My online search for writing intensive mathematics courses yielded many results. However, I found the vast majority of them to be statistics courses (there were a few mathematics for business courses and one geometry course). Further, many of the courses had writing assignments that basically asked students to explain in words a mathematical problem that they had solved. While I see the value in doing that (the ability to communicate what one does mathematically is important and the exercise might even make clearer in our own minds the work we are carrying out), these assignments didn’t feel like they were enough to me. We have in our seminar considered the idea of writing to learn in our discipline but also what writing is and looks like in our discipline. I was hoping for a course with assignments that fostered good mathematical writing, valued revision and taught students how to write as a mathematician would write. Then I came across a syllabus Math 341: Probability and Statistics II at Carrol College in MT and an article written by a professor in that school’s mathematics department explaining not only the assignments but the motivation behind them. Writing in this course was not just a way of proving what you knew, not meant only for one’s instructor to read, and actually went beyond reflecting on a problem. The document notes, “the point of good mathematical writing is to write simply and plainly, to take a complex idea and explain it with clarity” and that the course intends to prepare students to write in this manner.
There are three main writing assignments. The course emphasizes peer review and begins by having students read papers from the prior semester’s course. The students in that prior semester know that their papers may be read by the next class of students and that since they are doing so early on, their familiarity with the statistical concepts learned in the course will be minimal. As such they are pushed to write in a manner that is clear and that makes complex ideas simple – simple enough for someone without a thorough grounding in this mathematics to follow. The students in the course read these papers and rank them highlighting the strong and weak aspects of each. The professor notes that this exercise helps students focus on what good writing in the discipline is not by being told what it is but by discovering it through the examination of these papers. This assignments also reminds me of the peer review process. In discussing and writing about these papers students learn how others might view their own papers.
The second assignment is a statistical survey. Students select any topic of interest to them and create a survey that they then administer to a large population. Large is left to the student to define as it is important mathematically that one knows when a sample might prove too small or flawed in other ways (ie. finding the average height of york college students by surveying the basketball team). Students then analyze their survey data using statistical procedures learned in class. Finally they write up their findings much in the same way as researchers would write up the results of their work to be shared with a broader audience. The third assignment is similar but involves a controlled experiment. The student develops a question to study, gathers a sample, randomly divides the sample in two groups, treats these differently in some way and the analyzes statistically the differences, if any, between the groups. Again, the findings are then written up in a paper.
What seems most useful to me about these assignments is how often researchers do just this. That is, the assignments ask students to do what those in the field do: to share results obtained using statistical measures in a way that is understood by a wide enough audience. Knowledge of the mathematics (or lack their of) comes through in the assignments even though these are not limited to having someone write up an explanation of a problem they solved. The assignments seem authentic somehow. The syllabus notes “mathematical writing is an essential skill for any mathematician, whether in government, private sector or an academic career” and the assignments seem to push students to develop this skill.
Finally, the syllabus notes that students revise the assignments they write a number of times drawing on feedback from their peers, their instructor and even themselves (there are revisions that are submitted after a student writes a critique of their own work, for example).
