the information necessary to do your job well.

Here are some things you'll want to find out about and do at the beginning

of the semester:

1. Basic facts - course meeting time/place, textbook, syllabus, prerequisites, exam dates, etc.

2. Classroom - Be sure to visit the room your class will be in and check that there is enough chalk.

3. Homework - Decide when you want it handed in and how it will be graded, then coordinate with your grader.

4. Office hours - Decide when and where to hold your office hours. If possible, take student preference into account.

5. Online - Check out the umbrella webpage for your course, and also your own section page. Figure out how to use it, if indeed you are going to use it.

*A word of advice:*

It is tempting to think of each lecture as a presentation during which you must cover a certain list of topics. Given the set syllabus and structure of our calculus courses, the latter is in fact true. But keep in mind that the goal of teaching is not just to present material, but to help students learn it. No matter how perfectly you can present the topic of differentiation, if your students don't understand it, then ultimately you have failed.

There are many different ways to teach, and you will have to find your own unique style. That said, no matter what that style is, try to engage the students in the learning process as much as possible. Make eye contact with them, ask questions, and allow them to ask you questions as well. When you ask questions, wait until you get an answer. If you get the same question three times, try to find three different ways to answer it. One of our main goals is to help students develop their curiosity about the mathematical world. Curiosity leads to questions. We should try very hard to get our students to talk to us.

*Getting Help:*

Your course coordinator can answer any questions you have about the logistics of teaching your particular section. If you want help or advice on improving your teaching skills, then take advantage of the math department's Lang Lunches (once a week during spring semester) or Yale's Graduate Teaching Center, www.yale.edu/graduateschool/teaching/. The GTC offers a wide range of teaching workshops and online resources to help you become a more organized, effective instructor. GTC staff and fellows also provide one-on-one consultations so that you can discuss any issues you have (e.g. lack of student enthusiasm, disruptive student, etc.) and work out a solution together. You can even request to have your class observed or videotaped. For more information, have a look at the GTC website or email Kat Orekhova (math GTC Fellow for 2011-12). Also, Prof. Michael Frame has been teaching longer than you’ve been alive, and he is always happy to offer help and advice.