PDEs Course: Wrap Up and Reflection

I haven’t been posting much because of the busy-ness of last semester. Now that grades have been submitted, I’ve been reflecting on the partial differential equations (PDEs) course that I taught. (All previous posts about this class can be found here.)

I firmly believe that we must evaluate our own teaching if we want to improve, and that one of the best ways to gather data on our teaching is to ask our students. Students aren’t always the best judge of how much they have learned, but I trust my Mudd students’ ability to tell me about their experiences and opinions about the course. Here is what students said in their comments on an end-of-semester evaluation survey.

Comments about students’ perceptions of the course and their overall experiences:

I really appreciate your comments at the beginning of class that you realized that most of the applications you were planning on presenting were thought up by dead white guys and that that might cause some people dismay. I think that recognizing that that’s a problem in math/science that permeates into classrooms is important, and you saying that out loud helped me feel more like I belonged in the classroom even if I am not a white male.

This class somehow made me enjoy solving PDEs even though the past three DE classes I’ve taken convinced me I just really hate DEs. Nice job.

I started solving random PDEs in my free time, from which I deduce the class was pretty interesting.

I also want to thank you for being such a dedicated teacher. Your lectures and notes in numerical analysis and PDEs were effective in delivering material and it never felt like there was anything “hidden” about the subjects that I couldn’t figure out without some closer reading. I also think that the structure of this class was awesome, because it encourages you to learn all aspects of the subject, even if you missed that specific part of the semester.

I feel that [Prof. Yong] is extremely understanding and is very approachable to students, regardless of how comfortable they are with the material.

Overall, I noticed that student engagement was high. I was really pleased that I was able to change some students’ opinions of differential equations.

On the end-of-course survey, I asked students to indicate their affinity for the following statements on a scale from 1 (strongly disagree) to 5 (strongly agree). (A total of 32 students responded to the survey, though not every student responded to every question.)

  • “The students and instructor for this course created a welcoming community of learners.” Average response: 4.59 / 5
  • “In this class, I was able to express myself (whether it was to answer a question, or to say that I didn’t know how to do something) openly without judgment or ridicule from my instructor.” Average response: 4.81 / 5
  • “I generally felt secure and confident to speak in this class (to answer a question or ask a question or something else) when I wanted to.” Average response: 4.44
  • “I feel secure and confident to speak in my classes at Mudd in general.” Average response: 4.13 / 5
  • “I feel like an outsider in this class.” Average response: 1.68 / 5
  • “The instructor was respectful to all students in the class.” Average response: 6.91 / 7

Student comments about the proficiency assessment system:

Since the proficiency assessment (PA) system was a big change for me and students, naturally there were lots of comments about this part of the course. I tallied up all of the types of comments that I received about the system:  16 favorable comments, 4 negative comments, and 1 mixed comment.

Here’s a selection of the positive feedback:

The proficiency assessments are spot on in encouraging learning–I feel like I’ve learned from them while satisfactorily representing my understanding.

I’ve never had a class where I could schedule tests like this one, but wish I had! I have gotten a lot out of this freedom to prepare when I have time, and to take more advanced versions once ready for them.

Also, there seems to be the philosophy that students deserve credits when he/she knows how to solve the problems and not only when he/she can solve the problems within the exam time. I feel like this grading philosophy is more applicable to the work in real life.

Since I could take it many times, I didn’t care much about getting the right answer. Instead I was able to focus more on improving myself each time I take the PA.

I like how the proficiency assessments encourage me to understand the material at my own pace in a less stressful way.

There were several classes that I’ve taken at Mudd where I didn’t learn the material by the time the exam came, and so there was no reason for me to learn it afterwards. I also like the ways in which [the PA system] discouraged cheating: since you have the opportunity to retake exams, there is less of an incentive to be dishonest about it. For me it was also great because it meant that it was never too late for me to try to catch up. One of the most depressing situations that I encountered at Mudd was having several exams during one week and feeling like I could have performed better if the schedule had just worked out differently. I personally think that your curriculum is the right direction for a lot of the classes at Mudd, so thanks for being willing to try something new out.

On the whole, I think I was able to meet my objective of coming up with a system to assess students’ understanding but in a way that gave students more agency and flexibility, and that promoted students’ growth mindset about learning PDEs.

On the end-of-course survey, I asked students to indicate their affinity for the following statements on a scale from 1 (strongly disagree) to 5 (strongly agree).

  • “The proficiency assessments fairly assessed my understanding of PDEs.” Average response: 4.56.
  • “I was able to demonstrate my understanding of the course material through the proficiency assessments and final exam.” Average response: 4.50

I will definitely use this system again in the future, but I need to figure out how to reduce the impact on my time and on students’ time. Also, I need to think more carefully about how students’ grades are calculated based on their assessment scores.

I ended up writing four sets of proficiency assessments, on four different subtopics. There were standard and advanced assessments for each subtopic. The maximum score attainable on a standard assessment was 23/25, and the maximum for an advanced assessment was 25/25. The standard assessments contained tasks that I would have used as final exam questions, and advanced assessments contained more challenging tasks that involved novel situations or challenges that they had not encountered, but that they could if they dug deeper into the course content. My rationale for this arrangement is that a standard level of attainment would correspond to a 92%, which in my mind is an A-. To get an A in a course, I feel that some effort above and beyond the normal set of expectations is required. I required students to reach the standard level of attainment before attempting a more advanced PA. This had the effect of requiring students to take at least eight separate assessments, if they wanted to get an advanced level of attainment for all four subtopics.

I’m really mixed about the PA format. On the one hand, I think I’ll probably have learned the material better than usual by the end of this course, simply because I’ll have had more tests on the subject scattered throughout the semester. However, I also feel like the PAs took up so much time (both for the student and the instructor grading them) that they caused more stress than a midterm would have.

I feel that the course had too many disparate requirements. The presence of PAs, homeworks, a final test, and a final project made it an overwhelming experience. I would advocate for a more efficient PA system that doesn’t require as much time outside of class, since the current PA system feels more like it’s testing students for how much of their free time they can sacrifice as opposed to their actual knowledge.

I liked the concept behind PAs, but found it somewhat annoying that in order to get full credit on all of the PAs you would have to schedule 8 different time slots. One idea I had to ease up on this sheer time commitment would be to have on each PA the option to choose between the 23 point problem or the 25 point problem.

I don’t feel that the PA system ended up fairly assessing my understanding. I feel that they got close to providing a good assessment, but with the time restrictions I’ve faced this semester, I was unable to take the advanced PAs. I had a very busy schedule this semester, and I was sick for multiple weeks in the middle of the semester, so I didn’t get to take my last regular PA until the end of finals week.

I got perfect scores on the 3 PAs I’ve gotten back so far, and I suspect I also did perfectly on the last PA I took this morning. But I just didn’t have the time to attempt the advanced PAs, especially given that my score isn’t even guaranteed to increase, so it was very hard to justify adding something else into my already exhausting schedule. I feel that I have a very strong understanding of the material, but my time restrictions only allowed me to demonstrate a “basic” understanding.

Personally, I feel that scheduling time for four 90-minute assessments isn’t a huge burden on students, but some felt that way. One thing I will try in the future is to set aside some class time for students to take the proficiency assessments, so they aren’t required to use out-of-class time.


Overall, I’m really pleased with how the course went, even though it was my first time teaching the course and I was experimenting with lots of new ideas. I was trying to attend to students’ sense of belonging to the class all semester, and I think I was successful at that.

I consider the proficiency assessment experiment to be a strong success. I want to continue to refine and improve it. One important side effect of the proficiency assessment system is that I got to know all of my students much better than I normally would have. Another side effect is that the system enabled some students who would probably failed the course otherwise to pass and do well. For example, one student who had some family issues and was absent for almost 2/3 of the class was able to finish the course on time.

3 thoughts on “PDEs Course: Wrap Up and Reflection

  1. Hey Daryl, it’s Matt Engle from PCMI. Just want to say that I’m super excited to see this type of assessment being considered at the college level! I am really intrigued by your system and I’m looking forward to seeing more posts about it later. It just makes so much more sense based on how people learn. Is this something others are using or did you come up with this particular system yourself? I’ve just bookmarked your blog, I’m working on starting my own up and it should be up in not too long…

    • Definitely didn’t come with it myself. I was inspired by folks using standards based assessment, or criterion referenced assessment. Yes! Would love to read what you are up to these days. Let me know when you’re started your own blog!

      • Okay so it’s been like four months but I finally have my blog up! I’m still working on the rest of the website, but you can check it out at gogrowmath.com/blog. The resources menu has a page describing my grading system, which I’m about to update soon. I’d love it if you check it out, I haven’t had anyone read it yet that I know of, and I’m not sure how to have people on the MTBoS actually look at it haha.

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