Post-midterm musings

Today, I gave a midterm to my undergraduate class; I proctored it via a videoconferencing tool. Near the end, a student was red in the face and looked visibly upset. He conveyed that he was frustrated because he’d studied so hard and this was even harder than the previous exams.

I’ve had this kid in office hours; he’s one of the most diligent attendees. His questions reflect some surprising and pretty serious gaps in preparation. I am not sure how to help him except plug a hole once it becomes visible. But his facility with algebra, trigonometry, and calculus is just not high enough for him to be able to do well in this course, plus I don’t think he’s getting the concepts that well either; my guess is that spending too much energy being bogged down in the weeds of highschool math that he doesn’t have enough CPU cycles left to process the higher-level stuff. In this major, and this course in particular, you cannot be getting tripped up on the cosine of an angle plus pi/2, or struggle with performing a vector product. These need to be done lightning fast, so you can actually get to the good stuff.

I do explain what I can. When I identify a bigger gap in understanding, I try to go back and do my best to plug it. But, with many students, it’s like trying to keep water inside a colander: the holes are too numerous and, try as a I may, I cannot close them all.

Mostly I’m sad for students who struggle so much. There have been bimodal distributions of grades in undergrad classes pretty much since I started working here. Older faculty say it wasn’t always like that, that distributions used to resemble the normal one much more. These days we do have two modes, on either side of the mean, and there’s nothing but tumbleweeds where the mean is.

Another issue I try to help with when I can, but often cannot, is “I worked so hard.” There are infinite ways of spending a lot of time on little learning gain. If a kid comes to office hours, and he or she is struggling, we talk about learning strategies and test-taking strategies. Maybe it helps. What doesn’t help is that the students in our major tend to be extremely busy, so I wonder if they have the time to really let the material sink in. Then again, I also felt that time moved very slowly when I was that young. Maybe times have changed, or I’m misremembering, or both.

How’s your weekend going, blogosphere? This weekend, I’m looking forward to catching some well-deserved zzzzz, and then I will grade.


  1. Sounds like the student needs to spend some quality time with khan academy over break.

    I’m currently at a virtual conference working on my discussion for my panel tomorrow. There’s so few people at each of these sessions that I’m wondering if it’s worth putting any effort on the discussion at all given that the paper is already forthcoming. Still, I would rather be discussing a very nice forthcoming paper than be in the situation of the discussant on our panel who got an email saying there wouldn’t be a paper, but maybe the discussant would come up with something to say while watching the talk at the conference.

  2. I teach electronics to biomolecular engineers—they not only have the attitudes of biologists towards math (that it is a mystery best left unexplored), but they don’t see why they’ll ever need electronics.

    The math I use in the electronics class is much less sophisticated than that needed even in freshman physics (I do one optimization with derivatives, and we take derivatives of e^(j 𝜔 t) with respect to time to derive the formulas for impedance), but almost all their work just involves algebra with complex numbers and fractions. Even so, the inability to do simple algebra (like solving a single-variable linear inequality to change a current constraint into a resistance constraint) really holds them back.

    They’ve also been trained in lower-division biology and chemistry classes to think that learning consists of memorizing and regurgitating. This makes doing a design course that combines calculation using complex numbers and 7th-grade fractions with design problems that are underconstrained and so have multiple solutions very frustrating for them. Requiring them to write their design reports in good English with proper punctuation also challenges them, as does responding to e-mail from their lab partners.

  3. “Requiring them to write their design reports in good English with proper punctuation also challenges them”

    Grading reports on simulation projects makes me want to nuke the k-12 system.

  4. Now that my 3rd kid is in 4th grade (i.e., my long-term study has included N=3 subjects), I can with confidence ask: Who the fuck checks and corrects the kids’ punctuation and grammar, and when/how exactly does it happen? Because I keep waiting to see corrections on the kids’ assignments, and I just don’t. I guess they’re supposed to learn by reading books? Is it happening in some secret places and in secret ways that are invisible to us parents through the kids’ assignments? Or — more likely — it’s just not happening. Now that we’re at home, I have more insight than I ever wanted to have into the daily schoolwork in 4th and 8th grades, and I can tell you that nobody except me seems to be correcting anyone’s grammar or punctuation.

  5. @xykademiqz, I think that the at-home, online education has been eye-opening for many parents. I suspect that we’ll see a big rise in faculty either home-schooling their kids or seeking private schools (though, surprise!—the private schools aren’t really any better on average than the public schools, just more expensive).

    We had only one kid, who is far from typical, so I doubt that many parents will find the path we took useful for their kids—it involved public school with literacy instruction in Spanish with native Spanish speakers (already reading well beyond grade level in English, learning Spanish for the first time), 3 years of private school, 2 years of a different private school, 1 year of public high school, then 3 years of home schooling (with lots of outside providers: the high-school transcript ended up with 13 different providers, despite our providing some of the core instruction).

  6. @xyk DC1 and I have been wondering that ourselves. English is such a joke that I’m being a bad parent and saying things like, “Don’t spend more than two hours on that blog post about why you’re thankful because you’re going to get a bad grade on it no matter what. Oh, and remember to put some pictures in because she likes those.” And I don’t know what I could do to get him practice either, other than making him write essays for me, which, who has time? i guess technically DH does, but he is best at a specific flavor of technical writing.

    They write so many fewer essays than I did in high school. I vaguely recall that writing across the curriculum was “in” when I was in high school so I got a lot of essay practice from Spanish, History, etc. We even had to write the occasional essay in math.

    DC2 is getting a lot more instruction from her fourth grade teacher this year, but I think that’s just because her fourth grade teacher is awesome. Still, there’s not as much correction on free-style writing as there could be. I think there’s a belief that correcting spelling and grammar hurts children’s creativity, but if points aren’t taken off I don’t see the harm. DC2 would certainly like to write Spanish better.

    And to be completely honest– I see so many typos, misspellings, and straight up grammar errors in the stuff my kids’ teachers put out on schoolology that I’m not convinced that they all know how to write themselves.

  7. Just tell your kids to spend some time on Khan Academy’s writing instruction and this can all be sorted out.

  8. Yeah, bimodal distributions in intro/sequence classes is hard… I just redesigned our intro physics course to hopefully help some with that, and our major is doing a LOT of outreach to advise students into more math classes earlier. For school with more instructional resources (I’m at a SLAC), I think I am on the side of pre-test and track students into a suitable intro course plan… My large state school PhD program did this for engineering students with poor math backgrounds – their intro physics course had twice the contact hours as the regular one to help get them up to speed. It did help increase the diversity of students who successfully completed the engineering major, but I don’t know if it resolved bimodal grade distributions.

  9. I think students are fortunate if they have an instructor who can tell them “you have not yet mastered concepts XYZ to the level required for success in the subject matter.” That helps narrow it down from “math” to something more actionable. I certainly had a hard time identifying specific topics that I was weak in, and most of the feedback I would get about my weaknesses was often more along the lines with “it’s ok, some people struggle with this topic, maybe this isn’t for you” than “you need to master these 5 topics if you want to succeed in this class.”

    This is only somewhat related, but few years ago I volunteered as a tutor at a local “inner-city” high school (it seems strange to type that but it’s accurate). The girl I was tutoring was struggling with algebra, and it was clear that her more fundamental issue was that she never mastered negative numbers. So she could do some of the introductory algebra problems and seemed to understand the concepts, but when it came time to manipulate negative numbers she got things wrong.

    During our tutoring sessions, I started giving her lists of 20 or so warm-up problems that involved manipulating negative numbers. She could do those on their own, and seemed to be a bit insulted that I was giving her those problems to do, but after this warm up the algebra work went much better. I suggested to the tutor coordinator to give her warm up negative number problems before her test (There was a test she had to re-take). This apparently worked quite well. She was, once again, surprised/insulted that someone would have her do warm-up problems that were so easy, but taking the test after this warm up led to a much improved test score and her teacher was very happy.

    I think what I learned from this is that many students are capable are doing better than they seem to be doing, but it takes a lot of work to figure out how to get there and many places don’t have good systems in place. My university had a lot of peer tutoring. I had to overcome some initial pride to go use it and even once I did, some of the tutors were just bad and would basically just give us answers to homework questions. Some of them were good though, and helped, and some of the tutors were kind and encouraging and made studying more fun. So I think many students can do better than they are doing, but it takes a lot of resources achieve that and there are many pitfalls in the process.

  10. N&M,

    Sorry, didn’t mean anything negative by it, just hopeful/helpful. Khan Academy can do great things for writing instruction. Didn’t realize such a suggestion would be seen as negative.

  11. Anecdotally, remote learning seems to lead to even less success for the students who would normally struggle. I teach a soft social science methods class with some VERY basic data analysis–I’m embarrassed to tell you hard science types how basic. But some of my students are really intimidated by any kind of formula and by using Excel. This year they’re even more lost. Only two people showed up to my optional but heavily advertised (and usually heavily attended) “excel bootcamp.” The others just forgot, I think, or maybe they didn’t have the bandwidth for another hour of zoom. It was also harder to help them during the lab. Usually I bop around the computer lab looking at what everyone is doing. This year they took turns sharing their screens when they had questions but was harder for me to point at things that way and I somehow couldn’t get to as many people. I really like some aspects of remote learning and think I may do some sort of hybrid going forward, but the mathy stuff seems to work better for my students in person.

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