Fall Break fantasy

As I make my way through the stack of grading I've set up for myself over Fall Break (it's not so bad, spread out as it is over four days), I can't help but fantasize about a course that will likely never be.

Let's call it MATH 301: Introduction to the Philosophy of (Mathematical) Feedback.

Audience? Math majors.

Prerequisites? Calc I, Calc II, Calc III, and MATH 280 (Introduction to the Foundations of Mathematics).

(Stated) purpose? To introduce math students to the important role played by written feedback on various assessment instruments given by the instructor to her or his students.

(Unstated) purpose? To offer a pool of qualified instructors to assist in the grading of homework, quizzes, and exams.

Let's face it: a public school the size of UNC Asheville simply does not have the resources to provide support for student graders for all of its calculus classes, and it's not likely that any of our majors are going to simply volunteer themselves as unpaid class lackeys, however rewarding the tedious experience might ultimately prove to them.

The solution? Offer a one- or two-credit class in which the students enrolled would first be trained in the offering of appropriate, effective, and meaningful feedback on a number of different assessment tools (homework, quizzes, and exams), before being unleashed on actual course work provided by the department's various instructors.

I envision three or four weeks of training, on topics including appropriate writing style; interpreting students' writing; common concerns, mistakes, and missteps; the basics of evaluation; and advanced grading philosophies (partial credit, curves, revision opportunities, feedback on qualitative work). Some of the training would take place through lecture, but much of it would be hands-on, in a "workshop" environment. The students' homework for the first few weeks would include sample grading of artificial homework and quizzes, as well as short papers on the various philosophies underlying grading and feedback.

In the weeks following the first few, students would be considered qualified to serve as graders for any of the following courses: Calc I, Calc II, Calc III, Precalculus, STAT 185, and Nature of Mathematics. In order to "earn their hours" for the course, students would be expected to meet for one (or two?) hours per week in order to grade together, sharing their travelers' tales of problems encountered as they offer feedback to their less-experienced peers. Of course, such "grading parties" could serve incredibly effectively as social events, and students in the course would be encouraged to meet in this manner on their own time, more often than is required.

Would it be a required course? Probably not, but as it would be most meaningful for those intending to pursue teaching or graduate school careers, maybe we could require it of the students in the Pure and Licensure concentrations.

If it weren't for the relatively light writing load, the class could even qualify as a writing-intensive course, so rich a picture of mathematical writing does it offer the enrolled students.

I really think it could be a rewarding experience not just for the students but also for the instructor who provides the training, and clearly for any faculty who take advantage of the resulting pool of student graders.

They may say I'm a dreamer, but what the hell, why not dream?