Certificate of College Mathematics Teaching Preparation

Math 827 is taught every Spring. Its main goal is to prepare second-year graduate students for teaching their own sections of calculus. The course meets twice a week for 75 minutes on most weeks, for a mix of theory and practice. Regular meetings are sometimes replaced by extra teaching practice, such as giving classes to an undergraduate audience in the evening.

For purposes of the certificate:

Gibbs instructors/postdocs/lecturers will be expected to:

• Attend approximately twelve of the seminar lessons (Topics: introduction; calculus at Yale; active learning I and II; lesson design; inclusive teaching; digital tools; public speaking; demonstrations of calculus teaching by current graduate student instructors; assessment and grading; underrepresented groups and Title IX (guest class by Dean Gladney); difficult conversation and constructive feedback.)
• Participate in several advanced lessons that will be given on days when the graduate student seminar does not meet. (Sample topics: midterm evaluations; alternative assessments; class observations; inquiry-based learning; mid-semester surveys; advanced course design; advising and mentoring students). The format of these lessons will be primarily presentations and discussions by the program participants. 

Graduate students will be expected to pass the seminar in their second year, and the advanced lessons after they start teaching.

This is an all-day event in August run by math lecturers, for all incoming postdocs and graduate students, as well as all instructors who are scheduled to teach calculus during the year. It includes an introduction to teaching at Yale, as well as several sessions on active learning and other inclusive teaching strategies.

The workshops can be chosen among:

• Poorvu Center’s ATW’s (= Advanced Teaching Workshops). You can find a listing of these workshops by going to YaleConnect(Link is external) , once you join the group called “Poorvu Center: graduate and postdoctoral teaching development”. Note these must be the advanced teaching workshops, not the intermediate ones or the fundamentals. 

  Recommended ATW’s include peer observations and teaching statement, as those align closely with other components of the certificate. Other topics of interest include writing recommendation letters, syllabus design, diversity and inclusion, instructional technology, or other topics of personal interest. 

• CIRTL workshops / short courses. Some of the CIRTL workshops are not about teaching, so please check with Brett and Miki before you sign up, to make sure that we will count the workshop(s) you chose toward the certificate. 
• Sometimes there is a workshop organized by the math department, or another kind of training that we might count. If you are thinking of a workshop that isn’t listed above, just drop us a line and we’ll tell you if you may apply it toward the certificate. 

To sign up for the Poorvu Center newsletter, with lists of upcoming ATW’s, follow these steps:

1. Visit Yale Email Subscriptions.
2. Sign in using your CAS credentials.
3. Using the search bar, look for “CTL Graduate and Postdoctoral Teaching.”
4. Select “Subscribe.”

We recommend that you observe one mathematics instructor, and one instructor in another department. The Poorvu Center’s ATW on peer observations will give you tips about what to look for during observations, and they can help you match with a peer outside of mathematics. 

You should check in with the instructor in advance, to learn about their topics and lesson goals for the day. After the observations, you will need to schedule a follow-up meeting where you can compare notes, discuss the lesson, and teaching strategies in general. The last item required is for you to write a brief reflection about the experience, for your portfolio. 

Specifically, you need to have observations by:

1. A peer in the program
2. Lecturer in the math department, or someone from the Poorvu Center

You will need to share a brief statement on lesson goals with the observer in advance,  schedule a follow-up meeting afterward, and write up brief reflections about the experience. 

You can request a Poorvu Center observation through their website. For the peer observation, the program coordinators can help you match up, or you can be matched with a peer outside of the department at one of the Poorvu Center ATW’s on peer observations. 

In this learning community, we discuss the courses we are teaching, talk about logistical and practical teaching-related issues that come up throughout the year in math, reflect on readings, and meet different member of the community (such as representatives of the undergraduate math societies, math department Chair and DUS, teaching and learning specialists from the Poorvu Center). 

This series runs every Fall, during lunch time. The day and time varies from week to week, so as to make it possible for everyone to participate in some of the sessions. (In Fall 2021, our meetings were Mon / Tue at 12 / 1pm.)

To get credit for the lunch series, you need to attend at least four meetings. If you have to miss too many sessions due to conflicts, let the organizers know, and we will find an alternative way for you to earn the credit. 

• Calculus instructor meetings
• Poorvu Center Course (Re)Design Institute
• Any two Math or Poorvu Center learning communities

Each calculus course has weekly, one-hour long meetings to discuss upcoming topics, share teaching strategies and activities for students, prepare for exams (writing, proctoring, grading, post-exam meetings with students), etc.  Participation in these meetings will automatically grant credit toward this category. 

For those who do not teach calculus, another option is to attend the  Poorvu Center Course (Re)Design Institute(Link is external). It typically takes place after the Spring semester ends. 

The last option is to attend two Math or Poorvu Center learning communities. Existing math series include

• Math for Humans journal club was established in 2020-21 by the Math Climate committee. It meets about once a month to read and discuss short articles and essays focused on inclusion and belonging. You will get credit for the community after attending four meetings. 
• Lecturer pedagogy reading group. These are on more advanced topics, and require reading ahead of time. Contact Jamie Barnes to sign up. 

Poorvu Center learning communities can be found on their website(Link is external).

The intent of this component is to help you prepare your job search portfolio. We recommend attending the Poorvu Center ATW on writing teaching statements. You can also request an individual consult from the Poorvu Center. 

These are syllabi that you can include in your job search portfolio, particularly for positions that seek additional teaching materials. If available, these are usually syllabi that you wrote for your own classes. If you have been teaching only courses where someone else wrote the syllabi, you can put together a syllabus the way you would do it if you were in charge (for the same courses, or for other courses that you would like to teach in the future). 

The Poorvu Center runs workshops on syllabus design. 

The annotations give you an opportunity to share your thought process behind the components on the syllabus. For example, you can mention whether you have taught the course before, what you changed from the previous version (taught by yourself, or someone else) and why, etc. A brief annotation can help the reader appreciate the thoughts that went into your syllabus design. 

Some schools ask to see student evaluations, which means sharing the full set of student responses to the “Strenghts and weaknesses of the instructor” question. These can be exported from the Yale course evaluations system(Link is external). 

The annotations give you an opportunity to highlight the evidence that your evaluations provide about your teaching. You can also use them to put the numbers into context - for example, to provide course-wide or department-wide course rating average, which helps the reader interpret yours. 

For this component, you need to write some reflections on your teaching, particularly while participating in the certificate program - for example, what was useful to you in your teaching, what you did not find useful, anything you would like to see and have not (or not enough), areas where you feel your teaching has improved while participating, areas that you would still like to work on, etc. 

The very last component to be done is a meeting with the Poorvu Center, to talk the program and your experience in it (and anything else that you would like to discuss). As of Fall 2025, the meetings are with Julie McGurk, who can be reached at julie.mcgurk@yale.edu  . Be sure to e-mail Julie well in advance, so that she can fit you into her schedule.