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MOOCs and calculus

December 14, 2012

I’ve really enjoyed the discussion on my post from yesterday about MOOCs and how I predict they are going to affect the education world. I could be wrong, of course, but I think this stuff is super interesting to think about.

One thing I thought about since writing the post yesterday, in terms of math departments, is that I used to urge people involved in math departments to be attentive to their calculus teaching.

The threat, as I saw it then, was this: if math departments are passive and boring and non-reactive about how they teach calculus, then other departments which need calculus for their majors would pick up the slack and we’d see calculus taught in economics, physics, and engineering departments.

The reason math departments should care about this is that calculus is the bread and butter of math departments – math departments in other countries who have lost calculus to other departments are very small. If you only need to teach math majors, it doesn’t require that many people to do that.

But now I don’t even bother saying this, because the threat from MOOCs is much bigger and is going to have a more profound effect, and moreover there’s nothing math departments can do to stop it. Well, they can bury their head in the sand but I don’t recommend it.

Once there’s a really good calculus sequence out there, why would departments continue to teach the old fashioned way? Once there’s a fantastic calculus-for-physics MOOC, or calculus-for-economics MOOC available, one would hope that math departments would admit they can’t do better.

Instead of the old-fashioned calculus approach they’d figure out a way to incorporate the MOOC and supplement it by forming study groups and leading sections on the material. This would require a totally different set-up, and probably fewer mathematicians.

Another thing. I think I’ve identified a few separate issues in the discussion that it makes sense to highlight. There are four things (at least) that are all rolled together in our current college and university experience:

  • learning itself,
  • credentialing,
  • research, and
  • socializing

So, MOOCs directly address learning but clearly want to control something about credentialing too, which I think won’t necessarily work. They also affect research because the role of professor as learning instructor will change. They give us nothing in terms of socializing.

But as commenters have pointed out, socializing students is a huge part of the college experience, and may be even more important than credentialing. Or another way of saying that is people look at your resume not so much to know what you know but to know how you’ve been socialized.

It makes me wonder how we will address the “socializing” part of education in the future. And it also makes me wonder where research will be in 100 years.

Categories: math education, musing
  1. Barry
    December 14, 2012 at 8:08 am

    “Instead of the old-fashioned calculus approach they’d figure out a way to incorporate the MOOC and supplement it by forming study groups and leading sections on the material.”

    This is the “flipped classroom” model that has recently become so trendy. (I know because this is my third year on a hiring committee at a teaching-focused college and the number of mentions of “flipped classroom” increased from zero the last two years to a couple dozen this year). Students watch a video before class, maybe answer a few questions, and then you discuss the video and other stuff in class.

    It is ironic that the flipped classroom is considered by many to be revolutionary. It’s actually old-fashioned. Basic study skills used to include preparing for class by reading the source materials to be discussed. This is no longer the norm, but there are still a few of us who require this (I’ve probably seen ten applications mention reading in three years of hiring, and most of them only indicate that it is a desire, not a requirement.)

    My students enter college not knowing the slightest thing about how to read or communicate technical material. They don’t understand the importance of learning and using precise terminology and definitions, the importance of knowing, presenting, and analyzing underlying hypotheses (or even the difference between the words “assumption” and “conclusion”), don’t recognize when details (or hypotheses) are elided from an argument, don’t understand the words of quantification and when examples are acceptable vs. a more general argument, don’t understand the importance of thought experiments when problem solving, etc. etc.

    They don’t get any of this because they haven’t been forced to take any responsibility for their own learning.

    All their lives, they have learned math by having some teacher tell them how a procedure is done, and then on individual worksheets (or in groups, for pedagogically “advanced” classrooms) practice those procedures. The teacher distills certain information out of more general contexts and the students never have to look at the details of those contexts themselves. Some teachers even only write distilled problems — here’s a big word problem, but now I’m going to write down a quadratic equation at the end of it and ask you a question about it — rather than problems asking a student to determine from context if a quadratic equation is even an appropriate model and then to set one up and solve it, interpret the solution, and reflect upon the whole process, including identifying hypotheses, etc. etc.

    The main error with your prediction that I quoted at the top is it still accepts the model of teacher as “distiller of otherwise impossible-to-access content”, the emphasis being on content. If that’s all you are, then yes, you will be replaced by video. (Yes, that video can be revolutionary for students who lack other opportunities). Overpriced poorly written textbooks that serve only as distilleries will also be supplanted. But students who want to learn how to learn real mathematics, and not some pale distilled nonfat version of it, will never get that by watching a laboratory-grade distillery of a MOOC.

    Is there a market of such students? Yes, and not only at elite universities. In my college of <2000 undergraduates, I have 32 freshman math majors in my honors calculus class, and every one of them is taking responsibility for her own learning.


    • December 14, 2012 at 9:02 am

      I think you are assuming that the videos will be no better than the average teacher at getting kids to engage in their learning beyond prescriptive process-oriented regurgitation. But the best MOOCs will incorporate more than that, hopefully.

      Moreover, once they do, it will be a lot easier to revolutionize the field of calculus teaching by having everyone engage with a computer program than by trying to reteach the very large group of calculus teachers.

      In other words, I challenge your vision that MOOCs have to be laboratory-grade distilled pale, nonfat mathematics. If that *is* the best they do, then no revolution will happen, nor should it.

      If however we manage to build a program that actually succeeds in getting (a majority of) students to understand what is an assumption and what is a conclusion, and why we need to prove things, and when we decide to apply formulas, then we should be all means use it widely. I think we are in agreement about that.


      • Dan L
        December 14, 2012 at 9:54 am

        I agree with you. Even with all of the natural advantages of actual human interaction (which I do believe are very significant), I doubt that I (or most teachers) could teach calculus any better than the hypothetical awesome calculus MOOC of the future, featuring lectures from a truly great calculus teacher, supplemented by a well-made interactive homework system and online interactions with TAs.


      • barryrsmith
        December 14, 2012 at 11:04 am

        “Laboratory-grade” meant that they would be much better than the average teacher. I agree that such videos will be made and widely watched. For instance, Dick Gross is a wonderful lecturer and his abstract algebra videos, from what I have seen, are quite engaging (as far as lectures go).

        You missed my main point: the medium is wrong. A video will never ever be as good as print for carefully crafted precise description of information. It is simply much harder to do all of the revising and editing that you can in print, and the density of the content in print is much greater than the density of content in a video on the same subject. Print isn’t going anywhere, but plenty of our math majors cannot use it effectively when they leave college.

        What a typical lecturer does is tell the students a summary of what’s in the book (with perhaps some examples that weren’t those in the book). I challenge you to find me even a high quality lecturer who doesn’t spend the majority of their time doing this. Students don’t do the major abstracting themselves — the lecturer does it for them. Students don’t do the puzzling over the intricacies of definitions and theorems — the lecturer does it for them. Students don’t do the reflecting —- the lecturer does it for them. It’s all distilled — summarized; they cannot sieze hold of the much richer print (or electronic print) sources that a good course will be based upon.

        I haven’t even addressed other skills, like oral presentation, that won’t be developed by MOOCs.

        Students who are only exposed to traditional lectures, even good lectures won’t be able to obtain technical content from print later in their lives unless they have already naturally developed that talent on their own (such students are not the norm.) I can easily see MOOCs supplanting the large lectures at large public universities. But I don’t see how they will muscle in on the traditional liberal arts education.


    • Nathanael
      December 23, 2012 at 11:50 pm

      This is all wildly beside the point. The problem with calculus classes is nothing to do with the calculus classes themselves; I’ve found they’re mostly the same.

      The problem with calculus classes is that students come in without the prerequisites: a really solid grounding in analytic geometry, enough set theory to understand relations and functions, basic predicate logic, and even *critical thinking*. I’m sure there’s a lovely MOOC for each of those things, but students don’t even know that they need to look for it!

      It’s true that your students ender college without knowing what they need…. but it’s not because they “haven’t been forced to take any responsibility for their own learning”, it’s because they haven’t been offered a course in any of it. Most people don’t learn critical thinking on their own.


  2. JSE
    December 14, 2012 at 8:50 am

    I’m not sure why you think MOOCs don’t directly address credentials. What do you think the product they’re selling is, if not credentials?


    • December 14, 2012 at 8:57 am

      They aren’t directly selling anything since it’s “free”. But what they are offering is learning. And yes they want to attach credentialing to it, and they will, and those credentials will be worth something, but not as much as they hope. That’s my feeling. So if I built a model of people’s fit for a company I’m hiring for, I expect a MOOC credential to be a positive but weak signal. Much more important is how they perform on the test I build to directly gauge their knowledge on things I care about, as well as an in-person interview to see if they are sufficiently compliant and team playerish.


      • Dan L
        December 14, 2012 at 9:46 am

        The for-profit MOOCs will absolutely charge money for their courses and offer credentials at some point. Since they are allied with legitimate universities, this will not be hard to do. The universities will sell these credits and degrees as something “less than” their “real” degrees so as not to degrade their brands too much, but it will still count for something. (I have in mind stuff like Harvard extension school credit or those cash chow program “certificates” that business people buy.) And employers will accept these credentials, because the MOOCs will be able to make credible claims that the MOOC students are taking the same exams from the same professors as the real university students. (As I said before, in-person testing is the only barrier, and it is a low one.)


    • December 14, 2012 at 9:33 am

      The biggest problem now is that, in the current state, the credentials are easily attainable through cheating. There is no verification on who signs up and actually does the work.


      • December 14, 2012 at 9:36 am

        Agreed, that’s a huge problem, but it’s a problem for all education, including Harvard, as we should all know by now. That’s why I think people will depend more on their own tests, where they can see a job candidate doing it in person (on a computer) as well as in-person interviews.


  3. Zathras
    December 14, 2012 at 9:30 am

    “Once there’s a really good calculus sequence out there, why would departments continue to teach the old fashioned way?”

    Because all of these calculus classes are for make-work programs for professors and post-docs. If they are not teaching these courses, math departments will no longer be able to justify their size. Everything set up at universities are for the benefit of professors. To paraphrase a common comment about Facebook, at universities, students are not the customer; they are the product.


    • December 14, 2012 at 9:38 am

      You are even more pessimistic than I am! I don’t think this is intentional. I think most math professors just don’t think about it. Moreover, they are directly rewarded for research, at least at research institutions, and not rewarded for caring about calculus. So it’s an incentives problem as well.


    • Dan L
      December 14, 2012 at 9:49 am

      I think it is both overly cynical and laughable to think that “everything set up at universities are for the benefit of professors.” To take just one rather obvious and large example, if what you’re saying is true, then where the hell did big-time college football come from?


      • Zathras
        December 14, 2012 at 11:15 am

        Okay, it’s a bit of hyperbole. Not everything is set up for the benefit of the professors. Just that nothing is set up for the benefit of the students, other than keeping them as a profit center.


    • December 14, 2012 at 8:48 pm

      “Because all of these calculus classes are for make-work programs for professors and post-docs.”

      My experience is the just opposite: demand for calculus comes from outside the math department, as requirement for majors like engineering and economics. For instance, at my university we added a sixth 250-person section of vector calculus this fall to try keep up with rising enrollments in engineering, and everything still filled to capacity. You’re right that math departments justify their size based on these enrollments, but it’s not like we create them.


    • JSE
      December 17, 2012 at 10:18 pm

      “students are not the customer; they are the product.” But wouldn’t this be all the more the case at Coursera or Udacity, which, unlike universities, have profit as their basic purpose?


  4. December 14, 2012 at 9:44 am

    An elementary school in the Netherlands is starting a pilot: in the virtual world Wonderland groups of 3 children play /work/ learn with the “game” DragonBox. They talk with each other, ask questions and give advice. With the game DragonBox kids learn the rules of algebra without knowing that. By talking about their strategies, they learn from each other, they learn to talk, to collaborate, and they have fun.


  5. December 14, 2012 at 9:54 am

    As soon as there will be more “games” like DragonBox, the educational landscape will change for the better. Combining such tools and collaborative learning environements with proven educational practices like in Finland
    can be very interesting.


  6. Joe Smith
    December 14, 2012 at 11:52 am

    What does the future hold? UK university applications have fallen in line with fee rises and the government predicts a funding crisis by 2020. When you combine this with the MOOC launch, by a partnership of red-brick UK universities, to challenge the US dominance, it certainly appears the next few years will see radical shifts in higher education.



  7. December 14, 2012 at 9:07 pm

    “Once there’s a really good calculus sequence out there, why would departments continue to teach the old fashioned way?”

    Even within the narrow range of research universities, calculus courses differ quite a bit in pacing, content, and emphasis. From my direct experience, the calculus courses at Caltech, Harvard, Illinois, Chicago, and Oregon State are all different enough that swapping a course from one campus to another would vary from requiring substantial restructuring of other courses in the curriculum to an outright disaster. Which isn’t to say that there aren’t clusters that do teaching pretty much identical calculus courses, or that said clusters couldn’t all use the same MOOC, but that this isn’t going to be a “one calculus course to rule them all” situation. After all, most universities offer several variants of calculus just for their relatively homogenous student bodies…

    Overall, I’m skeptical that MOOCs will have much impact on universities. I just don’t see what they have that mixes of things like textbooks, correspondence courses, community colleges, and various other things have been providing for a long time. Other departments here have tried incorporating MOOC-like aspects into their large courses with decidedly mixed results. For instance a large social-science course tried peer-grading (disaster and students hated it), and a hard science went to video lectures (students hate it, want actual lectures for their tuition dollars).


  8. Richard Séguin
    December 15, 2012 at 12:06 am

    My worries about MOOCs:

    (1) This is yet another aspect of our lives that would be funneled through our non-sensual flat panels, and those flat panels are both social insulators and isolators.

    (2) JSE is correct that dominance of MOOCs would be devastating to research. Private industry long ago dropped any interest in basic science research. Who will do it?

    (3) Many areas of study require hands-on lab work or field work, such as engineering, chemistry, physics, astronomy, biology, forestry, archaeology, and anthropology. Music requires performance spaces. Flat panels fail miserably here.

    (4) Barry Smith is correct to worry about the reliance on video degrading textual skills and that text is a better medium for sheer depth. In addition, video tends to degrade attention span.

    (5) Learning becomes a commodity with MOOCs.

    (6) I enjoy math blogs and videos of math lectures, but they just doesn’t motivate to the extent that a live person does. I find that attending a math talk gives me a “charge” that a video doesn’t, even if it’s about something that I know little about.

    (7) Many years after having been in school, I still have vivid memories of certain math professors, and those memories continue to motivate me. I don’t think I would get that from a totally impersonal video. Weirdly, in the last couple of years, R. H. Bing has occasionally made a ghostly day-dream appearance behind my shoulder sternly urging me on.

    I can’t say much about calculus courses. I never taught it as a TA. I had an excellent experience as a student in a small honors calculus class taught by Ed Fadell.


  9. Agent Smith
    December 15, 2012 at 7:06 am

    All I hope is that it doesn’t become a TEDification of math. Philosophy didn’t dissapear, it just was engulfed by psychology and the likes and became the argument of Matrix.


  10. eballen
    December 17, 2012 at 3:00 pm

    “Once there’s a really good calculus sequence out there, why would departments continue to teach the old fashioned way?”

    I think one benefit of MOOCs could be that there would not be _one_ great calculus sequence. There should be several great calculus sequences aimed at different types of students — the depth of learning, the place on the abstract/applied spectrum, the learning style. In theory students at the same physical institution could choose the version best suited to their style and interests, and then interact with local professors and students on the topic of calculus from this diverse lecture background.

    With respect to the concerns about video (and all) lectures degrading textual learning skills and attention span, I would argue the 1) this is probably true, but learning quickly and efficiently about a broad array of topics is going to be more important throughout their careers for most people than deep textual learning and 2) in the cases where deep textual learning is important, it should be taught specifically, not by making students reinvent the wheel by extracting basic material from texts. This would be a great role for local universities and professors as a supplement to intro level courses and especially for advanced courses within a major. Where it seems particularly important in my experience is in keeping up with a fields ongoing research (which frankly is not something the majority of students will ever need to do). Looking back on my education, some of the most valuable experiences for me as a science major were upper level seminars in which we analyzed current journal articles on relevant topics and wrote up our own lab experiments in the form of journal articles. These courses involved lots of interaction with my professors and fellow students and wouldn’t be the same in online form at all. However, all the basic lectures on science in the first couple years of school that led up to these experiences would have been excellent in MOOC form.

    Another great thing about the MOOCs is for post-graduate continuing education. As a professional there are times when taking a course on a topic is very helpful but getting the access to and time to handle a traditional university course is prohibitive.


  11. Bruce
    December 25, 2012 at 3:17 pm

    Those pronouncing MOOCs as the greatest thing since sliced bread remind me of events in another realm some forty years ago.

    There are some interesting parallels with the community mental health movement of the late ‘60’s and early 70’s. The movement came about with the advent of antipsychotic and anti-depressant drugs and a simultaneous series of exposes of the miserable conditions in large mental hospitals. Many mental health professionals promoted this community based approach as a solution to failing large scale residential mental hospitals which had been to date poorly funded and staffed. Those suffering from major mental health problems could remain in their communities at home; visit the mental health center for psychotherapy and medication administration and supervision; and be productive members of their communities. Politicians loved this since it would be a much cheaper alternative to making the needed improvements in staffing and facilities at the hospitals. The funding base for residential mental health intuitions slowly began to erode. Unfortunately governments failed to adequately fund the community centers and when communities were budgeting mental health concerns they were not as well represented as demands for public safety, education etc.

    The net result is that we have poorly funded community mental health centers, and regional residential mental hospitals have all but disappeared. The assumption that everyone with major mental health problems could be treated on an outpatient basis without integrating these services into other allied services has proven to be disastrous. Few patients are self-motivated enough to follow through on appointments, take their medications, and seek help when needed. As a result we have patients being admitted to general hospitals psychiatric wards because they have gone of their meds and become a danger to others or themselves just to stabilize and then release them. Civil libertarians may argue their case but a very large proportion of the homeless are seriously mentally ill and not being treated in any meaningful way. Finally when the largest single mental health intuition in the USA is the Los Angeles County Jail something has gone seriously wrong.

    So how is this relevant to the current discussion? As an early adopter and a true geek (I used to wear white socks, pocket protectors and a slide rule at my side) I still think we need to temper our enthusiasm for such fundamental changes to the extent that we don’t oversell them and throw the baby out with the bath water.

    Physics, my original college major many years ago, morphed into a career in psychology. I have been teaching Internet on-line courses, hybrid, and in-person lecture psychology classes, some since the 60’s, and feel that all of these have a place in the continuum of higher education student learning. I have found that for students to thrive and do well in an on-line environment takes a high level of self-discipline. These personality traits exist only in a small minority of students. It has been mentioned that the flat screen interface still lacks in so many of the social nuisances that happen in a face-to-face learning environment. Try doing psychotherapy through a flat screen.

    My bottom line is that we should incorporate these new teaching paradigms into the continuum of teaching/learning environments but not let our enthusiasm cause us to overlook unintended consequences. I teach in a state that is touted to be the most connected in the US, with the most personal computers per household in the country and I still am often surprised at the lack of basic computer literacy of some of my students. To place one of these students in a MOOC no matter how dynamic the instructor and assume they will find the same excitement I do in learning, follow through on projects, participate in group work – well we all know what assume spells.


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