In my upper-level courses — especially the two senior-level math majors courses I teach, Modern Algebra and Topics in Geometry — traditionally I’ve seen timed tests and so forth as being ineffective in assessing the kinds of advanced problem-solving that students in those classes have to do. Mainly the problems are ones in which they have to prove a theorem. It’s hard to do that under a time pressure because it’s a creative endeavor.
So typically I’ve given such problems out as homework, with the instructions that students may work together on understanding the problem and drafting up a sketch of the solution (Polya’s stages 1 and 2) but the main solution itself, as well as any reality-checking, has to be done individually.
This article from the Harvard Crimson from a year ago captures exactly what I wish this process would look like on the students’ level. The article is about Math 55, called “probably the most difficult undergraduate math class in the country”. How do these students handle the homework in this class, which is assigned frequently and hits like a ton of bricks?
Georges Bizet’s Carmen blares from the computer of Menyoung Lee ’10. The boys sit scattered around their gray worktable, their eyes telltale red and fingers sore from countless hours at their laptops, dutifully LaTeXing problem sets. They have been here since 2 p.m. and will work for almost 12 straight hours to complete the problem set due the following day.
As the hours pass, they discuss the problem set. They formalize and write the solutions on their own for academic integrity. Despite the class’s cutthroat stereotype, this session is about community, not competition. [emph. added]
They work hard as a group — they have to — but when it comes time to actually write the solution, they voluntarily break off to work the solution out on their own, because they have a sense of academic integrity. It’s a community, but not a commune. Nobody is taking anybody else’s work and turning it in as their own, because I suppose they have pride in their work and in their abilities. As far as I can tell there are no timed assessments in Math 55 to hold them individually accountable.
I wouldn’t want my Geometry and Algebra classes to be as hard as Math 55, but I’d love it if students would have a solid sense of the correct point when working together on problems needs to stop and individual work needs to begin, and then make that switch from group to individual work as a matter of personal ethics and an understanding of what it means to learn a subject. And I’d love not to have to shift assessment of problem-solving over to timed tests as a result.
Do students in high school and certain college courses where group work is stressed more and more frequently understand that this point exists?