PDEs Course: Progress Update #4

Proficiency assessments (PAs) are proceeding nicely in my partial differential equations (PDEs) course. I’m posting some of the logistical details here in case it helps other instructors. PAs are my attempt to allow students more flexibility in demonstrating their mathematical proficiency in my class. I wrote more about my intentions behind these PAs in this post.

First of all, I’ve reduced the number of PAs from 5 to 4. Here are the four PAs for this course:

  • Be able to solve a first-order PDE using the method of characteristics, in both linear and nonlinear cases. (Nonlinear PDEs may involve shocks.)
  • Be able to use the separation of variables technique to solve a homogeneous PDE problem.
  • Be able to solve an inhomogeneous PDE problem using an appropriate change of variables, or the eigenfunction expansion method.
  • Be able to use integral transforms (Fourier and Laplace) to solve PDE problems involving infinite or semi-infinite domains, and be able to identify how general solutions are convolutions involving Green’s functions.

The initial list of PAs was created while I was still constructing the class and once I got deeper into things I realized that one of the things that I listed on my previous list was better assessed on the final examination.

Scheduling 40 students to take these assessments has been a bit of a challenge, but I think we’ve solved that problem. Each PA is supposed to be completed during a 90-minute session without notes, calculators or outside assistance. But, students can use more than 90 minutes. That time is just a suggestion for the length of time to block out in their schedules.

I’m not terribly worried about cheating because of the strong honor code here at Harvey Mudd, but I want to be careful since the assessments can be taken at any time and I don’t want copies of them floating around. So, I needed to find a way for students to make appointments to take a PA. With the help of the students, I came up with this mechanism for taking PAs. There are four different ways to schedule an appointment:

  1. Students can email me to set up an appointment. I have a calendar online so students can see when I have open blocks of time when they can sign up for an appointment.
  2. Students can also contact our department administrative aide to make an appointment during business hours (Mon-Fri).
  3. I have two graders/tutors for this course and they have additional tutoring time on Wednesday evenings. Students can arrange to take a PA under their supervision.
  4. Finally, a group of students can get together and arrange to take an assessment together, at any time, even nights and weekends. These “group-proctored” sessions have turned out to be the most popular so far. I make arrangements to leave the assessments in some secure place, then they put the completed assessments in an envelope and slide it under my door if I am not at work at that time.

Some of you might be skeptical about students taking an exam/quiz on their own without supervision. it really does work here at Mudd, though. When students want to set up a group-proctored session, I also email the entire class to let them know about the opportunity. That gets groups of students together who aren’t in the same friend groups, so there is a bit more accountability.

So far, I’ve been meeting with each student after every PA to talk briefly about her/his performance. It is taking a lot of my time, but I really like having that personal connection with every student. I have far more information on how well each student is mastering the material than I have in previous classes.

Finally, I’m also really enjoying starting every class with 2-3 minutes on some cool application of PDEs: traffic simulation, tsunamis, bread baking, digital image restoration are some of the more interesting ones so far, in addition to the usual diffusion, advection/convection, Laplace problems. Students seem to really enjoy it too. If you have have more cool applications of PDEs to share, please let me know!

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