Grouchy Musings on Teaching, Part 2

I have issues with some of the advanced teaching strategies as I see them implemented in my department. (Flipped classroom, I am looking at you, and all other eggcellent paradigms.)

My main complaint is that the responsibility to sit down and understand the material and work until proficiency is achieved is being taken away from students and moved entirely to instructors. Instead of the students taking ownership for their own learning, we the instructors are supposed to devise lectures to be tutoring sessions (the flipped classroom model), so the students don’t have to think about the material alone at home… But working alone is the only way you really learn! Instead, we hold their hands while they work through problem sets, smoothing out the kinks as they go along, misleading the students into believing that the road to problem solving is easier than it really is. I have seen some pathetic products of flipped classroom instruction, as the students come to my class with an A in a prerequisite that was taught in a flipped format, and they can’t tell their a$$ from their face (because the class is all about a$$ vs face recognition, of course); they don’t understand anything, and they certainly can’t do any relevant problems that they hadn’t specifically seen before. We try to remove the natural and necessary discomfort that comes from learning, being challenged, being required to stretch beyond where we are. And this incessant insistence on everything being with other people, like flipped classrooms and group projects, is an introvert’s nightmare. Can’t we let people think in peace?

This is completely opposite to my own teaching philosophy. I, as the instructor, need to be there to help when help is needed, but the student has to think and grapple with the material alone FIRST; this is absolutely key. Ideally, this is the sequence: come to class, read the book (or the other way around); start on the homework early and on your own, do as much as you can on your own; then ask friend/come to discussion/come to office hours AFTER you have thought about the problems on your own really hard, because by then you will be sensitized to what you are missing and what you don’t know, and therefore much better at remembering explanations and clarifications. Instead, I see many students work in packs, with a pack leader who’s a strong student and the rest contributing little, but still feeling very good about their command of the material; studying in packs works well for their grades, as long as homework and projects carry a lot of weight. But in the setting such as the one I have for a core undergraduate course, it is all exam heavy and it shows how much each individual student knows, and the students can get surprised by how little that is. Yet, this class is important and I need them ALL to not only sort-of understand the material, but to actually know the material really well and to be able to calculate things.

{A related aspect that peeves me is students complaining that we somehow need to test their understanding only. I say that we test both understanding and proficiency. No, you don’t get to be just a concept thinker until you have demonstrated that you can actually do some basic problems, start to finish. [You should see the grumbling because I expect everyone to be able to, at all times, calculate the horribly complicated integrals of x^a (a\neq -1), sin x, cos x, 1/x, exp(a*x)].}

Another aspect that I am very tired of is students constantly asking that we only teach them the practical stuff that will get them a job and none of the useless abstract crap, presumably because at the tender age of 19 or 20 they know exactly what it is that they will or won’t ever use. Employers want what they want, and most don’t want to pay for it; they want a new graduate to come trained in all the minutiae that the employer (any employer!) could possibly want. The employers have no qualms about wanting the universities to act as trade schools, but they are not and they shouldn’t be.

Sure, we should provide training in the latest and greatest tools and techniques, because I agree that our students should be employable upon graduation. However, what peeves me is how joyously these kids rush towards becoming corporate cogs today, without stopping to think what will keep them employed 20-30 years from now. Why? Because the jobs that exist today didn’t exist 30 years ago. The only way you remain competitive for jobs over the long term is if you have a good, solid base in many basic sciences (for the physical sciences, that’s first and foremost math, then physics, chemistry, computer science, statistics…) as well as in writing and speaking. The stronger and wider your base, the better able you will be to change careers if needed.

I do my part, but I wish we collectively a did better job of communicating to our students that our job as educators is not to just ensure they get their first job out of college, but to give them the knowledge base and the self-study skills that will keep them nimble, growing, learning, and ultimately employable throughout their lives.


  1. In the UK, the success of a department/university in making students “employable” is measured by where the student is 6 months after graduation. Which is INSANE – degree level education is about preparation for LIFE, for potentially multiple careers, citizenship, raising and mentoring younger or less advantaged people, being part of a complex and techonological mostly-democracic society. It is NOT about getting the first job.

    It’s especially annoying in my end of STEM and at my kind of regional university, where the typical graduate likes to travel/volunteer/”recover”/”work out what they really want to do” for at least a few months after they graduate. I get a LOT of reference requests for a very wide range of “graduate jobs” or specialist master’s programmes from students who graduated 2-3 years ago. I always ask what they did in between, and whether we at Northern Uni could have done more to help them get ready for this stage earlier, and they talk about growing up, about how badly they needed a break from education after being in a mark-driven course-work intensive system since they were 5 years old, about following a partner to a new city and taking time to find their feet, about how temping helped them realise the kind of environment they wanted to work in, or how their volunteering helped them get a scholarship, or the fabulous time they’ve had being a mother’s helper in the US or teaching English to little kids in the Far East or bar-tending their way around Australia and how they’re now ready to get serious about building a career and settling down a bit. They say they wish they’d made better use of their time with us, but they also say that we offered what they needed, they just didn’t KNOW that they needed it. I occasionally get emails 5 or 10 years after graduating from students saying “just thought I’d let you know that SuchAndSuch was so useful to me this year”… I try to make them weigh more with me than all the petulant complaining in the evaluations. But it’s hard when we are assessed on whether they immediately get the job thing “right” straight out of college…

  2. I hear you about student incompetence, but I don’t think the flipped-classroom is to blame. I see exactly the same lack of understanding from students who took traditional lecture-homework-exam courses. And I mean serious misunderstandings, like not being able to apply Ohm’s Law to a resistor in series with a current source to determine the voltage—after having done that exact same problem nearly every week!

    As faculty, we love to blame the previous instructors for the lack of prerequisite knowledge in the students who come to us, but I can see that only about 1/3 of my students are really learning anything this quarter, no matter what I do. Most of the rest will squeak through the class without having retained anything useful, and a couple will fail either by giving up or by being so totally incompetent that no one else will work with them to help them out. (Only the competent students are coming to office hours, and there are only 12 hours a week of lab time for me to help them—6 hours for each section, though I am adding an extra 4 hours a week for the last 3 weeks of the quarter for students who need to make up labs.)

    Even some of the top students are incapable of simple multiplication with a calculator, getting off-by-a-factor of 10 (or 1000, or, sometimes 10^9) routinely.

  3. I hear you on only 1/3 of all students actually getting the material. One of the best teachers I have ever had told me, as I was about to start my faculty job, “20% of the students will do great no matter how poorly you teach; 20% will do poorly no matter how well you teach; but there is 60% in the middle where your teaching will make a difference, so they are the ones you aim to teach.” Maybe the percentages were not universally 20-20-60, but I think he was definitely right.

    But don’t even get me started on the calculator. My Eldest will take precalculus next year as a high school sophomore. The first thing they told them to buy is a graphing calculator. Why? WHYYYY? I have never in my life owned a graphing calculator. Teach them how to actually get an intuition about functions, asymptotes, how steeply the curves ascend and descend, how to tell if the function is monotonic or will have extrema and how many… Just basic reasoning that can be applied to any function you’ve never seen before.
    In my college class the students couldn’t sketch straight lines with slopes a and -a through some point on a 2D graph, or straight lines with slopes a and b where a>b.

    The problem is too many people don’t have the math background to major in the physical sciences. It’s like wanting to write a college essay, but not being able to spell. However, we don’t force remedial courses because everyone wants to be done in 4 years in view of the cost. So what the heck are we doing? We keep making accommodations for underprepared students without actually having them challenge the poor preparation. How is it that all students in my undergrad courses who went to high school outside of the US (they are not all strong students) can all actually analyze functions and do basic calculus properly, but only the best Americans can? Why can’t we teach kids math? Math is cheap to teach, doesn’t require labs, but does require good teachers and a mindset among students that’s not “math is boring and hard and useless.”

  4. I will dissent on the graphing calculator–I think that the ability to play with the shapes of many different functions very quickly can be a fantastic way to develop one’s intuition. When I got a graphing calculator in 9th grade I couldn’t stop playing with it. However, this only works if (1) your son will actually play with it on his own, i.e. do more than the minimum for this week’s assignment, next week’s test, passing this semester, etc. and (2) the intuition from playing with the graphing calculator is combined with more rigorous paper-and-pencil work.

    That’s the reality. You have to do more than the minimum, and you have to have a blend of engagement on the “let’s play and have fun because this is neat” level and engagement on the “this part isn’t as much fun but it is very necessary so let’s get it down rigorously” level. There is no substitute for a lot of work beyond just whatever is necessary for this week’s assignment. To quote the Mad Hatter from Once Upon A Time, “That’s the problem with this world: Everybody is looking for a magical solution to their problems but nobody wants to believe in magic.”

    Also, the universities have this idea that poor high school math preparation can be remedied in 1-2 years. At most universities, they offer roughly 2 years of math coursework below the level of calculus. They typically stamp the “remedial” label on only one year of that coursework, while stamping the “college-level” label on another year of it. At my institution, you can take a year-long math sequence that covers (roughly) Algebra II, Trig, and Precalculus, and those courses have “College Level” stamped on them in all of the official paperwork. So a student can come in, test into those courses, and be told that they have tested into “college level” work, which is accurate in the sense that they have tested into a course with “college level” stamped on the official description, but they will NOT be able to finish a math-intensive major in 4 years if they tested into those courses. So “college-ready” is something of a misnomer.

    Even worse, the courses that come before calculus (whether labeled “college level” or “remedial” are generally taught by part-timers with little support, little security, and little status, and the mode is that students are in courses that meet 3-4 hours/week. If they had done well in high school (where a course generally meets 5 hours/week, and is taught by a “regular” full-time teacher with the status and compensation of a regular, full-time employee) this wouldn’t be necessary. But they are behind, and we have this idea that a failure to get on track in 4 years of high school can be remedied by 1 year of 3-4 hours/week with a person getting little support. It’s a big exercise in fantasy. I respect part-timers as people, and I know that many of them do a great job, but I also know that you cannot expect uniformly rigorous upholding of standards from people with little security or status when the mantra from above is “Graduation rates, graduation rates, uber alles!”, nor can you expect people shuttling between 2-4 campuses on a part-time basis to put in the tons and tons of office hours and one-on-one assistance that poorly-prepared students need.

    Either we fix the high schools, we massively invest in remedying deficits after high school, or we accept that not everybody will be successful in a math-intensive major.

  5. I have mixed feelings on graphing calculators. They are the only ones allowed on the SAT and AP tests (when calculators are allowed at all), so students need to learn how to use them. The most common TI ones have an awful user interface, so it takes a lot of practice to learn the arcane interface.

    My son won 4 graphing calculators in middle school math competitions, and had one stolen at school, so he still has 3, one of which he uses occasionally (he prefers using a calculator app on his laptop).

    I’ve never bothered to learn to use a graphing calculator—when I want to look at a function, I use gnuplot or (sometimes) matplotlib, so that I can have a decent-size image and control over the axes. When I just want a quick calculation, I prefer the RPN interface of my HP scientific calculator. But I’m not prepping to take exams that only allow graphing calculators.

    Most of my students have graphing calculators, and it doesn’t seem to have helped their number or function sense at all.

  6. I shed a tear recently because my old TI-85 went kaput and it doesn’t seem to be any of the batteries. (DH thinks one of the internal components burnt out.) It definitely helped me with my intuition– I really got an understanding of how shifts work and what asymptotes are and why log (0) = – infinity and so on. A lot of my classmates programmed basic games on theirs and we’d transfer them to each other. And so very nice to not have to do matrices by hand. (These days, of course, I just use matlab.) Oh man, I love math so much.

    I think that like different teaching methods, whether a graphing calculator helps or hinders is largely based on the user.

    What I’m really struggling with right now is getting DC1 to play with hard math problems rather than feeling like there’s exactly one way to solve a problem and if he doesn’t get that way right away he turns off. I wonder how I learned to do that. I think maybe with a large dose of Martin Gardner, but it had to be more than that. He seems to respond a bit better to learning specific techniques like “proof by exhaustion” and so on, and I’m trying to get him to start by writing down what he knows in a word problem and then trying to use that to find new information whether he needs it for the problem or not, but it’s an uphill battle. Oh man, I love math so much. (I just dug up and washed a bunch of my old college math shirts, so I’ve been feeling nostalgic. Maybe I’ll wear one to work tomorrow now that it’s summer.)

  7. I can see how “flipped classroom” might work for discussion-oriented courses, like in the humanities. But for quantitative technical material, I agree with you that the only way to learn the shittio is to work through problems on your own.

  8. @CPP
    I don’t know that flipping necessarily means that students aren’t working on problems on their own.

    All my best technical classes have combined lecture and brief time to work on the problems at one’s desk (usually with the professor walking around and giving small amounts of help or the class going through the at-desk problem right after). That’s a form of “flipping” but one that’s been standard practice forever. The combination means that you can ask questions/become not lost before the lecture continues. Straight lecture becomes useless if you’re missing a foundational piece. Of course, the same problem occurs in technical when you’re just watching a video lecture at home where you can pause but can’t ask clarifying questions if you’re lost.

  9. In principle a student in a flipped class can and should work problems outside of class.

    In practice, I’ve heard people say “I flipped my class because students weren’t studying outside of class, so this way I at least know that they are spending 4 hours/week working on problems.” Also, a common (though not universal) feature of flipped classes seems to be video lectures. There’s very much a refrain of “Students don’t read but they will watch videos, so therefore…” However, it isn’t clear to me that pandering to an aversion to the written word is a good thing, nor is it clear that they are actively pondering the lecture as they watch it, rather than “watching” it while also browsing Facebook or whatever.

    I know somebody who has gone on the public record with reports that students can pass his general education course without doing any reading outside of class. He sees this as a testament to the quality of his in-class interactive group activities, rather than a confession of first degree grade inflation with intent to distribute. This is not me gossiping, this is me restating what is in published articles that the person signed his name to. It is only the thinnest pretext of civility that keeps me from naming the name.

  10. I think that students are being ‘babied’ a bit too much. There is this notion that the instructors need to dance like a monkey till the students ‘feel comfortable’ with the material.

  11. “It’s like wanting to write a college essay, but not being able to spell.”

    The proportion of kids who can’t spell (or even write a coherent sentence) is very similar to those who can’t do basic math. I don’t know if it has ever been thus, but it is amazing how many college students (smart kids, clearly) don’t have the basic skill sets.

    My take is that I’m tough in class, demand quality, and scare the kids early with very low test scores. I find that most of them really do stick it out and learn something. My attitude is that I’m doing them a favor by teaching them what I know, so they had better work for it, not that they are doing me a favor by taking time in my class.

  12. Some odds and ends:

    Mathematica/Maple are the HP calculators of calculus
    so why bother?

    Active learning has a lot to offer, but is a lot of work to teach because you have to monitor it closely

    No one learns alone, what that mostly does is cement false models. Small groups are best.

  13. I don’t know much about flipped classes–I never had the chance to take one.

    But I can say that I pretty much never learned anything from a lecture even when it was from someone famous who everyone said was the best teacher, etc. Usually I would show up and get lost in my thoughts and stop paying attention. Or get super bored watching someone else solve a problem on the board involving lots of tedious algebra.

    By the time I got to grad school I just basically gave up on going to class most of the time. I’d just did my best to learn by doing the homework sets by myself and reading texts when I was stuck.

    Now as I start my first year as a professor, I’d really like to try some sort of active flippy thing…would you say it is just never useful?

  14. Grumpy, there are no absolutes. I think there are topics that are better suited for flipping than others. For you as a new professor, I would say you also need to think about how much time you spend on teaching (hint: not all of your time, if you are at an institution that requires or values research). The flipped classroom courses take a lot of time initially to prep, plus I really would not recommend them for a newbie professor.

    What I would do if I were you is start by incorporating active learning elements into a more traditional classroom (I believe that’s referred to as a “blended classroom”). This means you mostly lecture, but you incorporate one or more of the following: a) in-class quizzes, perhaps once a week (students are always very positive about these in my classes); b) if you teach 3x a week for 50 min, for instance, you can plan on 25 min lecture and 25 min problem solving; c) if your institution provides classroom layout that’s not a traditional lecture hall but rather smaller tables with chairs around them, get one of those and then you can even do small group work (give them a problem, a few minutes to sketch a solution, then have someone come out to present a solution, or you do it on the board, or have them teach one another); small group work is most effective when you have enough TAs to cover the whole room. (If you have the likes of me in your class, they will hate it. My least favorite thing ever is working in groups like that, because I always ended up helping others and never got much out of it myself. But American students seem to be accustomed to group work and don’t seem to mind.)

    I am guessing you are teaching a graduate level course, as is common for beginning profs. In that case, you are dealing with smaller classes and generally interested students, so you have more flexibility in terms of what you try.

    But I beg you, please, no death by power point! And be mindful of the fact that teaching will expand to fill all of your time if you let it. If yours is a research-intensive position, you have to limit the teaching efforts. As you get more experienced, you’ll be able to experiment and still stay within a reasonable amount of time.

    Good luck!

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