€ Mini-research paper, usually involving an interesting (and entertaining) application of calculus or linear algebra

These are at least five pages long. Students are highly motivated to do this assignment as it helps them review for their senior comprehensive examination. I used to have students do this assignment in groups of 2 or 3, but now have them do the assignment individually as it provides better practice for the real thing, the research paper. I have the students peer review these. See Research Project Guidelines for more information.

€ Reaction papers on readings such as Paul Halmos's "Mathematics as a Creative Art"

I usually require only one of these, but would require more if we had time because the papers always are so wonderful! I require only one page, but usually get more. No revisions. See Research Project Guidelines for more information.

€ Formal research proposal

These are 3-5 pages long. I always intend for the students to do just two drafts; they usually end up doing 3 or 4 drafts! This is not because their writing is poor, but because they just haven't thought enough about their projects. We start these with some in-class free writing, followed by a discussion about how to get started on a paper, how to overcome writer's block, etc. During my most recent incarnation of the course, I used tiny bits of class time throughout the semester to discuss grammar and slightly larger bits of class time to discuss reader expectation theory (which is exactly what it sounds like), but don't know how much class time I'll use for this in the future. See Research Project Guidelines for more information.

€ At least 3 preliminary research reports of 3-5 pages each

I require students to prepare the research proposal described above followed by preliminary reports so that they will get started on their research projects early and then work on them steadily throughout the semester. Reminding students that their preliminary reports will become parts of their final papers and that early feedback from me and from their peers will help them write better final papers seems to motivate them to prepare these reports conscientiously.

For one of these preliminary reports, I have students review one another's written work. Unfortunately, there isn't time to have them peer review all three preliminary reports. (Students do get frequent feedback from one another on their mathematical work during three or more preliminary oral presentations of their research.) My experience has been that the seniors give each other much constructive criticism as well as much encouragement on both written and oral work without much prompting from me!

See Research Project Guidelines for more information.

€ Abstract for the formal research presentation

These are only a paragraph long, but writing abstracts is an important skill. See Research Project Guidelines for more information.

€ At least 2 drafts of the research paper (usually 3 drafts, 20-30 pages each)

A 20-30 page paper is quite long for a mathematics paper. See Research Project Guidelines for more information.

Beery: 1/93, revised 5/96