Home > math, math education, musing > The coming Calculus MOOC Revolution and the end of math research

The coming Calculus MOOC Revolution and the end of math research

January 20, 2014

I don’t usually like to sound like a doomsayer but today I’m going to make an exception. I’m going to describe an effect that I believe will be present, even if it’s not as strong as I am suggesting it might be. There are three points to my post today.

1) Math research is a byproduct of calculus teaching

I’ve said it before, calculus (and pre-calculus, and linear algebra) might be a thorn in many math teachers’ side, and boring to teach over and over again, but it’s the bread and butter of math departments. I’ve heard statistics that 85% of students who take any class in math at a given college take only calculus.

Math research is essentially funded through these teaching jobs. This is less true for the super elite institutions which might have their own army of calculus adjuncts and have separate sources of funding both from NSF-like entities and private entities, but if you take the group of people I just saw at JMM you have a bunch of people who essentially depend on their take-home salary to do research, and their take-home salary depends on lots of students at their school taking service courses.

I wish I had a graph comparing the number of student enrolled in calculus each year versus the number of papers published in math journals each year. That would be a great graphic to have, and I think it would make my point.

2) Calculus MOOCs and other web tools are going to start replacing calculus teaching very soon and at a large scale

It’s already happening at Penn through Coursera. Word on the street is it is about to happen at MIT through EdX.

If this isn’t feasible right now it will be soon. Right now the average calculus class might be better than the best MOOC, especially if you consider asking questions and getting a human response. But as the calculus version of math overflow springs into existence with a record of every question and every answer provided, it will become less and less important to have a Ph.D. mathematician present.

Which isn’t to say we won’t need a person at all – we might well need someone. But chances are they won’t be tenured, and chances are they could be overseas in a call center.

This is not really a bad thing in theory, at least for the students, as long as they actually learn the stuff (as compared to now). Once the appropriate tools have been written and deployed and populated, the students may be better off and happier. They will very likely be more adept at finding correct answers for their calculus questions online, which may be a way of evaluating success (although not mine).

It’s called progress, and machines have been doing it for more than a hundred years, replacing skilled craftspeople. It hurts at first but then the world adjusts. And after all, lots of people complain now about teaching boring classes, and they will get relief. But then again many of them will have to find other jobs.

Colleges might take a hit from parents about how expensive they are and how they’re just getting the kids to learn via computer. And maybe they will actually lower tuition, but my guess is they’ll come up with something else they are offering that makes up for it which will have nothing to do with the math department.

3) Math researchers will be severely reduced if nothing is done

Let’s put those two things together, and what we see is that math research, which we’ve basically been getting for free all this time, as a byproduct of calculus, will be severely curtailed. Not at the small elite institutions that don’t mind paying for it, but at the rest of the country. That’s a lot of research. In terms of scale, my guess is that the average faculty will be reduced by more than 50%, and some faculties will be closed altogether.

Why isn’t anything being done? Why do mathematicians seem so asleep at this wheel? Why aren’t they making the case that math research is vital to a long-term functioning society?

My theory is that mathematicians haven’t been promoting their work for the simple reason that they haven’t had to, because they had this cash cow called calculus which many of them aren’t even aware of as a great thing (because close up it’s often a pain).

It’s possible that mathematicians don’t even know how to promote math to the general public, at least right now. But I’m thinking that’s going to change. We’re going to think about it pretty hard and learn how to promote math research very soon, or else we’re going back to 1850 levels of math research, where everyone knew each other and stuff was done by letter.

How worried am I about this?

For my friends with tenure, not so worried, except if their entire department is at risk. But for my younger friends who are interested in going to grad school now, I’m not writing them letters of recommendation before having this talk, because they’ll be looking around for tenured positions in about 10 years, and that’s the time scale at which I think math departments will be shrinking instead of expanding.

In terms of math PR, I’m also pretty worried, but not hopeless. I think one can really make the case that basic math research should be supported and expanded, but it’s going to take a lot of things going right and a lot of people willing to put time and organizing skills into the effort for it to work. And hopefully it will be a community effort and not controlled by a few billionaires.

Categories: math, math education, musing
  1. January 20, 2014 at 8:36 am

    Cathy, I’m sorry I missed your panel at the JMM: my talk on quantum cohomology was scheduled at 3 pm, exactly in the middle of your panel.

    As an ‘early-career’ mathematician, I’m disturbed to say that I think you’re exactly right about pretty much everything you say above. I’ve been watching the changes from a different perspective than tenured folks and I think they’re asleep at the wheel because they have too much s(*& on their to-do lists. You are hired/rewarded for putting your research (or maybe teaching) above all other professional stuff, and between that, family, recommendation letters, and committee meetings, there’s no time. Spending too much time thinking the thoughts you’ve outlined above is not rewarded.

    I wrote about the MOOC panel discussion at the JMM at http://www.limitinstitute.org/blog/mooc-panel-in-baltimore/ and MOOCs in the media at http://www.limitinstitute.org/blog/moocs-in-the-media/; I’d love to hear people’s further thoughts about who/what is going to find the economic sweet spot of math higher ed in the future.


  2. Jason Starr
    January 20, 2014 at 9:34 am

    I know I have said this before, and I apologize for being contrary, but I respectfully disagree. However, I completely agree with point (1). I am sure that we can find statistics for total numbers of employed mathematicians before and after WWII, as well as total enrollment in math courses. What I have been told of the history is, colleges adopted math core requirements after World War II and this, together with the “space race” and the baby boom, led to rapid expansion in math departments.

    I believe that MOOCs do not address the major problems in mathematics education, which are (a) poor college preparation, (b) disengagement by students, and (c) increasing pressure from administrators and other departments to admit and “promote” calculus students who fail basic competencies. These are not problems that mathematicians can solve on their own, but we should be working harder to address these problems. The best strategy that I have seen is one-on-one tutoring. Perhaps call-center tutoring could be a threat in the future. However, with the current fee structure of for-profit tutors, college instructors are a better value. In fact, I think MOOCs are a step in the wrong direction: they do not offer the facetime and feedback that students need, they feed into student disengagement, and by cutting out the usual “quality control”, they are more “gameable” by administrators. If you research those public universities that have experimented with MOOCs for core courses, I think you will see that.

    Perhaps you are saying, that *because* they are “gameable” and *because* they offer (false) hope in the face of such difficult problems, MOOCs will be adopted in spite of their failings. Certainly faculty, regardless of disciplne, need to be vigilant against lame pedagogy supported for political purpose.


  3. Zathras
    January 20, 2014 at 9:53 am

    “Calculus MOOCs and other web tools are going to start replacing calculus teaching very soon and at a large scale

    It’s called progress, and machines have been doing it for more than a hundred years, replacing skilled craftspeople.”

    MOOC’s are very elite-zetigeist-y. The elites have been convinced that MOOC’s are the way of the future, and this fact has considerable momentum towards being a self-fulfilling prophesy. There are 4 questions worth asking here.

    (1) Do MOOC’s convey the same quality of education for students in general, as compared to traditional classes?

    (2) Do MOOC’s convey the same quality of education for some sub-sample of students, as compared to traditional classes?

    (3) Will we able to tell the difference in effectiveness between MOOC’s and traditional classes?

    (4) Will schools expend the effort to determine that effectiveness?

    I don’t know what the answer is to (1). I’m pretty sure the answer to (2) is yes, but it might be tricky to determine that sub-sample. I think the answer to (3) is also yes. As for (4), I’m worried about the incentives. Schools generally charge the same for MOOC’s as for traditional classes, although MOOC’s are much cheaper. So the incentive for schools is to go to more MOOC’s, and tip the balance in their favor. Does a school really want to determine whether MOOC’s are less effective?


    • January 20, 2014 at 3:05 pm

      1) No. Too many 18-19 year old students get their basic academic motivation from being in a residential environment. Only a small fraction of residential college students will find MOOCs interesting.

      2) Yes but its probably a relatively small subset. Some self-motivated kids in the top 5-10% of their high school classes will be able to learn as much or more from a MOOC than a traditional college class. Just like they’ve always been able to by visiting the library or asking knowledgeable people. It’s not at all clear that MOOCs are producing good results from typical US high school graduates.

      3) Yes, if you define “effectiveness” in a very narrow sense. In a broader sense, the question might be “Are we helping folks develop their dreams and aspirations along with the skillsets and habits of the mind needed to achieve them?” I doubt we can measure that effectively.

      4) Academics will collect data to show whatever is in their self interest. It will certainly be possible to show that highly motivated students can be “educated” in a narrow test-taking sense just as effectively in a MOOC as in a traditional class. At the same time, 90%+ failure rates in the more challenging MOOCs (like the Coursera Calculus class referenced in the post) say something about the effectiveness of this approach with less highly motivated students.


  4. January 20, 2014 at 9:55 am

    Thanks Cathy. This is very similar to what happened in physics after the Cold War ended. Most departments started shrinking and professorial positions decreased dramatically across the country. I finished my PhD in physics in 2005 and at the time the rumour was that it took an average of 3 to 5 postdocs (another 6 to 10 additional years) to get an assistant professorship in physics at a university. I don’t regret studying physics. After all, it is my biggest passion. But I do wish someone had had this talk with me about how hard it would be to get a faculty position due to the scarcity of openings in the last 10 years. And this is also the reason why a large number of physics postdocs have flown to financial or technology firms. Great post!


  5. January 20, 2014 at 10:07 am

    This is the first time, as a non-mathematician, that I’ve heard of the idea that math research is funded through intro calculus classes. And if true, this really disturbs me, given how unpleasant standard calculus classes are for many, many people who are forced into taking them, and get turned off math forever (when they could have in many cases, e.g., prospective computer science majors, profited more from learning, say, algebra, graph theory, combinatorics).

    So my jaw is just dropped right now.


    • DJ
      January 20, 2014 at 4:17 pm

      The idea that calculus subsidizes math research is generally true, but by itself this problem is very easy to solve. At my university, algebra is a required first-year course along with calculus. We have 1500 students in calculus and 1500 students in algebra in a given year. Our first-year algebra course is a legitimate algebra course, teaching modular arithmetic, Chinese Remainder Theorem, the Euclidean algorithm, complex numbers, and polynomials. It is no easier than calculus and in fact most students find it harder. We most emphatically do not drop the ball on students who need algebra instead of calculus (although they are forced to take both). I think any university with a large enough number of STEM majors could do the same thing.

      Of course, adding algebra to the conversation does not change the larger issue, which is that a MOOC can teach students alegbra as (in)effectively as it can teach them calculus.


  6. Joe
    January 20, 2014 at 10:19 am

    How do you square this with your previous post that taking a rich person’s money was the wrong thing to do? If you reduce that argument to it’s core, it seems like it’s the same problem here by depending on money that doesn’t relate to the core activity that you want to continue.

    You seem to be arguing that you should keep an inefficient system in place because it funds a completely different activity that you want to preserve.


    • January 20, 2014 at 10:36 am

      I don’t think I’m contradicting myself. I’m suggesting that calculus teaching is being “disrupted” and that fact will change basic things about how math research is done. I value math research and think we should consider how to deal with these changes head on. I don’t think appealing to billionaires should be the only trick in our bag.


  7. JSE
    January 20, 2014 at 10:40 am

    My thoughts about this from a year and a half ago:


    Bullet points, because that post is kind of long:

    1. It’s not exactly calculus courses that fund math research, it’s the ability to offer an accepted credential CERTIFYING that a student has taken calculus. The question of whether a MOOC (or a textbook, or any other mechanism) teaches calculus better, worse or the same as my class isn’t relevant to the funding question — all that’s relevant is whether people will decide to accept an inexpensive credential in place of a college degree.

    2. It’s a new feature of the last 50-60 years that there’s been a huge publicly supported math research program in the United States (or really anywhere, I think.) Harvard math professors in 1910 taught 3-3 and if they wanted to go to Germany for a conference they paid their own way. So yes, I think we could go back to that. On the other hand, I think it’s anything but a certainty.

    Not from that post:

    “Why isn’t anything being done? Why do mathematicians seem so asleep at this wheel? Why aren’t they making the case that math research is vital to a long-term functioning society?”

    I think lots of people are keenly aware of this issue and lots of people are trying to make that case. I think you should be asking “Why aren’t they more successful?”


    • January 20, 2014 at 11:36 am

      I think one factor in the lack of success so far is the fragmentation of the aware. I have been thinking about this for a while and talking to mathematicians and many seem pretty unaware. It’s only in the last 6 months that I personally have started connecting with other folks who are aware and — more significantly — active.

      What is going to bring together the aware and interested? What institution or mechanism is going to increase their influence? The AMS and MAA have started addressing the economic and technological changes in higher ed, but they alone are not able to show us the possible futures.

      JSE, you present one possible future in your post. In order to be successful, we mathematicians need a more compelling possible future. I have not seen one articulated.


  8. anon
    January 20, 2014 at 11:15 am

    I have never really bought into the idea that MOOCs will change everything – correspondence courses have been around for ages and have never killed in-person introductory courses. Online courses have already existed for more than a decade (I took AP Stats online since my high school didn’t offer it, and there were two of use in my class of 300 that had ever taken an online course), so I don’t really understand why re-branding them as MOOCs suddenly means they’ll rocket up in popularity.


  9. January 20, 2014 at 11:21 am

    There is another danger to using MOOC’s for calculus. The test questions will need to be written to be machine graded. This means an emphasis on performing algorithms to get the correct closed form and/or multiple choice questions. But wait this is what we do already. A typical calculus test is mostly questions that require demonstration of the processes of taking limits, differentiating or integrating – because they are easier to grade and easier to teach. Any credible CAS can do this now. If our tests asked predominately questions that required understanding calculus concepts – continuity, accumulation, the relation between a function and its rate of change and applying such concepts, our jobs could not be replaced by machines. The questions are just too hard to write and grade. I don’t think there is a machine that can presently grade a nuanced essay on how the expression for a line integral in polar coordinates is derived or how to express the speed of a camera tracking an antelope escaping a cheetah. Back to grading papers.


    • January 20, 2014 at 1:56 pm

      No – MOOC assessments are not necessarily machine graded. The Coursra MOOC English classes are using peer review of essays rather successfully. A typical essay gets 4-5 peer reviews and at least a couple are as good or better than the feedback you’d get from a university grader/prof.


      • Michelle
        January 20, 2014 at 9:36 pm

        “The Coursra MOOC English classes are using peer review of essays rather successfully.”

        I’ve taken 3 MOOCs, two because I wanted to know the stuff and one early on to see what it was all about. These were technical (math / science) MOOCs. And “rather successful” is not at all how I would describe the peer grading system used in every one of those courses. “Unmitigated disaster” comes a notch closer.


        • January 20, 2014 at 10:50 pm

          I took two Coursera composition courses, one from an Ohio State prof and another from Duke. In one, we were taught how to go about reviewing papers, given detailed rubrics and turned loose. I learned more from the reviewing process than writing and editing the papers. I wondered whether there was some machine process that matched higher quality essays with reviewers that also wrote such essays. Frankly, the writing feedback was better than what I received during my entire dark age undergraduate education.

          I’ve taken other MOOCs that didn’t turn out so well. The process used to teach students how to grade peers likely separates the successful efforts from the “unmitigated disasters.”


    • March 3, 2014 at 12:01 pm

      Well, you do it the “easy to teach — easy to grade” (=mechanical) way — you lose it to the machines.


  10. Deane
    January 20, 2014 at 12:15 pm

    I’ve always envisioned a hybrid teaching model combining a MOOC with in-person human TA’s (I don’t see a call center as being effective). This definitely leaves tenured professors out, but it was always a misfit having research-oriented faculty teaching service courses.

    This leaves the question of how to fund mathematical research, especially pure math.
    For this I see funding by the government and private foundations supporting researchers both in universities (where they would also teach primarily math major courses and run Ph.D. programs) and research institutes. This, by the way, is somewhat similar to the European model.

    This will definitely reduce the number of research mathematicians. Unfortunately, I don’t see this necessarily as a bad thing. There are already too many math Ph.D.’s being produced without enough research-oriented positions for them. Right now the production is driven mostly by departments needing to justify the existence of their Ph.D. programs, leading to overproduction.

    An alternative is to modify the Ph.D. program so that it trains mathematicians who are actually useful in the real world. I think the way graduate students are trained is abysmal and not a lot better than most calculus courses. They memorize theorems and proofs and learn to use them in rather superificial ways. If you ask a typical Ph.D. a question that can be solved using only elementary methods (say, up to freshman calculus) but not through boilerplate approaches, too many have no idea what to do. I learned this from interviewing job candidates for both a Wall Street position as well as a calculus instructorship. It was a rude shock that frankly made me quite angry.

    This by the way is closely related to recent stories about social scientists and medical researchers misusing math and statistics in their research. We all tend to blame them for this, but I think it’s about time for the mathematical community to recognize that a significant cause of this problem is the superficial manner in which we teach math and to do something about it.


    • March 3, 2014 at 11:44 am

      Right on!


    • Suhyoung
      March 5, 2014 at 12:00 am

      I agree with you. The basic thing is that we see the same thing for the math students entering the grad school and so on. The basic reason seems to be that the students today are pressured to obtain “scores” and they can easily pass the course without doing any independent thinking. One just has to be passive and follow the course and do the expected things. This is how much the professors these days can do. Clearly, this was not what was going on in 50s and 60s unfortunately. The university education everywhere has devolved. Too much financial, teaching, and research accountability come to my mind as being one of the cause. There are other significant reasons of course. Also, I think that MOOC is exactly opposite to solving this problem.


  11. darfferrara
    January 20, 2014 at 12:27 pm

    Calculus started as a research project that was privately funded (Halley financed the Principia after the Royal Society blew its publication budget on The History of Fished). Private funding can work well.


  12. Pangloss
    January 20, 2014 at 12:34 pm

    Calculus MOOCS increase the supply of math education, but they could also increase the demand. If more people actually wind up learning calculus, that’s more people who can be taught linear algebra. This could be a really big effect if MOOCS help high schools to teach calculus to more of their graduates, which seems to be the the trend.

    I suspect that most people who take only calculus in college just want to challenge themselves with a serious math course. If calculus comes to be perceived as a basic math course they will take something else. That other thing would likely be less amenable to computer grading, since nothing is more amenable to computer grading than a calculus class.

    So I think we’re safe if MOOCS are terrible or if they are very good.


  13. quasihumanist
    January 20, 2014 at 1:01 pm

    (I’m going to make two comments, because they are entirely orthogonal to each other.)

    I don’t think MOOCs are really the issue here. To see why, look at English departments. The war against mass instruction in First-Year Composition has been won. Almost every university teaches their Composition classes in sections of 15-35 (the exact size depending on the wealth of the university). Almost no one seriously considers putting all these sections together into large lectures with nearly automated grading of essays.

    I am sure that, thirty or forty years ago, many scholars of (English) Literature thought research in their subject was much safer than the rest of the humanities because there would always be a source of funding from the need to teach Composition to virtually every college student. That hasn’t happened. Except at elite universities, Composition is taught these days almost entirely by grad students and adjuncts, overseen by someone either with a PhD in Communications or a PhD in Writing Education. Literature research has been (worse than) decimated.

    The only reason this hasn’t happened in mathematics is because there hasn’t until recently been a steady supply of cheap adjuncts.

    Unless the economy improves in a way that dramatically improves employment (and I’m not optimistic about this), convincing everyone to teach Calculus Michigan-style (in 30 person classes with lots of interaction and conceptual exams) won’t do anything for Mathematics research. Calculus instruction will just go the way of Composition instruction, with armies of poorly-paid, non-research-active (because they’re poorly paid with high courseloads) adjuncts who are otherwise unemployed MA or PhD holders in various STEM disciplines overseen by someone with a PhD in Mathematical Modelling or Mathematics Education. Michigan itself might just be barely elite enough to escape this fate, but other places won’t hire a postdoc to teach 2 sections of calculus; they will hire an adjunct to teach 4 sections at 2/3 the pay.


  14. January 20, 2014 at 1:39 pm

    (And the promised second comment. I’ve made similar comments in the flesh, so if you think you know who I am in real life, you’re welcome to e-mail me and confirm.)

    When it comes to arguing for direct funding of research, I think the mathematics community as a whole has been making the wrong kinds of arguments. I mostly hear people talking about promoting the importance of mathematics, pointing out mathematics occasionally generates ideas that look purely intellectual but turn out to have practical use many years later, pointing out the importance of mathematics to various scientific or engineering pursuits, arguing against scientists who claim research mathematics is irrelevant, et c.

    I think this is entirely the wrong approach. We are all being pursued by a bear, which is the point of view that research is worth funding primarily because of its likely contributions to our physical safety and material welfare. The approach outlined above is basically trying to run away from the bear faster than the other disciplines, breaking their legs and throwing them behind us if necessary. We are lucky that we naturally run a lot faster than Literature or History or Philosophy or Classics (the last of which has already been swallowed pretty much completely). We might even be able to outrun Physics. They’ll get eaten first, and the bear is only so hungry, so it won’t eat everyone at once. However, Engineering and Medicine are way ahead of us, and the bear will catch up to us sooner or later.

    It makes much more sense to join up with everyone and fight the bear. We need to argue that research is worth funding because it is a fundamental cultural achievement that enriches people’s lives in non-material ways, and because our self-governance as a democratic society improves when we have a variety of modes of thoughts, embodied in specific ideas from different fields, broadly available to sizable groups of citizens who understand enough about the field to recognize the significance of the idea.

    This means spending enough time with folks in English or Philosophy to understand the significance of what they do and communicate how what we do is like what they do. It also means coming to their defense when their subjects are attacked. As an ambitious goal, perhaps we can resurrect Classics.

    Of course, maybe I’m biased because I also like (the other parts of) the humanities.


    • Bobito
      January 21, 2014 at 3:27 am

      The problem with this approach is that presently in advanced countries public funding for activities already recognized as “fundamental cultural achievements” is very small. You put the examples of English and Philosophy and Classics – all areas where public funding is marginal, if it exists at all.


      • January 21, 2014 at 12:07 pm

        My point is that funding for Pure Mathematics will eventually be at the level of funding for English and Philosophy and Classics, so what we should be doing in the meantime is trying to improve funding for the humanities in general by working to change our society’s view on what is worth funding.


  15. Fats Grobnik
    January 20, 2014 at 2:00 pm

    So, I’m not a mathematician. I was trained as a physical chemist. I have no desire to see math departments or research suffer, but I can see two major problems with how things are going:

    First, science funding is largely sold to the public through practical application. This is why NIH has a budget of ~$29 billion and NSF has a much smaller budget of ~$7 billion. Scientists have been following the money for decades, and getting better and better at selling the practical nature of their work to the public. In my case, I study biopolymers (microtubules), which play a central role in cell division (cancer, developmental defects, etc.), neurons (neurodegenerative diseases), cell polarity (wound healing, etc.), and cell transport (i.e., how pancreatic cells release insulin or adipose cells take in glucose). I study them because I’m fascinated by the strange and wonderful behavior of these biopolymers, not because I’m driven to solve the diseases that involve them (though that would be nice). However, my work may have an impact on our understanding or treatment of these diseases and it’s fair to let the public know this.

    In my experience, many pure mathematicians are almost disdainful at linking their research to anything practical, as it somehow sullies the purity of their work. They aren’t even very good at communicating the relevance of their work to other academics, let alone the public. Their work doesn’t have large capital costs and operating expenses like a phys/chem/bio lab does, so they don’t need the grant money. My take on it is that, because pure math doesn’t have to routinely justify grant money, as a field it hasn’t been forced to improve its public outreach.

    Second, I don’t have particularly good experiences learning mathematics from mathematicians. I use applied math daily: calculus, linear algebra, ODEs/PDEs, prob./stat. I learned most of it from a strong high school curriculum (taught by a former chemical engineer and a guy with a B.S. in math) and college physics and physical chemistry classes. Sure, I took the math classes in college, but the ideas were cemented and given meaning in physics and physical chemistry. While I knew what an eigensystem was, but didn’t really understand how central it was until I took quantum mechanics.

    The biggest problem I see with undergrads: they’ve taken calculus but cannot apply it to actual problems they encounter in a different field. The ability to map calculus onto the world is not developed; calculus is firmly entrenched in a “math class” box. It takes shaking the box, sometimes hard, for those skills to escape. And it’s a crying shame: calculus is beautiful, and how it maps to the real world is both incredibly useful and quite insightful.

    Which is to say that, in my experience, mathematicians need to do a better job linking abstract concepts to concrete things. It goes part and parcel with explaining their importance to the public.


    • deaneyang
      January 20, 2014 at 3:19 pm



    • deaneyang
      January 20, 2014 at 3:38 pm

      It would already be major progress if we could make sure that every science and engineering major could formulate and execute he solutions to straightforward but novel problems using nothing more than 8th grade math. In my experience this is all my engineering colleagues want their students to be able to do, and they are frustrated when the students can’t.


      • January 20, 2014 at 4:19 pm

        It would already be major progress if we could make sure that every college student could formulate and execute the solutions to straightforward but novel problems whose solution requires nothing more than what they learned in elementary school. In my experience this is all my colleagues in all departments want their students to be able to do, and they are frustrated when the students can’t.

        (Apologies for the snark, but I think viewing mathematics as having a special problem here is fundamentally wrong. That does not mean that potential solutions won’t look different in different fields.)


  16. January 20, 2014 at 3:46 pm

    Almost nobody wants to see residential colleges disappear and have 19-22 year olds taking MOOCs while living with their parents. And it would be pretty hard to justify residential colleges featuring MOOCs, web tools and glorified tutors. If the shift away from tenured profs in higher ed occurs, it will take place over decades, not years.

    1) What percentage of our youth are best developed through a university education?

    There’s a strong case to be made that we have excess capacity in US university education today. It’s not at all clear that we should continue to serve students who’ve put little effort into high school and lack basic math (algebra 1) and communications skills. It seems pretty clear that we need to find other ways to get these kids engaged into something they’ll find meaningful rather than trying to force more dreaded academics down their throats. The Germans and Swiss are doing a much better job engaging their youth and have far lower percentages of university graduates.

    2) How many people do we need in academic research? The number has exploded over the past generation. Are those at lower-tier institutions adding value to their fields relative to their costs?

    In the 70’s and 80’s there was very little support for research at regional institutions outside of flagship state schools. Now, virtually all state supported schools have research missions that rival those of the flagships a few decades ago. Same for many regional private institutions. This has led to reduced teaching loads and drives education costs far higher.

    3) Is the value of the additional research produced by those at schools with newly adopted research missions worth the debt servitude of millions of students?

    The quality of journals and conferences dedicated to disseminating this stuff is often disappointing. Some border on fraud. Perhaps these faculty could engage directly with researchers at primary venues in a support role rather than trying to develop their own agendas at lower-tier venues.

    The costs for this new set of researchers have been heaped on the backs of students in the form of sleazy government-backed loans that university’s refer to as “refund checks.” Most of the marginal college students have no idea what they are getting into, graduate owing the equivalent of 2 car payments for school loans, and have minimal prospects of finding a job that will get them out of debt servitude.

    I’ll agree that support for math research and other academic research is at risk. But not from MOOCs and web tools. The money river flowing into higher education may be drying up because student loan default rates are too high. The impact of the defaults on employ-ability far outweigh the benefits of educating students who’d never be considered for university education in any other country.


    • January 20, 2014 at 4:13 pm

      If you’re going to adopt a Continental view of higher education, then you also have to adopt a Continental view of democracy, which is that the people get to choose who runs the country from a diversified (intellectual) elite, rather than the people directly running the country.

      You could argue that’s actually better, or that it’s what’s already happening in the US now, but I’m not ready yet to give up on traditional American notions of democracy.


      • Nathanael
        March 4, 2014 at 10:45 pm

        In the US now, we sort of get to choose who runs the country from an undiversified and unintellectual elite, and even then, not really.

        I’m not sure what “traditional American notions of democracy” means, but it certainly has nothing to do with the Electoral College or the US Senate or gerrymandering, which are the key features of the federal government… let alone the Supreme Court picking the President as happened in 2000.


  17. Brayton Gray
    January 20, 2014 at 4:29 pm

    This is a good point. But what it means is the end of math research in the United States. In Europe, the bread and butter you speak about is usually taught before entering the University, so the funding of research does not depend on calculus. The other effect of MOOC will be the dumbing down of the mathematical abilities of “educated” Americans (yes there is more room at the bottom!).


  18. January 20, 2014 at 9:40 pm

    To me, as someone who learned the same calculus twice, first in a chemical engineering degree, then in a statistics degree (because the maths school who ran the first statistics subjects considered, wisely, that my maths knowledge had gone stale in the interim), it is actually surprising that calculus continues to be taught so widely to engineering students. From the point of view of completing the course, it was rare that anything beyond the chain rule and integration of linear combinations of polynomials and trig functions were required, plus knowledge of what a differential equation was, but not really how to solve one (they can always be solved numerically by a computer, at least in undergrad engineering). Realistically, what the engineering department really required was a revision class to make sure everyone had really learned all of high school maths. When I graduated, working engineers were often proud of having deleted maths past year 9 from their memories. Linear algebra was the first item taught, then never referred to again, in my recollection ( of course, as a statistician, if I could increase my knowledge in one area only, it would be linear algebra). Most of my fellow engineering students resented the maths department’s intrusion on their time, and the resentment was maintained when the maths department’s promise that we would use this in engineering subjects failed to eventuate. Those students are on their way to being leaders of the profession, and it seems like any disruption to calculus teaching, including the MOOC challenge, could provide a catalyst for questioning the value of it at all.

    I say this in spite of the obvious value of calculus (and linear algebra) to engineers in whatever stream. For me a feature of re-learning calculus was correcting and deepening my understanding of most of the rest of my, by then, half-remembered engineering education. It is my hope that some of the less proud-to-be-ignorant engineers around use MOOCs as way of having that same experience.


  19. January 21, 2014 at 1:25 am

    While I agree that major change in the circumstances of mathematical research is likely to come soon, I don’t share your pessimism. As I see it, funding by calculus is but one business model for supporting mathematics and, can be replaced by a different model
    if needs be..

    Much of my optimism comes from what I am seeing happening nowadays in the functional language meetup community in New York City where I am seeing the first glimmerings of
    such a new model. What we have here are people who have advanced degree in math
    who are no longer in academia but nevertheless are interested in continuing their
    research careers and finding creative ways of doing so aided by the internet. For instance, last fall, a seminar on a cutting edge area of mathematical research, Homotopy Type Theory was organized and run by such people and is still going strong and, the other day, I received an announcement of a mew math meetup group which will kick off early next month with a lecture on Wiles’ proof of Fermat’s Last Theorem.

    While it has a way to go, I see this as at least a first proof of concept of an alternative
    socioeconomic foundation for mathematical research. Even in a worst-case scenario
    where online teaching renders undergraduate calculus instruction obsolete, I think that
    a plausible outcome would be that the 50% of mathematical research they carried out
    would instead be done part-time by non-academic mathematicians.

    To support this assertion, let us consider what a university environment has to offer. I
    would say that the basics are a salary, colleagues to interact with, and a math library.
    As you point out, for most academics, research is a part-time activity; I would posit that
    computer programming, data analysis, or finance is as suitable a day job for a research
    mathematician as teaching elementary courses. Although there is still much to be done,
    the web has the potential to provide the functional equivalent of colleagues in one’s
    department and the university math library; moreover, as an independent scholar, one
    still can have some degree of access to academic resources, especially if one can make
    use of alumnus status or has suitable contacts. Also, I expect that a good number of
    employers would recognize part-time research and publications as valuable assets on
    a resume.

    Thus, I feel optimistic that, as it has done in the past, basic math research will continue
    even if the rug disappears from under calculus teaching. Moreover, as someone who
    has been involved for several years in community efforts related to mathematics, I also feel confident in the ability of the community to self-organize new institutions and support mechanisms for research.


    • DJ
      January 23, 2014 at 12:25 am

      There is a synergy between teaching and research that cannot be matched by any other business model. Teaching supplies a steady stream of student labor for research which is both cheap and enthusiastic. Teaching solidifies one’s understanding of core concepts which are necessary for progress in research. Likewise, active research leads to new insights which serve as valuable teaching tools. I do not think that this model can be replaced by corporate overlords. Both research and teaching will be the poorer for it. Fortunately I don’t believe that MOOCs will overthrow the existing research/teaching model. Students will pay a premium for good learning environments. We see this even today: university enrollment is not diminishing, despite the growth of cheaper alternatives such as community college. The synergies mentioned above ensure that the best teachers, on average, will always be active researchers, and not in want of support. We may well have fewer research positions, but I do not expect a drastic collapse to the point where it threatens the research enterprise itself.


    • Suhyoung
      January 26, 2014 at 10:32 am

      Of course in this case, the quality control is very hard. There were some amateur mathematicians who were powerful politically and but were bad mathematicians pushing for a proof that was incorrect. There were of course amateur mathematicians who were good mathematicians who were ignored by professors. I think that the elite department model is a good one that we should keep and hold onto. Otherwise, we will have no accountability or ways to check validity and so on. We might be going into pseudo-mathematics if amateur mathematics is the only option.


  20. Bobito
    January 21, 2014 at 3:25 am

    With MOOCs there is still a need for one-on-one tutoring. Also it is necessary to prepare materials (problems, labs, notes, etc.) to accompany them. They generate as much new work as they destroy. Most of it still has to be done by professional mathematicians.

    MOOCS offer an opportunity to improve teaching. One selects charismatic and skilled lecturers to give the lectures, and uses the remaining faculty to give more individualized instruction and assistance on site. Access is improved and there need not be any reduction in the quality of instruction; rather impersonal lecturing can be supplemented by personal attention. The support workload is simply shifted to other areas. More time can be spent on designing quality exercises and evaluating them, etc.

    Finally, it’s not at all clear that teaching calculus via MOOCs is really cheaper than using adjunct faculty and poorly paid postdocs (on their third postdoc) to do it. Administerting a functioning online course requires competent computing support and transfers to some administrative staff an administrative workload that used to be assumed by teaching faculty.


    • FormerMathMan
      January 21, 2014 at 1:07 pm

      I agree with your last point: I’m also not sure MOOCs are really cheaper. When I was a calculus instructor (at a very good, but not elite, school) the department paid me $7500 per course for 200-300 students. That works out to $25-40 per student for a course; I’m not sure many MOOCs can compete with this. I know it’s sad that I have to use low labor cost of academics as an argument in our favor, but there you have it 🙂


      • January 21, 2014 at 3:27 pm

        Just as with the MOOCs, so too with the colleges we should total all the costs involved
        before making a comparison. In addition to paying the instructor and the graders, there
        are administrative costs and the cost of maintaining the building where the classes meet.

        In your case, I would guess that each student pays something like $1500-$5000 in tuition
        to enroll in the course. Thus, the salary of the instructor works out to a few percent, with
        the bulk of the rest presumably going towards administration and building maintenance.

        As every homeowner knows, maintaining a building, especially something the size of a lecture
        hall which can seat several hundred students, is a pricey proposition. Thus, the impression I
        get is that the key financial factor in favor of the MOOCs is that they don’t have to pay for a
        brick-and-mortar classroom.


        • DJ
          January 23, 2014 at 12:30 am

          Campuses are presently binge building to an unprecedented degree. I do not see any evidence that they are interested in saving money on infrastructure. To the contrary, even mediocre universities seem to be competing voraciously to out-do each other in the level of excess that they lavish on facilities. The buildings are a sunk cost and are not a place where MOOCs generate savings.


        • January 23, 2014 at 12:21 pm

          While the cost of erecting a building is a sunk cost, the cost of maintaining it is ongoing. Especially for a lavish building, the costs of utilities, grounds-keeping, repairs, insurance, and the like can add up to a sizable sum, and need to be paid on a continual basis throughout the useful lifetime of a building. To clarify, what I was proposing above was that these ongoing costs (not the one-time cost of purchasing or erecting a building) should be taken into account when comparing brick-and-mortar institutions with their virtual counterparts.


        • DJ
          January 23, 2014 at 1:21 pm

          Typically, even universities of modest rank fund the vast majority of their facilities construction from the last 50 years through directed donations. The donor gets their name on the building, and there is an implied covenant on the part of the university requiring them to maintain the building in active use as a condition in exchange for receiving the donated funds. There is no flexibility on the part of the university to divert or reallocate these expenses.


        • January 24, 2014 at 10:04 am

          Increasingly, such buildings are funded with bonds to be repaid with future student fees. “Debt Service Fees” are now common at universities of “modest rank” and add thousands to the debt loads of their graduates.


  21. January 21, 2014 at 1:24 pm

    Cathy wrote:
    1) Math research is a byproduct of calculus teaching

    Math research is essentially funded through these teaching jobs.

    2) Calculus MOOCs and other web tools are going to start replacing calculus teaching very soon and at a large scale

    3) Math researchers will be severely reduced if nothing is done

    Accepting 1) and 2) for the sake of argument, conclusion 3) seems to assume that it’s the younger, calculus-burdened set that does the important bulk of (basic and applied) math research, rather than the older established and less-burdened set, which I suppose is arguably and largely the case — although outliers will certainly always be found throughout history.

    Cathy wrote: “Why aren’t [mathematicians] making the case that math research is vital to a long-term functioning society?”

    Hmm, well maybe the case could be made that the high volume of math research in recent years (say since the Fed-subsidized explosion in STEM staff and courses after the Dawn of the Space Race in the early 1960’s) did not really correspond to a higher level of quality in the research.

    There has certainly been a massive increase in the number of quantitative-journal pages, but as an example of that which should apply to being “vital to a long-term functioning society”, the development of meaningful statistical knowledge with respect to so-called econometric mathematics has been appallingly dismal in relating to reality, which brings into question whether such a set of it and similar fields even qualifies as trying to use scientific methods, much less qualifies as Science with a capital S.

    Cathy wrote: “But I’m thinking that’s going to change. We’re going to think about it pretty hard and learn how to promote math research very soon, or else we’re going back to 1850 levels of math research, where everyone knew each other and stuff was done by letter.”

    An example of a mathematical Cash Cow in the 1850’s might be argued to be the remarkable effort to educate many mathematicians (and also a large percentage of physicists) in the highly abstract and tortuously difficult (no doubt boring and painful) arena of Hamilton’s Quaternion “calculus”.

    Although it was never fully developed as a legitimate field of Analysis in the 19th Century, it was viewed for many years (late 1840s – early 1890s) as vital to the rapidly developing quantitative sciences in the major universities throughout Europe and even several in the United States. Its powerful and concise notation and many of its basic concepts came to dominate completely for instance the rise of Maxwell’s unifying electromagnetic theory and even the early expression of Einstein’s four-dimensional special relativity.

    Quaternions rapidly died at the dawn of the 20th Century (after the tempestuous journal-editorial battle of the early 1890’s) as being far too complex and arcane to be continued as a universal university curriculum, when much of its glorious pioneering development was subsumed into far simpler and more digestible components such as vector analysis, Clifford analysis, tensor analysis (as rendered through matrices), and more abstractly by the broader arena of Grassmann spaces.

    Quaternion analysis as a proper, unadulterated, unfractured area of math (beyond its Number Theory origins) has only recently been somewhat restored to respectability within applied math by the advent of computers, which can easily take its vicious complexity in stride, and has become vital and the method-of-choice in the relativistically-accurate 4-dimensional calculation of satellite, astronomical and celestial spheres removed from Mother Earth. Within the speculative dream world of basic research is now growing its approach in the very fundamental Penrose Twistors and the Multiverses of gradually-winnowing String theories (which, who knows, may all become unified via Quaternions?).

    Cathy wrote:
    “…in about 10 years, and that’s the time scale at which I think math departments will be shrinking instead of expanding.

    I think one can really make the case that basic math research should be supported and expanded

    And hopefully it will be a community effort and not controlled by a few billionaires.”

    Basic math research has never been the object of large support and (even with the remarkably-exploding worldwide education being brought about by MOOCs) is unlikely to expand significantly beyond the capacity of those few souls capable of it, regardless of the resources made available.

    What has grown beyond all reasonable bounds is the applied math “research” driven by academic and financial interests seeking out the ever better Golden Road to Riches, resulting in a colossal collection of unsubstantiated nonsense based on a growing and ridiculous set of Nobel prizes that have uncovered nothing but astounding contradictions founded on fantasy assumptions.


  22. S Haust
    January 22, 2014 at 10:03 am

    You mention the Coursera offering at Penn, so I had a look and then listened (watched?)
    about 20 seconds of Lecture 4, “Computing Taylor Series”. My God, that stuff is awful.
    The “professor” looks like a shill for some disreputable product and uses a most annoying
    tonal rise at the end of each sentence. Obviously, he is talking to a machine and knows it.
    That means you, dear student; you are the object of this. Possibly, one could actually
    learn some topic or course material from this stuff but the distractions are so extreme,
    I would almost puke on every piece of paper.

    Please, give me a break. I have used a bunch of video recorded courses and, though
    I didn’t care for some of them, none was as bad as this stuff. If I were back in my student
    days, I would have to wonder seriously what I was doing there and why I should stay.


  23. January 22, 2014 at 10:10 am

    As a blogger who has written many posts on the potential impact of MOOCs on public education (http://waynegersen.com/?s=MOOCs), I found this post to be one of the most insightful analyses I’ve read. Of all the comments, the one that got my attention was Cathy’s response to a comment, where she promised “…to write a follow-up with a few suggestions on how mathematicians can try to take early and strong control over a definition of success and a design of testing of this so that the debate isn’t completely co-opted by people with purely commercial interests.”

    In public education the debate has already BEEN co-opted by privatizers and the effect has been a retrenchment into the status quo by those who are techno-phobic and/or traditionalists… and in public education we have decided to measure what is easy to measure instead of what is important to measure… mainly because it is cheaper to use multiple choice tests for most content and scanner-friendly algorithms for essays. My advice to colleges: keep your eye on USDOE! They will be developing the metrics and designing the tests that will be used to define “success”… and if the proposals I’ve read so far are any indication colleges, too, be on the defense. USDOEs “Race To The Top” has resulted in a race-to-the-bottom for wages and some nice paychecks for privatizers.


  24. eddie sacrobosco
    January 22, 2014 at 1:03 pm

    The developmental courses at the community college where I teach have already been co-opted by computer adaptive learning, so the students’ work is now completely individualized. The highly motivated self-starters move through the material quickly and can finish two courses in one term. Unfortunately, this is, at most, 25% of the students. The rest need instruction, but the college (for some unspecified reason) refuses to offer these sections anymore – all courses below the 100-level are required to use the software. Of course, if you think that these developmental algebra courses are high school material – that’s true. However, there is no guarantee that the high schools teach this material at all, or, if they do teach it, that a passing grade=learning. I taught high school for six years and lived through the “Math Wars” of the 1990s – this is why I now teach at a CC.

    Losing the give and take of the classroom and having all the students working on the same problems at roughly the same creates a learning community that is a special thing that many people won’t appreciate until it’s gone.

    This is a long-winded way of saying that whether students “like” MOOCs or not is irrelevant to administrators and privatizers – when you force everyone to take the technology based courses and do away with face-to-face learning, it doesn’t matter what the students want. If you control the market, you don’t have to sell a working product – if crap is all that’s available, then the crap will sell – until it doesn’t.

    If you think that administrators wouldn’t gut their institutions and drive students away by only offering courses that the students hate – remember – it’s not a bug, it’s a feature. When public education goes away, people won’t have any choice but to seek out for-profit education (this phrase makes me gag almost as much as for-profit health care).


    • Nathanael
      March 4, 2014 at 10:43 pm

      <blockquote cite="#commentbody-55758" If you control the market, you don’t have to sell a working product – if crap is all that’s available, then the crap will sell – until it doesn’t.
      If you think that administrators wouldn’t gut their institutions and drive students away by only offering courses that the students hate – remember – it’s not a bug, it’s a feature. When public education goes away, people won’t have any choice but to seek out for-profit education (this phrase makes me gag almost as much as for-profit health care).
      This is why I believe that academics are going to have to go back to the future and found their own, faculty-controlled universities on the co-op model, where the rich guy/trustee/administrator cabal is simply not permitted to control it. Remember, *this is how Oxford and Cambridge started*, before the colleges got their endowments.
      I don’t see any other way to have working institutions. It’ll be a tough slog at first because the existing institutions are well-funded, but since the administrators are trying to gut their institutions… well, you see what I mean.


  25. curlydan
    January 22, 2014 at 2:55 pm

    Good post. After reading your post, I see two trends. 1.MOOCs are likely to decrease the number of grad students who are getting scholarships/grants. 2. The big data trend, though, may increase the need for math/stats knowledge.

    What could be the result of these two trends? Similar numbers of math/stat grad students but less money to pay them. So math moves more toward a pay to play degree. That would be sad since too many careers already require students to load up on debt before they start getting paid. My M.S. in stats was nicely paid for by teaching undergrad business stats, so I had very little debt after getting out of school.


  26. January 22, 2014 at 9:17 pm

    What about Kahn Academy? Does that work? Has all of this effort been applied to “Limits to Growth? Azimuth is a good blog to see where some of this is being considered. The defunct “Oil Drum” had lots of engineer types doing all kinds of math that sort of by passed the material that H. Smil has covered.


  27. January 23, 2014 at 8:10 am

    Cathy this is a brilliant insight. Way to think two steps ahead.


  28. January 23, 2014 at 8:17 am

    Mathematicians hate being asked “What’s the point of all this?”. They will have to learn to answer that question a lot better if they want to go on as anything but “independent researchers”.


    • January 23, 2014 at 8:19 am

      …if MOOCs do really knock out the intro calculus & statistics classes, I mean.


  29. Suhyoung
    January 23, 2014 at 9:32 am

    I am not completely sure if the universities today are so expensive. Probably they are less so than my time when people are making much less money and the credit was very hard to obtain. Also, we can cut our cost of the university education by cutting down many expensive programs not related to education but related only to “job getting contact with business world”. These do not deliver anything. Let us downsize these glorified programs and let’s see where we stand. Eventually, MOOC might become competitive but we don’t really have a good enough AI. The singularity people are vastly wrong. Listen to what Chomsky says about these. Language is too complex. See what Google did to get machines to recognize computer pictures even. Some amazing computational power is needed for simpest human flexibility. They cannot substitute people in teaching absolutely.


  30. January 23, 2014 at 12:19 pm

    It’s brilliant that you are linking the two. However, I think of the issue differently:
    a) regarding the intro calculus courses… if true that the reason for offering them is to fund math research, that would be very sad indeed.
    b) the educational community is at fault for not talking about the elephant in the room – MOOCs are like your unregulated off balance sheet company; no one has figured out how to evaluate students and prevent cheating. Pete Norvig gave a talk about MOOCs last year, and he told the audience there is no way to verify students or prevent cheating, and it’s the “wrong question to ask”,.. basically, let us grab eyeballs first. Students prefer MOOCs because it’s an easy A since you can find someone else to take the exam, or cheat in oh so many ways. The end result is we have generations of students who get As in Calculus MOOC and can’t tell differentiate from integrate.
    c) the notion that there is one way to teach any (intro) subject that works for everyone is nonsense. There will always be different approaches to teaching the same subject, and different students will always respond to different styles. MOOCs are anti Big Data in the way that it presupposes that everyone should be taught in the same way.


  31. davidmfisher
    January 23, 2014 at 1:16 pm

    I actually think it is quite indicative that it is U. Penn where MOOC calculus is most successful so far and MIT where it might catch on next. The first two places I taught during my career were Chicago, where as a student I taught a lot of calculus, and Yale, where as postdoc I taught some. Since then I’ve taught at Lehman College and Indiana University. While most Yale and Chicago students might do just fine with a MOOC, I’d be pleasantly surprised if most students at Lehman or Indiana were up to them. This really matters for research funding, since I think Penn, MIT, Yale and Chicago all have the resources to continue funding research even if they don’t teach calculus and it is places like Indiana and Lehman where jobs for research mathematicians will disappear if calculus enrollments do.

    One thing missing from the discussion is how much support a typical university offers it’s calculus taking undergraduates. Not only do they have a professor and TA’s, but there are also departmental help rooms, and help sessions in dorms and if one needs even more than that,
    lots of tutors readily available. Heck, even at University of Chicago, the lowest level of calculus met 5 times a week and involved a graduate student instructor plus 3 undergrad TA’s for roughly 30 students. Anyway, you cut it, there is a lot of live one on one hand holding and helping going on to get the great mass of students through calculus. I’m just not convinced that all these students will be able to replace all that extra help with reading Calculus Overflow. Or asking questions in webforums. At IU we even have the possibility of asking questions for low level courses via email connected to online HW systems. The only students who use email are the ones who do their HW too late the night before it is due to use a one on one interaction. And they generally find it much more difficult to understand email answers than one’s given in person.

    Maybe all of this can be overcome by video conferencing with call centers in India or some such, but I think there are still a lot of obstacles to overcome. So I suspect that if this has a big impact, it isn’t for another decade or more.


    • January 23, 2014 at 1:19 pm

      I agree that the in-person hand-holding is useful and not going to leave soon, if ever, for most students. That said you can have plenty of calculus help rooms staffed with cheap help and get rid of the math professor, and maybe the grad student TA’s, and you’d still be unhappy.


  32. January 23, 2014 at 3:38 pm

    if i may add my thoughts (having been in the middle of some of this):

    1. i agree that if mathematicians justify/fund their existence solely though the teaching of low-level courses, then the field will experience a dramatic decline as technology makes teaching low-level courses more efficient. you can argue about the efficacy of MOOCs, but the platform will quickly adapt and improve. this, i think, is inevitable.

    2. given that assumption, why would any mathematician with a soul build a MOOC? because they will be built by someone. if mathematicians don’t build them — and build them well — then physicists and engineers and economists will build calculus MOOCs that teach math as a bag of tricks to be memorized and endured: these will then be adopted. that would be a disaster of an even greater magnitude than the disaster that calculus-text-publishing already is.

    3. i believe that this moment of increased attention to education and pedagogy is a great opportunity for the math community to build high-quality courses/materials/MOOCs so as to exposit, explain, and advertise our beautiful subject to the world. with so many people [academics included] who don’t “get” what real mathematics is, we now have the chance to show them — in video, with with full panoply of color, motion, and flow that math entails.

    4. it’s very hard to predict the future. if i had to choose the right analogy for MOOCs, i might say “music”. once available only live, the technological increase in distribution and creation mechanisms did not put musicians out of business (entirely). the good part is that the total amount of music consumed skyrocketed, and new forms evolved. the (maybe) bad news is that not much of the gain was in “classical” styles and, indeed, much of contemporary music consumption mirrors the culture. i seem the same happening with MOOCs. no matter what we do, we will wind up getting “twerk your way through calculus with miley cyrus” or some such nonsense, and it will be wildly popular. but it is still up to us to build a high-quality alternative, and unveil as much of the beauty of our subject as we may.

    (actually, i think that video-games is a better analogy : shorter time-scale than music. the first games could be built by one person in a few months for peanuts. now, games are huge movie-like efforts…)

    5. i recognize there are a lot of strongly held opinions. i would urge anyone concerned to drop in on some of the math MOOCs and inspect. better still, critique, and help with building a better product.

    robert ghrist


  33. January 25, 2014 at 3:18 pm

    I can chime in here as an adult non-trad student who in the last three years has gone from not remembering basic rules for distributing exponents to finishing a fairly challenging math minor consisting of the Calc seq, Linear Algebra, Intro to proofs and Real Analysis (accompanying an Econ major). I am waiting on responses to PhD apps right now, which is to say I am a very motivated student. And I don’t think that I could have hacked it at all with just open courses and the internet. I gained, far and away, the most value from small learning environments, talented grad students and a few especially gifted (at teaching) professors. I gained the least value from large lectures where back and forth was mostly infeasible. I spent MANY, MANY hours in the math learning center using grad student tutors and did use some online courses to enhance understanding.

    I really, really think that math departments have little to worry about from online offerings and that Baumol’s disease is alive and well in the classroom. One person teaching a modest number of people in person still can’t be beat, particularly by the utterly impersonal and especially demotivating tool of online video playback. I concur with the commenter above that it may be the case that math is at a time of “peak lecture sections” and perhaps the need to keep grad students funded will end up fostering more small discussion style courses. Correspondence courses and video taped courses have been around for quite some time, just because the content streams fast or “there’s an app for that” does not really change anything fundamentally, especially given how low graduation rates for marginal students are already.


  34. Suhyoung
    January 26, 2014 at 10:44 am

    MOOCs can be used in some other model than replacing main lectures and help sessions. I believe that problem solving of individual examples can be stored and be reused by students many times. This is what MIT does. I like this model. The main lecture model can be bad if MOOC lectures are the only main lecture that they can attend. The problem is that the levels of the students are so vastly different between different colleges and universities and regions. MOOC is probably too ambitious. The unfortunately, the profitability forces this model that cannot work out, I think. If we go nonprofit and use MOOC wisely, we might have some good ways to assist calculus learning. This might even help math professors and grad TAs. MOOC as main lecturing model probably won’t work out and will damage the universities without just cause. I am very worried if the infusion of capital in this way will be very harmful. The present situation in the university instruction now may be costly but it might be more costly if we made a huge mistake of introducing MOOC without careful thoughts. The results may be 60-70% of students who can’t use calculus. Also, the current model of teaching is not the cause of the cost increase. The education cost can be controlled much effectively by cutting down some glorified programs. The students are subsidizing many government and business experimentations and so on.


  35. Will Farnaby
    January 26, 2014 at 1:13 pm

    S Haust :
    You mention the Coursera offering at Penn, so I had a look and then listened (watched?)
    about 20 seconds of Lecture 4, “Computing Taylor Series”. My God, that stuff is awful.
    The “professor” looks like a shill for some disreputable product and uses a most annoying
    tonal rise at the end of each sentence. Obviously, he is talking to a machine and knows it.
    That means you, dear student; you are the object of this. Possibly, one could actually
    learn some topic or course material from this stuff but the distractions are so extreme,
    I would almost puke on every piece of paper.
    Please, give me a break. I have used a bunch of video recorded courses and, though
    I didn’t care for some of them, none was as bad as this stuff. If I were back in my student
    days, I would have to wonder seriously what I was doing there and why I should stay.

    What an asinine post.

    S Haust refers to Calculus – Single Variable, developed by Professor Robert Ghrist, UPenn.
    You can take the quotes off: the “professor” really is a professor. Here is his CV:

    Click to access cv.pdf

    Why don’t you post your CV, S Haust? Let’s see how you compare to the “shill for some disreputable product”.

    The absolute inanity of – “uses a most annoying tonal rise at the end of each sentence. Obviously, he is talking to a machine and knows it. That means you, dear student; you are the object of this.” – does not warrant any further comment.

    I close by noting that Ghrist seems to well-appreciated by the students of the initial and current editions of his MOOC. Judging from the public record, they seem to find his teaching valuable, his style engaging, and the materials delivered through the course worth the effort.


    • Suhyoung
      January 26, 2014 at 2:52 pm

      Grist is a very reputable 1st rate topologist. His work is of great importance. But I don’t think that this medium is for him. That is another point: The medium can distort many things. I think that we need to view MOOC as an experiment and not implement MOOC as the financial people want: immediately.


      • Stephen Shank
        February 2, 2014 at 10:27 am

        I’m just curious, of great importance to whom? To other topologists? Or other mathematicians? Or other academics and scientists? What about to your average blue collar worker? Could sum up the contributions of a 1st rate topologist to a police officer, nurse, firefighter, construction worker, etc., and explain why their research should continue to be funded while others break their backs and risk their lives? I do not say this disparagingly, I am truly curious about the type of work that is performed, and just how important it is. I saw a fascinating talk on connections between algebraic topology and Maxwell’s equations and wish I understood more. But when you say the work is important, I would really like to know… important to whom?


        • Suhyoung
          February 4, 2014 at 5:58 pm

          I just wish to point out that pure math have been influencing the applied field for very long time and vice versa. There are many historical evidence for it. Pushing pure mathematicians into applied field has great danger. Applied fields shift interests very fast and the time and period and demand can be very difficult to catch up to. I believe that much applied math field can become wasted effort while the significant results in pure field can have more stable value to future. All applied math research are after all based on pure mathematics model.
          I think that this is true. Fluid dynamics for example can be a problem in applied math or just engineering but it can also be a problem in pure math, even topology. There just seems to be some kind of “angle” here in what you are saying.


  36. Stephen Shank
    February 2, 2014 at 10:19 am

    Interesting article, but I believe the statement about mathematics research being purely funded through these teaching jobs is a bit imprecise. For pure mathematics, I’ll agree, but applied mathematicians have tons of opportunity in government and industry if you are technically gifted and know how to communicate. I’ve had a feeling that pure mathematics will undergo a contraction and this article reenforces that. Which it should, I believe. But it should not disappear altogether, because pure mathematics at it’s most advanced levels is a form of art and deserves appreciation and support, and unexpected connections between pure and applied mathematics will continue to pop up and have the potential to contribute to scientific challenges and therefore further human progress.


  37. Suhyoung
    March 4, 2014 at 4:36 am

    Actually, I think that there will be much more demand for teaching for courses such as calculus and even higher level mathematics such as group theory, number theory, topology, and so on. The basic reason is that we will have to have higher math literacy for the employment of the future. It looks like that there will be much more jobs in the sector requiring higher level mathematics. (Government “should” be realizing this by now.) In fact the things are going now on at the universities. Many engineers are switching to looking at things from more pure mathematics point of view. Also, the distinctions between pure and applied mathematics are very fuzzy. If one defines “applied mathematics” as mathematics that are applicable, then the pure mathematics is always on the loosing side. The definition is self-defeating for all mathematicians. I think that this is a puzzling problem we have to study well and not jump to quick and easy conclusions.


  38. Nathanael
    March 4, 2014 at 10:38 pm

    FWIW, I’m fairly sure math research will continue in industry. Even pure math research.

    The problem is what gets done with it.

    When research is done at academic institutions, it’s published. When research is done by industry — as it was for most of history — it does NOT get published; it gets retained as a trade secret and knowledge fails to advance.

    To counteract this, researchers need to form some form of union to share their knowledge and fight against NDAs and similar.


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