M.I.T. professors Michael Artin and Haynes Miller developed the Project Lab in Mathematics, which was offered for the first time in 2004 and which has been refined by subsequent instructors.

Students work in teams of three on problems such as “If the reciprocal of a prime has a repeating decimal expansion, what can you say about the period with which the decimal repeats?” Each team works on three such problems during the term, collaboratively writing up their results from each project and presenting one of the projects to the class as a whole.

### Semester schedule

The first class is devoted to choosing teams and first projects. The next three class meetings provide guidance for teamwork, writing, and presenting. Thereafter, classes are devoted to student presentations.

Teams spend about 5 weeks on each project, with a week of overlap at the transition between projects. During this week of overlap, course staff read and provide feedback on a draft of the preceding project’s paper while students start thinking about the next project. Students then revise the paper before turning all of their attention to the next project.

### Logistics

There are typically 9 teams and 3 team mentors: each team meets with their mentor once a week and is expected to meet on their own as well. Teams submit a draft of each paper to receive feedback and revise before submitting the final paper for that project. Similarly, each team gives a practice presentation and receives feedback before presenting a project to the class. The feedback is provided by the team mentor and by a lecturer from M.I.T.’s Writing Across the Curriculum.

To simplify logistics, the class is advertised as meeting twice a week. The entire class meets on only one of these days; the second day is reserved for practice presentations (in the classroom) and for team meetings.

To ensure good presentations, a particularly strong team should be chosen to give the first presentation and set the tone for the term.

### Support for teamwork

Each term, at least one of the 9 teams is likely to experience some team friction. To help teams through such rough spots, various strategies are used to support teamwork.

In addition to the teamwork workshop at the beginning of the term, the following strategies have been used with some success:

- At the start of the term, we advise students to choose teammates who
- Are interested in working on the same projects: the primary predictor of team success is shared commitment to the team’s goal.
- Have compatible meeting times.
- Have compatible “procrastination indices.” Each person’s “procrastination index” is the answer to the following question (idea by David Jerison):

If you have a 10-page paper due at midnight on Thursday night, when are you likely to start?- 1: the preceding weekend.
- 2: Monday or Tuesday.
- 3: Wednesday.
- 4: Thursday before 7pm.
- 5: Thursday after 7pm.

- A third of the way through the term, after the completion of the first project, teams have completed a short team communication exercise at the end of class. Each student writes “A Wish and A Star”: one thing that the student wishes the team did differently, and one star for something that the team is doing well. Students then read their teammates answers and have time to talk about them if they like.
- When a team mentor becomes aware of significant issues with the dynamics of a teams, the mentor consults with the lead instructor and the communication instructor to develop a strategy, and then works with the team to resolve the issues.

### Publications

- A description of M.I.T.’s Project Lab in Mathematics is available on page 7 of the 2009 newsletter of M.I.T.’s Department of Mathematics.
- S. Greenwald and H. Miller, “Computer-assisted explorations in mathematics: Pedagogical adaptations across the Atlantic,” in
*University Collaboration for Innovation: Lessons from the**Cambridge-MIT Institute*, edited by D. Good, S. Greenwald, R. Cox, and M. Goldman, Sense Publishers, 2007, pp. 121–131.