DRP toolkit

Here is a sample timeline for a term-time DRP. Some details may differ depending on how the DRP is run (e.g. whether mentors select the project before or after being paired with students).

• Before or beginning of the semester: Advertise/solicit applications for students and mentors. DRP committee makes pairings and holds an orientation meeting with participants to outline the guidelines and allow student/mentor pairs to meet.

• Early in the semester: Student and mentor agree on a project/book. Mentor submits a project proposal to the DRP committee. Books are ordered (either by the mentor or the committee). Weekly meetings begin.

• Mid-semester: The committee should check with each project to catch any issues (e.g. the student has disappeared). This could be done through a "mid-semester check-in" (e.g. Google form) that is completed by both the student and mentor.

• End of the semester: Students begin to prepare for the presentations. Students submit titles/abstracts. Mentors help student prepare the presentation and give feedback on a practice run. The committee schedules, advertises and organizes the event for the presentations; this usually includes food. DRP collects final feedback and/or demographic data from students and mentors.

Remark: some programs do presentations at the beginning of the following semester. This can be a less stressful time for students and avoids overlapping with exams. It works well to have a presentations for Fall DRP at the beginning of the Spring semester, but it is less ideal to have presentations for Spring DRP at the beginning of the next academic year (some programs do this nevertheless).

Here's a detailed week by week checklist from the DRP program at Maryland with their timeframe. (if you want to share yours, we'd love another sample. Contact us!)

Some common ways to advertise the DRP to undergrads and encourage them to apply.

• Put up posters around the math department.

• Ask the math club to send an email to its members.

• Ask faculty to advertise during their upper-level courses. Better: have committee members visit undergrad classes to give a 2-3 minute spiel about the DRP and encourage people to apply.

• Get undergrads to attend the DRP presentations for the previous semester.

When designing your advertisements, it is important to consider which students are you trying to reach. Math majors? Curious non-math majors? Upper-level or first-year students? Women and historically underrepresented groups? Be purposeful in your advertising so that the answer to these questions is clear to applicants.

For more on advertising, see the page on Inclusivity.

Often programs have many more interested undergrads than grad students to mentor them. The role of an application is to select for students (and mentors) who will be a good fit, help make decisions if the numbers don't line up, and communicate some basic info about expectations.

Questions for mentors:

• Do you want a student who's background is elementary/intermediate/advanced?

• What subject areas are you interested in mentoring?

• Project proposal (if this is set before the pairing, as is done in some programs)

Possible questions for students:

• Major

• Courses and grades

• Math interests

• Motivation for DRP

• Soft question such as "tell us something from a math class that made you curious", or "have you ever had to explain math to someone else? Describe what was challenging to communicate"?

• Recommendations (optional. Some DRP's ask for names of two possible references, and the committee reaches out for an informal opinion)

• Demographic data

• Agreement to the time commitment required from the DRP. Possibly also a statement such as "The DRP requires a time commitment of at least 5 hours per week. How do you plan to balance that with your other courses and commitments?"

In deciding what to include, think about what is most helpful and what function each question serves. Ultimately, what you ask for may affect who ends up applying. You may also want to be clear with applicants why you are asking for certain information or how it will (or won't) be used. For example, asking for courses and grades might scare away students who have been struggling in the classroom but might excel in a one-on-one relationship. But grades can be used, for instance, to filter out students who typically take more courses than they can handle and might not be a good fit for a DRP! See the Inclusivity page for more discussion on this.

Evaluating applications. The committee should decide the criteria for evaluating applications. For example,

• how much do grades matter, and what information do you want to extract from them?

• should students who have not done DRP before be given preference?

• should older or younger students be given preference?

• what if a student wants to do a project in an area with no mentors?

• Decide ahead of time who you want to reach with the program, and what criteria for evaluation will help you select these students.

For more on applications, see the page on Inclusivity.

• Keep it sustainable: You can start a small pilot program and grow from there, but it's hard to recover if 95% of interested grad students mentor during the first semester, and then need a break the following year, leaving you with no mentors. Try to run well under capacity for the first couple of years.

• Grad student mentors are typically the limiting factor. Think about how many grad students are available. If your school has quals, a mandatory first year graduate course sequence, or similar first-year requirements, you may wish to exclude first year grad students from mentoring (for their own good!). Similarly, it may be unreasonable to expect students to mentor during their last semester, or during semesters of heavy teaching/TAing. Make an estimate of who's available, and then scale down (by half at least!) since not everyone wants to mentor for fun. Take into consideration that research is a priority and few people will mentor two semesters in a row.

• Can postdocs be mentors? One of the benefits of the DRP for mentees is that they are close in age or experience to their mentors. This near-peer mentorship has many benefits and makes a DRP distinctly different from doing a reading course with a professor. That said, if you have a shortage of grad students and the right postdoc approaches you wanting to be a mentor, you can consider it.

• Can grad students mentor groups of undergrads? While this might solve your numbers problem, mentoring in groups can take away the one-on-one benefit and replicate some of the competitiveness and inequality among undergrads experienced in classes.

Organizers, possibly with the help of the faculty mentor, should decide on a set of expectations for mentors and communicate them in a handout and possibly an orientation session. Here's a sample handout for mentors

Typically, guidelines include the following:

Overall, the mentor's job is to provide a structured environment for the student to learn. The mentor should oversee various aspects of the project, making sure that student knows what is expected and has the resources they need.

At the beginning of the semester, mentors should help students pick a good topic and decide on the scope of the project. It is best to pick a specific landmark (e.g. a theorem or application) to aim for. Try not to be overly ambitious, and keep in mind that the student will need to prepare a presentation at the end of the semester.

Mentors should set weekly reading goals and meet with student for 1 hour each week to discuss the reading. It often works well to have the student explain something at the board such as some of the material they read or exercises they have worked out. The mentor can also answer questions about things that were confusing. (Strategies for running meetings can be addressed at an orientation/training meeting if you hold one. If your program has been around for a few years, experienced mentors can offer tips to new ones).

Mentors should help their student prepare for the final presentation. This includes choosing what to present; keep in mind that the presentations are short and should be aimed at a general mathematical audience of mostly undergraduates. The mentor should also watch a practice presentation and give feedback on board-work, presentation skills, etc. Presentations should be aimed at a general mathematical audience.

Mentors need to contact the DRP committee if something goes wrong, e.g. the student does not show up to meetings or is not putting in enough work or does not want to continue the project.

Organizers should decide on explicit guidelines and expectations for students and communicate them with a handout and possibly an orientation session. Here's a (slightly outdated) sample from UT Austin. Common guidelines are as follows:

At most programs, students are expected to do 4 hours per week of DRP related work and (in addition) attend a 1-hour meeting with their mentor. Your program should decide on a required time commitment and communicate this clearly to students when they apply, so that they are not unpleasantly surprised after being selected!

A DRP is a reading, not a research project, the goal is to read and understand a selection from a book, or occasionally one or more articles.

At the end of the semester, students prepare a final presentation (~15 minutes). The presentation is not meant to cover everything from the project and should instead focus on specific a specific theorem or example or application. You will need to submit a title/abstract to the DRP committee. Students should consult with their mentor as they prepare and should give a practice talk to their mentor and receive feedback.

Students should communicate with their mentor or the DRP committee if they are unable to meet these expectations. Failure to do this could prevent the student from participating in the DRP in future semesters.

Books should be selected to match the level of the student. Keep in mind that some students may be inexperienced at reading a math text. Since the student will be primarily working through the text by themself it may help to choose a book with some exercises. Some programs have grad student mentors propose books ahead of time and match mentees with them, in some book selection is a discussion between mentor and mentee after they are paired. The former approach seems to work well in smaller programs.

• See resources page for collections of book lists from local programs.

• The AMS student math library is a collection of undergrad--accessible texts.

• Keep a record of past books from your own program (see data collection below) that mentors can use to help them come up with ideas.

• Some programs have a DRP library: a collection of DRP/department owned books suitable for projects. These can even be kept on public display if there's a suitable space as a way of advertising the program.

• See also Getting started for ideas on funding books.

See the "funding" section on the Getting started page.

The presentation is an opportunity to showcase what the students learned during the project. Each student gives a ~15 minute presentation with time for questions after each talk, and there is food. Ideally this event is attended by all the students, mentors, the DRP committee, and the faculty advisor. It is great if you can also encourage others to attend, especially undergrads (this is a great way to advertise the program).

Some programs schedule presentations in a department colloquium time slot, with great success!

It is a good idea to be strict in enforcing time limits (e.g. 13 minutes for presentation and 2 minutes for questions), especially if there are many presentations. If there are a lot presentations, it may be desirable to split the event into two days.

The Stanford DRP has written presentation guidelines for their students.

Mentors play an important role: they should give guidance on how presentaitons work and give feedback on a practice run (or two or three). Often this is the first time an undergrad will be talking about math at a board in front of an audience and an important part of a DRP is building this skill and the confidence to do it.

It's a good idea to collect information at the end of the projects from both students and mentors. This can help future semesters run smoother and help the program evaluate if its meeting its goals and serving its intended audience. Some possible questions to ask are:

• Name of project/student/mentor/book

• Rate the book for suitability for future DRPs (and rank the level: beginner/intermediate/advanced)

• Was the project interesting? Appropriate level? Would you recommend it for a future DRP?

• Demographic data: gender, membership in underrepresented groups, etc.

• For mentors: Did your mentee put enough time into the project? Would you recommend them for another DRP? (if your program takes students more than once), any other comments on the mentoring relationship?

• For mentees: How was working with your mentor? Do you think you put enough time into the project? Did you find the final presentation (or the process of preparing the presentation) useful/valuable?

• Did you find the orientation session (if you had one) or training, info handout, etc. useful? What should be added to it? [If you didn't have a training session, consider asking mentors and/or mentees if they retrospectively would have found some kind of orientation useful, or ask what they wish they knew going in]

• Did the DRP experience change how you think/feel about math, do you think you'll pursue more things like this in the future.

You can a sample form on the Resources page.

The DRP committee should aim to recruit new committee members each year to maintain continuity. It can help to have specific roles on the committee (website manager, event organizer, finance person, etc) and to train new committee members for specific tasks before older members graduate.

• Continuity is a challenge because of grad student turnover. Consider documentation and taking on new co-organizers each year who can continue for several years.

Role of Faculty mentor:

• not too heavy handed -- we believe DRP is best if "owned" by the grad students

• year-to-year continuity (remembering what worked/didnt 5 years ago), and keeping a repository (dropbox file, google drive) of info.

• aiding with the admissions process

• resolving or consulting on challenges, such as mentor-mentee relationship issues

• a point-person for navigating department funding

• possibly give input on applications

• good to have a standing 2x/semester check-in meeting, at minimum