June 15, 2010, 08:00 AM ET
Motivating Students with Application Projects and Poster Sessions
[This is a guest post by Derek Bruff, assistant director at the Vanderbilt University Center for Teaching and senior lecturer in mathematics at Vanderbilt. In prior guest posts, he has discussed the use of multiple-choice questions on exams and using WordPress as a platform for pre-class reading assignments. You can follow Derek on Twitter (@derekbruff) and on his blog.]
In recent years, I've taught mostly "applied" math courses like "Statistics for Engineers" and "Linear Algebra for the Social Sciences." The latter course I took over from my colleague John Mackey a few years ago. John suggested that I have students complete end-of-semester projects that would allow them to explore applications of interest to the students. I took him up on his advice, and, after tweaking the assignment over the years, my application project assignment is now an integral part of most of my courses.
Here's a recent version of the assignment description [PDF]. The final projects take the form of five-page papers and are usually due on the last regular day of class. Below, you'll find my thoughts on a few important ingredients.
The idea is to give students the opportunity to identify a "real world" problem they find interesting—for personal or professional reasons—and try to solve it using mathematical tools from the course. Since my students are often not math majors, I encourage students to find problems from their "home" disciplines. These projects need not be original research; describing problems that have been previously solved by others is fair game, too.
Here are some topics chosen by recent students.
- Optimizing student satisfaction with housing assignments (using linear programming)
- Determining if two samples of text are written by the same author (using Markov chains)
- Finding correlations between the amount of sleep students get and their GPAs (using linear regression)
- Predicting rates of growth or decline in populations affected by HIV/AIDS (using discrete dynamical systems)
- Recreating Windows screensaver animations (using linear transformations)
Giving students the freedom to select topics of interest helps motivate the students to work hard on these projects. I've had students select topics that seemed deadly dull to me (e.g. properties of different kinds of concrete) that really energized those students. I've also had students go above and beyond in collecting data for a project of personal interest, like the student who poured over inventory data from the college apparel shop where he worked in order to optimize inventory storage space. I've also had one student expand his application project into a larger study that was published in a political science journal.
After my first semester implementing these application projects, I felt that it was a shame that I was the only one to see the good work that my students produced. Since then I have almost always had my students create posters for their projects and share them during a poster session on the last day of class.
Since the students work on their projects in pairs (because they produce better work this way and because doing so gives me more time to provide useful feedback), I have one member of each team stand with his or her poster while the other team member checks out the other posters. Halfway through the class session, the team members switch roles. This means every student has the chance to explain his or her project and to check out the other students' projects.
This is a great way to wrap up the semester. In order to give students a reason other than curiosity to check out their peers' work, I award three prizes for the posters based on student votes: Most Interesting Application, Most Sophisticated Mathematics, and Most Attractive Poster. Winning teams receive 5 extra points on their final project grades. I always have at least a few students who take that last prize very seriously and produce very attractive posters!
My first semester using application projects, I didn't require students to turn in any kind of rough drafts. When I graded their projects, however, I realized that for some students, five minutes of advice from me early enough in the process could have greatly improved their projects. The next couple of semesters, I required my students to submit rough drafts, but providing feedback on these proved to be incredibly time consuming for me. Instead, I now have students submit proposals a few weeks before their final projects are due.
The proposals are only two pages long and are designed to provide me with enough information on the students' chosen projects (choice of problem, best guess at the mathematical concept needed to solve the problem, maybe a reference or two) for me to give them some useful feedback. My main goals when reading the proposals are to determine if the proposed project is hard enough but not too hard and if the proposed mathematical concepts really are applicable to the project.
I use an analytic rubric to grade these projects. Here's the most recent version [PDF]. I started with a basic rubric with a few general categories and descriptions of poor, acceptable, good, and excellent work in each category. Every semester I revise the rubric after I use it so it does a better job of capturing what I'm looking for. After a few semesters, it was in good enough shape to share with my students as part of the assignment description so they have a clearer idea of what I'm expecting.
Content counts for half of the students' project grades. Clarity counts for a quarter, and other issues like grammar and formatting contribute the other quarter. It's important that students accurately apply their mathematical knowledge to their problems, but it's (almost) as important to me that they communicate their work effectively. In the project description, I tell them to write their papers as if to another student in the course. Research indicates that students often write better when writing for their peers than for their professors. I realize I'm trying to fake this result, but I'm happy enough with the results.
One semester I had almost 60 students in my course instead of the 20 to 35 I usually have. I made a few tweaks to the application project assignment as a result. I didn't think I could handle grading 30 different projects, so after the project proposals were in, I had the students vote on their peers' proposals, knowing that the top four vote-getters would be the proposals from which they had to choose for their final projects.
This American Idol approach meant that each team needed to identify a problem appropriate to the math content of the course (an important learning objective) and each team had the chance to contribute a project idea of particular interest to them. However, I didn't have to grade 30 different projects—just 30 instances of four different basic project types. This made grading much more manageable. Once I had gotten my head around each of the four types, I could fairly quickly grade all the projects that used that idea.
Even better, limiting the final projects to four different topics meant that I felt comfortable handing my grading rubric off to my TAs to help with the grading. I had two TAs that semester, and each one tackled one of the four project types. I double-checked each TAs' work, but only after I had graded the other two project types. By that point, I knew where my rubric was a bit shaky, and I was able to quickly focus on the TAs' interpretation of those parts of the rubric.
It's Not Just Me
Last fall, I tweeted something about my end-of-semester poster session. Robert Talbert, who teaches at Franklin College in Indiana, saw my tweet and asked me about it. I told him about my application project assignment, and he tried it out this spring in his linear algebra course. He went a couple of steps further with his poster session, inviting colleagues from around campus to see his students' work and sharing some photos of the session on Twitter.
@RobertTalbert: "The linear algebra poster session was crazy-fun. People showing up from all over campus! Students did extremely well. Photos/video later."
Most Attractive Poster—A Game Theoretic Approach to Dating
Most Interesting Application—Genetics and Markov Chains
Most Sophisticated Mathematics—Ciphers Using Matrices
What About You? Do you have your students complete projects like these? How do you motivate students to do great work on these kinds of projects? And have you ever tried a poster session in one of your courses?