Against Inverted Classrooms

The "inverted classroom" (or as Wikipedia calls it, "Flip Teaching") is the idea that lectures can be watched (say, by online video) prior to class meetings, and then classroom time dedicated to questions and problem sets with the teacher's coaching and assistance in trouble spots. Obviously, it's the reverse of the standard math-class process of lecturing in class and then homework after.

When I heard about this a few months ago, I was really excited and initially felt like it was a great idea. Here's why: I agree that I've independently found the moment where I can help an individual student, working on a specific problem, and identify-fix-correct-clarify the exact location where they're making a mistake, to be the most satisfying and productive use of time for both student and teacher. I try hard to get as much time for those moments of practice and error-catching in my classes as I can. So it sounded like fully devoting class time to that process would be ideal. For my summer courses, I thought very deeply how much I could go in that direction.

So at the end of that analysis, I am now very skeptical that this technique will have legs and work long-term for mathematics education. Here are some of the reasons why I say that:

(1) It could have been done at any earlier time with books, but wasn't. It appears that online video lectures and published books are pretty obviously equivalent (in fact, I think books have the advantage in any way I can think to compare, especially for math). While other disciplines have commonly run classes with assigned reading beforehand, and critical discussion in-class (e.g., literature, history, law, etc.), math seems pretty ironclad in having avoided that in any place or time that I can detect. (Can you think of any counter-examples?) This suggests that there's something about math that demands live presentations in the first place.

(2) Questions still need to be asked during lecture presentations. One reason why the initial presentation has to be live: expert feedback isn't just necessary during individual problem sets, it's also necessary to clear up the initial presentation itself. Almost certainly some different level of detail will have to be presented for different audiences, and there needs to be live back-and-forth questioning in order for that initial lecture to be valuable in the first place -- and this value accrues with interest the more people are watching/present at the time. If a student simply doesn't have access to a particular necessary detail during a recorded video, no amount of rewinding or re-watching will conjure it up, and that time will be for naught. (It's been argued in the past that a fully hyper-linked presentation to arbitrary depth of detail could satisfy this need, but in practice that seems to have failed -- arbitrarily large amount of work on the part of the writer, and similar great workload and discipline needed by the student to follow all the needed links.)

(3) Nonstandard class times are particularly ill-suited for it. The inverted classroom might work a bit better for regular one-hour, once-a-day classes (students need to catch up on one-hour chunks at a time, etc.) But like a lot of methodologies it breaks down in other cases. For example, take my summer statistics courses: they run for 6 weeks, meeting twice a week for 3 hours at a time (other classes might be 4 hour sessions at a time). There needs to be an in-class test about every 3rd class session, which will last about an hour -- note that between one-half and two-thirds of the same meeting will be spent on some other lecture topic. Experience (if not common-sense) shows that students will not have presence of mind for any new topic prior to the test, either in-class or before. So I absolutely must resign myself to presenting new information myself after the test on test days, which themselves are 1/3 of the class meetings. Work out this staggered effect (including the very first class), and I saw that there's essentially no way to make "flip teaching" work in my evening summer courses.

In conclusion: It seems like the general student of any time period hasn't been able to learn math on their own (either from a book or a video) -- that's why they're in a classroom in the first place. It would be nice if there was an expert in the discipline with them at all times, during both initial presentation and homework. But since that's infeasible, the best we can do is some mix of presentation and troubleshooting together in the limited classroom time.


  1. Thought-provoking post! It does sound like the 'flipped' model doesn't really fit with the more intensive nature of your summer course. I would add a couple of comments in relation to the points you raise:

    (1) I have used pre-reading with maths students before, whether it's something in a historical or applied context, or purely to read about what's 'coming next' in the current chapter. A couple of advantages of the video lecture are that you can select and present your own examples and approaches and (debatably) the students can access them more easily from say mobile devices if they don't have their books with them. I think it's also invaluable for students to see maths handwritten 'live' which is another advantage of a video over a textbook.

    (2) Questions certainly do need to be asked, and it's my understanding that for many using the flipped model the initial part of a class is spent answering and discussing questions arising from the video. I think there's also a case for linking flipped teaching more with social media - perhaps using twitter, facebook or a college's online learning space, students can raise and answer questions out of class time. Can we encourage the students to develop independence from the teacher but co-dependence on each other?

    (3) I can't and wouldn't want to argue with your particular situation of intensive summer courses! It certainly seems to me a model better suited to longer standard courses.

    I have to admit, I haven't tried flipped teaching yet but it is going to be my project from September. It's interesting to read all the positive and negative views online. Thanks for giving me more food for thought!


  2. Stu, good thoughts and thanks for posting them. On item (1) I agree that I wish our books were open-sourced and digitized for mobile devices; and I also deeply wish that somewhere students were taught proper detailed math reading & writing (then they could just read the book and not need every process videotaped). On (2) I've seen the "social" feature as an anchor of something like UDacity's high-volume project, but again I suspect it's a two-way loss because (a) students aren't getting high-quality expert responses, and (b) the instructor is cut off from feedback on where their presentation needs improvement.

  3. (2)Regarding deeply linked text. Well, yeah, it's a ton of work. That's why no one has done it. But once it is done for one class people will realize how awesome it can be. It would need to be updated for decades until it's done.

    (1)I agree books are just as good as video. Except for motivation. Many people have done fine learning from the text alone (you will never meet them obviously - they don't need you). The advantage of signing up for a class is it basically forces you into expectations of homework, lectures, tests on a regular schedule. Just like quiting alcohol in a group is easier than doing it by yourself.

  4. That's all wrong--the idea of "flipping" is that students READ THE BOOK before coming to class. There is no point in them viewing a lecture. Then they might as well come to class. It's pretty much the same thing. But you do have a textbook for the course, I suppose. And if your classes are like mine, your students don't necessarily ever open the thing.

    So, the idea is that you make them read a section, give them a quiz to make sure they did that, and then, in your regularly scheduled "lecture", talk about all the higher level ideas that the author couldn't put in the book because it would offend the reviewers (yours truly is such an author...)

    I think this really is a good idea. I don't think I add value by telling my students basic definitions that they can find in the book. But the "how" and "why" is different. The books often don't cover it, and if they do, it's not as authentic for a student as a demonstration by a fellow human.

    1. Brilliant description. Short and sweet!

    2. I'll just say this: Many pedagogies suggest a quiz at the start of each class session. Any time I've calculated it (time, preparation, paper copying, handing out, proctoring, handing back in, grading, recording, handing back out) it seems like a net loss. You've traded communal discussion time together (yes, even the most basic definitions) for isolated quiz time. I'd rather have discussion together and off-load the quizzes outside of class.

    3. But the other thing I'll say is that I've heard equally determined proponents of "flip teaching" who say that videos and communal discussion (not quizzes) are the trick.

  5. I agree that trying to flip the classroom simply by students passively watching a video lecture may not accomplish much, the comparison to reading a textbook is apt. Perhaps for the humanities where there is a lot of reading followed by classroom discussion, then treating any lectures just like reading may be ok. For STEM subjects I think a more interactive approach like Udacity where the student answers questions as they go beats a lengthy lecture and can be made available before, during, and after classroom time (for review). The teacher can choose whether to have the students attempt the material before class or not. I'm not a huge fan of Khan Academy but I saw an interesting presentation showing how they are adding problem sets with real-time monitoring of how every student is doing with the problems. The teacher can see what concepts students are struggling with and adjust the course if it is the problem, or have a class discussion, or help individual students if only some are struggling. Trying to retain the same old lecture/homework paradigm and just switching which is done in class doesn't seem like enough.

  6. This was very interesting to read. Harkening back to my days as a student I think a flipped classroom using technology (videos and social media) would have accelerated the pace and depth of learning to an uncommon degree. The sad truth is that in nearly every higher level math class I had in high school or college the lecture was little more than a 3D depiction of something I could have seen on Khan had the technology existed at the time. So as I read the post I kept thinking "OK, so you're guessing at why it might not work, but you've never tried it to be sure." For every one reason that an educator can give why it won't work I think you will find students equally impassioned with two arguments suggesting that it will.

    1. Thanks for your thoughts. I think a skeptical stance is best about this and any other educational fad (as the last several decades should tell us). The cost in time of overhauling any class is very large, and we should require extraordinary positive evidence before making dramatic changes.