The inverted classroom and student self-image

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This week I’ve been immersed in the inverted classroom idea. First, I gave this talk about an inverted linear algebra classroom at the Joint Meetings in New Orleans and had a number of really good conversations afterwards about it. Then, this really nice writeup of an interview I gave for MIT News came out, highlighting the relationship between my MATLAB course and the MIT OpenCourseware Project. And this week, I’ve been planning out the second iteration of that MATLAB course that’s starting in a few weeks, hopefully with the benefit of a year’s worth of experience and reflection on using the inverted classroom to teach technical computing to novices.

One thing that I didn’t talk much about at the Joint Meetings or in the MIT interview was perhaps the most prominent thing about using the inverted classroom model on a day-to-day basis: how students react to it and change as a result of it. I was actually quite surprised that nobody at my Joint Meetings talk asked me a question about this, because honestly, the inverted classroom sounds great on paper, but when you start to imagine the average college student walking in on the first day of class and having this method of instruction described to him, it becomes clear that a significant amount of work is going to have to be done in order to get students — who are already resistant to any change from their accustomed modes of instruction — on board with the plan.

Students do tend to resist the inverted classroom at first. Some forms of resistance are more benign than others. On the benign end of the spectrum there are students with little experience with the course material or its prerequisites who get bogged down on the basic podcast viewing (which takes the place of in-class lectures in this model) or the accompanying guided practice, and instead of actively seeking a resolution to their question will wait for the instructor to clear it up — in class. On the other end is the student who simply doesn’t believe I’m serious when I say there won’t be any lecturing, who then doesn’t do the work, assuming I’ll bail him out somehow — in class. But in the inverted model, students are held responsible for acquiring basic competencies before class so that the hard stuff — what we refer to as assimilation — is the primary focus of the class time.

I break this distinction down for students, but not everybody buys into it. Those who don’t will have to undergo a learning process that usually looks like shock — shock that I won’t reteach them the material they were supposed to have viewed and worked on, while the lab assignment based on that material is going on. This can get very ugly in ways I probably don’t need to describe. Let’s just say that you had better not use the inverted classroom model if you aren’t prepared to put out a constant P.R. effort to convince students of the positive benefits of the model and constantly to assuage student concerns.

I’ve often wondered why students sometimes react so negatively to the inverted classroom model. I’ve come to believe it’s the result of a invasive, false belief that can arise in students about their ability to learn things independently of others — namely, that they simply cannot do so. I have had students tell me this to my face — “I can’t learn [insert topic] unless you lecture to me about it in class first.” Clearly this is not true. Toddlers learn their native language without formal instruction, just by assimilating (there’s that word again) the language going on naturally in their background. We all learn things every day without sitting in a classroom; we may seek out training data first through printed instructions, worked-out examples, YouTube videos, etc., but it’s almost never in a classroom setting. Learning new things on our own initiative and without formal instruction in a classroom setting is as natural to humans as breathing. Indeed you could say that it’s the capacity to learn in this way that makes us human. But somehow many students think otherwise.

Where does this belief come from? I think that it comes from its own instance of assimilation, namely the assimilation of a culture of programmed classroom instruction that takes place from roughly the first grade through the twelfth grade in this country. Students have so few experiences where they pursue and construct their own knowledge that they simply come to believe that they are incapable of doing so. And this belief is propagated most rapidly in mathematics. I’ve been reading in Seymour Papert‘s book Mindstorms: Children, Computers, and Powerful Ideas, and this quote hits this issue right on the head:

Difficulty with school math is often the first step of an invasive intellectual process that leads us all to define ourselves as bundles of aptitudes and ineptitudes, as being “mathematical” or “not mathematical”, “artistic” or “not artistic”, “musical” or “not musical”, “profound” or “superficial”, “intelligent” or “dumb”. Thus deficiency becomes identity and learning is transformed from the early child’s free exploration of the world to a chore beset by insecurities and self-imposed restrictions.

That last sentence (emphasis added) sums it up, doesn’t it? Deficiency becomes identity. Eventually, if a student is robbed of experiences of self-motivated learning, the student eventually adopts a self-image in which she is incapable of self-motivated learning. It is a false self-image that is ultimately dehumanizing.

Which is why I put such stock in the inverted classroom model. I think this method of teaching, along with other learner-centered modes of instruction like problem-based learning, is on the front lines in reversing students’ negative ways of thinking about how they learn. Students may (will?) chafe at the inversion at first. But in the MATLAB course at least, something really cool happened at the end of the semester. I made up a slideshow for students called “Five myths about how you think you learn that CMP 150 has busted”. Among the myths were “I can’t learn unless a professor lectures to me” and “I can’t learn on my own initiative”, and I gave concrete examples of work that the students had done in the class that contradicted these messages. In the end I showed them that through this inverted classroom process they had taken majors strides toward being confident, independent, skill learners and problem-solvers rather than just people who can play the classroom game well. And even the most skeptical students were nodding in agreement. And I think that makes it all worthwhile for everyone.

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Filed under Critical thinking, Education, Inverted classroom, Liberal arts, Linear algebra, Math, MATLAB, Screencasts, Student culture, Teaching, Technology

16 responses to “The inverted classroom and student self-image

  1. Daniel Ethier

    In discussing student resistance to the inverted classroom and their insistence that they need you to teach them, you say, “Toddlers learn their native language without formal instruction, just by assimilating … the language going on naturally in their background.” But this analogy is irrelevant. See David Geary on the difference between biologically primary information and biologically secondary information.

    Language is a biologically primary function. Our brains have built in structures to learn language. All we need is exposure. Linear algebra is most definitely not biologically primary. So you cannot learn it in the same way you learn language.

    In a separate observation, cognitive load theory may also help explain some of the frustration some students are experiencing with your inverted classroom. These students may be giving you valid feedback that you’re asking them to do something that is much harder than you are assuming.

    Perhaps these can help you structure that outside of classroom part to help address what may be legitimate issues expressed by some of your students.

    • That’s an excellent comment. I wanted to think about it for a day before responding.

      First of all, do note that my main instance of the inverted classroom model is for teaching MATLAB programming, not linear algebra. (I have used this technique in linear algebra on a targeted basis (so to speak), but the MATLAB course is the only one I do entirely inverted.) So that brings this discussion a little closer to that of learning/acquiring a language, and hence my example is at least somewhat relevant. Arguments could be made that the learning of mathematical concepts has a strongly linguistic flavor as well.

      It’s been a long time since my cognitive psychology class, and I haven’t read the paper you linked in a later comment, but it’s my understanding that the science behind “language acquisition devices” as you mention here is not settled. The LAD is Chomsky’s theory but there are competing explanations. However, I could be behind the times on that.

      As to your last two paragraphs, note that I made no statements about how hard or easy I think any of this is. And I also said nothing about the issues that students bring up during the course — just that there is usually an initial culture shock when students are still learning that class time is spent in a fundamentally different way than they might be used to. What I did indicate in the article is that student feedback shifts from shock to a realization that this way of learning helps them in a number of important ways that go beyond just the course material. That’s the feedback I get from students — what are the “legitimate issues” to which you are referring?

      You might be referring to cognitive load. I have this to say about cognitive load, especially whether the inverted model brings on too much of it. In any course, no matter how it’s taught, students are going to have to learn certain things that require more than just listening. For example, in the MATLAB course they will need to know how to write a program with a branching structure like an IF-THEN statement. In the transmission phase — the lecture — students can watch as the lecturer constructs and executes such a program. But then, in the assimilation phase, they have to build one themselves and debug it until it works. Student tasks and learning outcomes are the same whether the class is traditional or inverted. Which mode of instruction provides the greater amount of cognitive load on students? I would argue that, in this case, the traditional model does, because the most cognitively complex tasks — e.g. writing a function with a properly-executed IF-THEN statement in it — are left up to the student to figure out on his or her own, physically apart from the instructor. In the inverted model, the least cognitively involved task is put into that space — e.g. watching the lecture and playing along at home with simple guided practice. This is exactly what the student would be doing — listening more or less passively to a lecture — in class; it is not a more difficult task because it’s done online. And we use the classroom time and space to focus, with the instructor and in groups, on the assimilation tasks, and presumably with all that support readily available the cognitive load is reduced. In other words, because the inverted model puts instructor and classmate availability in direct, rather than inverse, proportion to the cognitive level of the task being performed, the overall cognitive load is reduced. It’s the same stuff taking place, just aligned better in terms of matching hardness of task with availability of resources.

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  3. Hey Robert,
    It’s nice connecting with you electronically, even though I completely missed you at the Joint Meetings in person.
    I’ve moved my pedagogy to problem-based learning over the last decade, prompted and encouraged a lot by the Moore-Method crowd, and other sources.
    It’s been challenging and rewarding, but a bit harrowing: as you remark, students can put up resistance, and when they express it on teaching evaluations, you can take a lot of heat.
    Still, it’s worth it. Most of us didn’t go into mathematics to play the classroom game, and problem-based learning and the inverted classroom are formats that (once we iron out the difficulties) are very satisfying for both us as instructors and refreshing for our students.

  4. I am very interested in this model, thanks for writing about it.

    Learning new things on our own initiative and without formal instruction in a classroom setting is as natural to humans as breathing.

    This is a very important note. In my experience, all pupils and most students will not feel that they are learning on their own initiative. You have to go to school, you have to take maths, you have to take Discrete Mathematics 101, you have to somehow get another eight credits and so on. Therefore, I feel it is of major importance to make sure the students understand that they sit in your classroom by their own choice. It can not work otherwise.

    Is yours a mandatory course?

    • Good point. The course is a prerequisite for Calculus III (that might get changed to Linear Algebra next year) so any student in a program headed in that direction will need it. I did have one student who took the course as an elective during its first run last year.

      So by “one’s own initative” I am referring not to taking the course as an elective, but rather how one goes about learning the material once you’re in the course. For example, if you’re watching a lecture about histograms and you do the guided practice on histograms, but you still just don’t completely get it, a student with initiative will go learn more through Googling and the Help system and try more examples. In a traditional class there is not much incentive for that kind of initiative; why go look things up in the help system, or go to office hours for help, when you can just get the prof to give a short lecture on it in class? In the inverted model initiative is incentivized in a number of ways, not least of which is probable poor performance on in-class activities if you don’t exercise it.

      • You are right. I was thinking of motivation, not initiative. They are, of course, closely related, but not the same. I have seen many a student who was lacking in (intrinsic) _motivation_ and therefore in initiative. I understand that there is a whole science around motivation, but it seems to be important that it is intrinsic and that the person knows that.

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  6. Thanks for writing this up. I’d love to see the slideshow with the ‘5 myths we’ve dispoved in this class’.

    @Daniel, can you point me to something good online that gives evidence for the need to make a distinction between biologically primary and secondary information?

    I have lots of experience with unschoolers whose kids have learned to read when they chose, with little or no instruction. It works well for many of them. I’m very interested in thinking about how much ‘instruction’ we really need to learn various things (math, in particular).

  7. Daniel Ethier

    Here is David Geary’s article from 2000:

    Click to access GearyEvoEd.pdf

    It’s long. Section 3.4 gets to the heart of the matter.

    I am wary of using anecdotes to say whether something is really possible. Often, when examined more closely, things are not as they seem. What fraction of children really teach themselves to read? Was there really NO instruction or teaching of any kind?

    Again, this doesn’t seem to me to rule out the inverted classroom model, but does perhaps imply that students may be expressing a valid point that the pre-class part may need to be somewhat different.

    Some other things that may be at play are the background knowledge the student’s bring to your class. Those with a stronger knowledge base will be better able to teach themselves. Those without will require more instruction. Some interesting research on this from Cognitive Load Theory.

    • I would stop short of saying students are “teaching themselves” outside of class. Nothing more than reasonable fluency with the most basic competencies is expected before coming to class. For example, here’s a guided practice (= pre-class homework) for one of the MATLAB classes: As you can see, it’s basically “plug this into MATLAB, see what you get, and explain why you’re getting it” in very simple mechanistic tasks. The hardest thing they do is play around with blocks of code and analyze their changes. It’s stuff we typically expect students to handle in an in-class activity, if they know enough to be dangerous.

  8. Anne

    I enjoyed looking at your presentation for the inverted model. I admit that the first thing that went through my mind is “What if students don’t do the prep work?”

    I am using one of the MIT open courseware classes to teach myself computer programming. I am doing this for two reasons: the first is because I have an interest in doing some mathematical programming and my last experience with programming was Fortran in the late 70’s. My second reason is that I wanted to experience this model of education. I know that in the past I have not been able to teach myself certain things once I get to a certain level. Sometimes the material in a certain topic ‘jumps’ to the next level. If that jump is too high for me, I sometimes can’t make the leap and my progress stalls. If I don’t have a resource, I get stuck and frustrated. It will be interesting to see if this happens in the programming class.

    To get back to the discussion: I think this happens to students in math class. There may be a jump (or several jumps) that they are not able to make. In most math classes, the instructor has to keep going. This gap creates other gaps and eventually the student will get stuck. I have actually seen students fail the same class 3 times in my community college. These are pre college level classes with material that I believe most students can master. But there is a percentage of them that cannot with our current model. I would not recommend an inverted model for them. But I think having access to the lectures at home would be helpful. This is not currently available

  9. @Daniel, Thanks, I’ll look at that.

    @Anne, These students (who’ve failed 3 times before) may be the most helped by the availability of the lecture portion of class online. (Yes, it is available online; check out,, and And YouTube.) I’ve required students to watch at least one video from one of these site. Some students love it, and watch one video over and over. Very helpful to them.

  10. Several years ago, I used a similar technique (but without the luxury of on-line lectures, which were not feasible at the time, Spring 2003). I posted the essay I wrote on the technique, which I referred to as live-action math, on my blog last summer:

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  12. Kayla

    I am piloting an inverted classroom, but designed for remedial high school students. I completely agree with the notion that by lecturing the students during the day, and then having them do all the dirty work by themselves is inefficient and does not lead to mastery.

    My program that I’m proposing will incorporate a lot of Khan academy and their practice software which is actually remarkable and well laid out. I also plan to have the student provide their own tutorials by taking a video of them doing problems and then posting it to youtube where they can see it to study later or others can benefit from the information.

    Do you have any advice about adapting this for a high school teacher. Since I am piloting it for the first time in the history of our district, I can take any advice I can get.

    Thank you,