Is online education good or bad for equality?

It seems like it would obviously be good — now kids who don’t have money and don’t live near universities have, in principle, access to much of the world’s knowledge as long as they have a cheap computer and an internet connection.

But in math, I’ve heard anecdotally that this isn’t really happening.  I thought we were going to see an influx of mathematical talent, smart kids from Mississippi who couldn’t get any math past calculus from their peers, their local high school, or the public library, but who trained themselves hardcore on Art of Problem Solving or Mathematics Stack Exchange.  But I don’t think this is happening so much.  (Correct me if I’m wrong about this!)

I thought about this when I read this article about MOOCs, which says that they’re primarily used by wealthy people who already have college degrees.  What a depressing outcome that would be, if a platform meant to make elite education available free to everybody and help undo the student-loan disaster instead mostly made life easier for people whose lives are already easy, and saved money for people who already have money.




13 thoughts on “Is online education good or bad for equality?

  1. D. Eppstein says:

    There is actually some research that shows a positive effect in mathematics. See Hu, Xu, Hall, Walker, and Okwumabua, “A potential technological solution for reducing the achievement gap between white and black students”, Knowledge Spaces: Applications in Education, Springer, 2013. They compared a computerized teaching system to a lecture class, both preparing for the ACT mathematics test. Their preliminary results show that “white students perform significantly better than black students in the lecture format but exhibit comparable performance in the online format.” The online numbers are a little worse than the numbers for the white lecture students, but much better than the numbers for the black lecture students. (Full disclosure: I am one of the editors of the book this was published in but had nothing to do with this research.)

  2. harrison says:

    It may be too early to pass judgment. Mobile phone technology has been around for a good 30 years, and for most of its history it mostly benefited elites. But today, 90% of American adults have cell phones, and in the wider world we have things like M-Pesa, which is a fantastic mobile payment system used by over half of the adult population of Kenya (including some of its poorest citizens).

    I don’t think that we should be surprised that wealthy people with a good deal of cultural capital are likely to be early adopters of MOOCs. They’re likely to be early adopters in general. The crucial thing is whether it grows beyond that population.

  3. Frank says:

    I personally know a kid from a small town in South Carolina who is *precisely* training hardcore on AOPS and who apparently is a very serious candidate to make the IMO team.

    There is another variable: his parents drive him to Columbia every weekend to attend the Columbia Math Circle, which is taught by someone *phenomenally* good. But without a doubt, AOPS is also doing this kid a world of good.

  4. JSE says:

    That’s great!
    Maybe, as Harrison suggests, it will just take time. I really don’t know.

  5. BConrad says:

    It isn’t enough to have that Internet connection — one also needs experienced trustworthy people to offer advice on suitable topics to study after mechanical calculus & linear algebra courses. I am guessing that MOOC math courses do not tend to replicate the hard theoretical honors courses one finds at good math departments, so after a kid is done with a cookbook course in matrix algebra then it isn’t necessarily evident to them either what to do next or that one should ask others rather than follow one’s own internal compass (that could lead in a non-productive direction, or an undue emphasis on doing well on math contests).

    Even though I was fortunate to go to the Ross Program in high school and a good undergraduate university, if I had done that but worked in isolation then I expect it would have been a disaster for me. It was only by talking one-on-one with people there whom I knew to trust that I gained confidence that my lack of good ability of math contests was irrelevant and that if I had interest in certain math topics then I would be well-served to study specific other topics which were not obviously related, etc. It isn’t clear that this is something one can gain from posting on websites. So I think some kind of genuine personal connection and mentorship structure is absolutely essential to the development of mathematical talent.

    Just by way of illustration, I had an email exchange with Andrew Ng recently, asking him what he thought about the merit of trying to create a MOOC on Galois theory and other kinds of typical undergrad math major courses. He said that while this certainly could have value, far and away the thing for which there was vastly greater need was in the direction of remedial-level math. I imagine that in the long run there will be occasional cases of remarkable talents who get “discovered” and push themselves through the MOOC format (like that physics kid from Mongolia whom I suppose is now at MIT), but this is a drop in the bucket. Perhaps if a mentoring structure can be created in the MOOC setting (e.g., lists of “sample course selections” for students wanting to gain expertise in certain fields of study) then there can be greater potential for what you are expecting, but it would also require the development of more suitable courses (since reading books in isolation and trying to resolve all confusion through the MSE website seems impractical for all but the truly exceptional and the AoPS website seems skewed towards the idea that performing well on math contests is the big goal). Anyway, it is early days for these things, as someone else noted, so one can be hopeful.

  6. Lots of institutions we think of as socially progressive, like publicly-funded museums, actually primarily benefit the wealthy, because the wealthy are better at taking advantage of what’s available, have better faith in institutions, are more able to take chances…. I don’t think that’s a reason to stop doing them.

    (Also, people who already have degrees are probably better at learning from college-style courses)

  7. I think people need to be careful about interpreting statistics related to MOOCs. As an obvious example (unrelated to the issue raised here), many cite the low percentage of participants who finish a MOOC they start. This statistic is completely meaningless and says nothing about the quality of the course or its value to society. Imagine if we rated books by computing the ratio between the number of people who finish the book versus those who opened it — what exactly would that tell us? (I guess it would tell us that comic books and graphic novels are of great value to society but there is really no point in writing a book like War and Peace).

    In terms of the topic raised here, selection bias is inevitable. The people who are most likely to take (and especially, finish) a MOOC are those who are self-directed and value education. Such people are also more likely to have previously taken steps to educate themselves and (no surprise) may already have a college degree. This fact really has no bearing on whether MOOCs are valuable to society or not.

    Brian Conrad: I think a MOOC on Galois theory would be a wonderful thing. There is no shortage of online resources already available for remedial mathematics (and as you noted, the availability of such resources isn’t really the issue). But there are virtually no MOOCs available for upper level mathematics. This is one of my pet peeves — the last thing we need is another calculus MOOC. I guess it depends on what your goals are. If your goal is to help as many people as possible, there are no doubt plenty of things you could do completely outside of mathematics that would have greater impact. But I’m sure you could put together a truly great online course on Galois theory (or any other topic you chose to address). The fact that fewer people would be benefit from such a course than, say, a malaria vaccine, should not deter you from creating it.

  8. quasihumanist says:

    I am currently teaching 20 students (actually really 17, once you don’t count the people who almost never show up) in a transition course.

    Let’s say all of them were able to go to MIT or Stanford.

    I think two of them would get B’s (they’re both pretty bored in my class), six or seven would get C’s, and most of the rest would be getting D’s (because they worked so hard, not because they would be thought to have learned anything).

    Alas, I think if we as a department gave such grades, we would no longer exist in a few years.

    I am reminded of a story found in the letters between Mozart and his father. Mozart was giving composition lessons to some noblewoman. He wrote in his letters about how he gave many examples of minuets, showed how a given minuet could be varied, and so on, but when he asked her to try to start one for herself, even just a few notes for the melody, she just came up completely blank.

    I used to think this noblewoman was particularly simple-minded, but now I’m not sure she is any less creative than average. Yes I do believe this level of creativity (remember this woman had already had a significant amount of musical education) is a necessary prerequisite for anything that could be called mathematical talent.

    Part of the problem is that development of mathematical ability requires some foundation of early mathematical education. A lot of people never understand place value, and most never really understand multiplication of fractions. Almost all high schools have stopped doing proofs in geometry. Indeed, many students go through K-12 math without acquiring any inkling that mathematical statements have justifications beyond ‘this is what you need to do to get your answer marked as correct on the test’.

    (Sometimes I get the feeling that many students manage to get out of university nowadays still thinking that the only distinction between facts and opinions is that people with power will judge you badly for disbelieving facts in ways they won’t for contradicting their opinions. In other words, without reading any Foucault, they have actually taken to heart a rather extreme interpretation of Foucault, probably one that Foucault himself didn’t believe.)

    Also, I think you are not being generous enough towards high school teachers and professors at regional universities. Not every high school teacher can or will do this, but it is quite likely that, if an exceptional student comes along (and, for a poor high school where students are coming from poor elementary schools, simply having the capacity to develop enough mathematical maturity to understand Galois theory before the age of 25 would be exceptional), someone would recognize the talent and refer the student to the local university, and someone in the math department there would very likely be willing to work with the student. I think pretty much anywhere in the world with reliable Internet access also has had for many years these kinds of informal networks to identify and promote exceptional talent. It’s perhaps the talents that are one level below exceptional (in the local context) who might previously have been lost.

  9. BConrad says:

    @AndrewVSutherland (not sure how to make this appear just under your comment, so it is here instead): I agree that a MOOC on Galois theory (or intro group theory or other math beyond cookbook level) would be wonderful, and I do have the vague plan to do something like it some day. I had a chat with some colleagues not so long ago in which we concluded that in the long run probably the valuable contribution we could make to MOOC’s would be in that sort of direction, and not so much in the direction of mass-market calculus (for which there are many who could create — or perhaps have already created — such a course far better than anything I ever could do). But the kicker, as I learned from talking with Dan Boneh about his experience designing and teaching a MOOC on crypto, is that the time commitment to create and deliver such a course is truly enormous (much more so than for a typical class). Moreover, although my university offers faculty incentives to design such classes, teaching reductions to compensate for the additional time required is not part of the deal (or so I have been told, if I am not confused). So it is really a matter of finding the time. Well, since I’ll be teaching Galois theory in the “winter” here, maybe I’ll get inspired to do something after that, depending on how it goes.

  10. @BConrad I’m definitely sympathetic to the time issue. I have spoken with a few of the edX people about the possibility of doing a MOOC based on the elliptic curves course I teach, but it is clear that extensive effort would be involved. Having said that, I am still intrigued by the idea. For me the interesting part would be figuring out how to make it as interactive as possible — I think a well designed MOOC can give students real-time feedback in a way that neither a textbook nor lecture can, and this can be extremely motivating. Last spring I signed up for Walter Lewin’s electromagnetism MOOC out of curiosity (I actually took the course from him in person many years ago, but of course I have forgotten most of the material), and I was surprised out how addictive the experience can be — every little green checkmark motivated me to proceed to the next question.

  11. NN says:

    As someone who did his math undergrad from a highly-regarded university in India, where both the system as well as the teachers (despite their good intentions) severely underprepared him for the graduate school that admitted him, I would have been immeasurably helped by an MOOC on Galois theory, especially by someone like BConrad. Not so much for the content of the course but for showing me how active mathematicians look at mathematics. (I had recently revisted my alma-mater to give a talk and found myself recommending Benedict Gross’ basic algebra lectures that can be found on youtube.)

    I hold the (hopelessly naive) belief that the really great thing about MOOCs is not only that it would allow a willing student to transcend the limitations of his/her context (insecure instructors, rote-based learning, etc.) but that it would ultimately force a change in the state of higher education in the country.

  12. rrogers31 says:

    Is a library a failure because most of the books are seldom read and only people who know how to read use it? I think libraries and MOOC’s are a cumulative good. Raising the general level of expected knowledge. Cultural change is always slow. Without the cultural expectation and the availability of resources, the level of common mathematical knowledge will not move. To me the immediate benefit is the availability of contemporary knowledge for those who are interested and not privileged. Take the case of Ramanujan: without the availability of the books he read in high school would his genius have been available for future generations? I am willing to bet that, outside the social class that could support advanced college education, the books were seldom read or used. He was truly an exception but I don’t believe his ability was disconnected from the rest of humanity; just an outlier in the continuum of human abilities. An indication of what treasure lies when knowledge is generally available. This reasoning is perhaps applicable only to a small fraction of humanity but, with 6 billion people, that is probably a large number. And that number far exceeds the number of elites that are forced to take mathematics courses or even the number of elites that are actually interested.
    Of course this is just a short term /immediate gain; the long term is a more rational global structure with higher expectations concerning facts and reasoning. That can’t happen as long as people are stuck in ignorance and superstition without any resources to do better.

  13. […] Jonathan Wai, a big-time researcher on gifted kids, pushes back on my WSJ article in Psychology Today.  I don’t think we actually disagree so much; in particular, he’s right that we don’t do much to nurture the many talented kids who, unlike me, grow up far away from money and universities.  I thought online education might be the answer to this but now I’m not sure. […]

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