MathThink MOOC v4 – Part 10

In Part 10, the final episode in this series, I talk about my key course design principle, I put forward an argument that in some respects MOOCs may be better than traditional courses,  and I show you the inside of the MOOC-production lab (where you will find a historic MOOC artifact).

The familiar, over-hyped and over-played media story about MOOCs was inspired in large part by (the possibility of) large numbers of students taking the same class, all around the world. And in one sense, the numbers are large. Though enrollments rarely reach six figures, compared with traditional physical courses, even a “tiny MOOC” (a TOOC?) can have several thousand students.

But those numbers can be misleading. In particular they appear to position MOOCs as being off the right-hand edge of the familiar universities maximum-class-size chart, where elite liberal arts colleges attract students (and their paying parents) with claims such as “None of our classes have more than twenty-five students”.

For some MOOCs, such off-the-chart positioning is, at least to some extent, appropriate, particularly the introductory-level computer science courses that dominated the first wave of xMOOCs coming out of Stanford and then MIT, where the pedagogy is largely instructional. Those courses are in many significant ways simply very large versions of their physical counterparts, with an Internet connection separating the instructor from the student, rather than the more traditional thirty feet of air. Indeed, some of the early CS MOOCs were built around recorded and streamed versions of actual physical courses, with real students.

But in many cases, that “large-version-of-the-familiar” picture is just wrong. Rather, for many MOOCs the educational model is one-on-one, apprenticeship learning. That is certainly the case for my course. I made that choice for, what were for me, two very compelling reasons.

One was my experience as an upper level undergraduate and then a graduate student, when a typical week was spent struggling for hours on my own or with a group of fellow students, interspersed with one or two private sessions sitting next to a professor, as I sought help with the concepts I had not fully grasped or the problems I had failed to solve. That was when I really learned mathematics.

The other influence was my experience in writing books and articles for newspapers and magazines, and in radio and television broadcasting. As with MOOCs, the popular perception is that those media are about conveying thoughts and ideas to thousands if not millions of others. But as any successful writer or broadcaster will tell you, in reality they are all one-on-one. The trick you need to master to make the communication flow is to imagine you are writing or speaking to just one person and to connect with them. (In the case of an interview, such as my “Math Guy” discussions with host Scott Simon on NPR’s Weekend Edition, there actually is a single discussant, of course – I am speaking with one person – and the listeners or viewers are essentially silent observers. The secret of being a good interviewer, as Scott is, is to be able to act as a representative of the viewer or listener.)

In both cases, education and mass media, the secret to success is to evoke thousands of years of human evolution in social interaction. Ritualized classroom education and mass media are relatively recent phenomena, but interpersonal communication is as old as humanity itself, and the successful teacher or broadcaster can take advantage of the many instinctive, powerful aspects thereof.

In the case of (basic) mathematics teaching, look at the huge success of Khan Academy. (I certainly did in planning my MOOC.) Salman Khan built his organization, and with it his reputation, around a large library of short, video-recorded instructional lessons. Though much of the content is not good, and in many cases mathematically incorrect, and the pedagogy poor (Khan is trained in neither advanced mathematics nor mathematics education), what he does as well as – I would say better than – almost anyone else in the business is successfully package “side-by-side, one-on-one conversation” and distribute it over the Internet via YouTube. He is every bit the master of his chosen medium as Walter Cronkite was of television news delivery.

In designing my MOOC, I set out to create that same sense of the student sitting alongside me, one-on-one. If you can pull it off, it’s powerful. In particular, if you can create that feeling of intimate human connection, the student will overlook a lot of imperfections and problems. (I rely on that a lot – though the reason I do not edit out my frequent fluffs is that I want to portray mathematics as it is really done.)

True, what I deliver is not the same as actually sitting side-by-side with me. In particular, the student is not able to talk back to me, nor can I begin by reading the student’s initial attempts and then comment on them. Other features of the MOOC have to provide, as best they can, equivalents of those important feedback channels in learning.

On the other hand, in a physical class of more than a dozen or so, it is not really possible for any instructor to provide ongoing, one-on-one, close guidance to each student.

In fact, strange as it may seem, I think it might be possible to better provide some crucial aspects of one-on-one higher mathematics education by making use of a platform designed to provide unlimited scaling, than can be achieved in a traditional classroom.

This is particularly true, I believe, for a course such as mine, where the focus is developing a new way of thinking, not mastering a toolbox of techniques that can be used to solve particular kinds of problems. Here’s why I think that.

The fact is, we don’t know how we do mathematics, or how we learn it. The people who do learn to think mathematically will tell you that they found it within themselves – ultimately, they had to figure everything out for themselves, just as learning to ride a bike comes down to discovering the ability within yourself. (Remember, I am not talking about mastering and applying procedures, which can largely be done without any deep understanding.)

Some, like the famous Indian mathematician Srinivasa Ramanujan (VIDEO), manage to take this step with no human help, working alone from textbooks borrowed from libraries. But most of us find we need the regular encouragement and feedback from one or more others or from a tutor. (See the full length documentary (52 mins) Ramanujan: Letters from an Indian Clerk.)

But how important is it to be physically co-present with that tutor? Is it the feedback that is crucial or do the encouragement and the provision of explanations and examples suffice?

After all, mathematics is, by its very nature, logical – supremely so – which means that it can be discovered by reflection. Particularly the basics of mathematical thinking.

Whether a particular individual has the desire or persistence to persevere with such reflection is another matter. Personality type presumably plays a big role. So too does innate mental power. And there has to be motivation.

But for those who are of the appropriate personality type and who have enough mental capacity and motivation, is it necessary that they spend a period of time physically co-present with an instructor?

Absent individual feedback, modern social media provide a powerful means for humans to come together. Maybe that is enough.

HW

The “video recording studio” in my home where I record all my instructional videos

(The face-to-face continuity pieces in my lecture videos are designed to make that human connection as strong as possible. That was the only part of my MOOC where we spent money, to get high quality video that conveys my presence. I recorded the handwriting segments in my home, using a cheap consumer camcorder, and I edit my own videos.)

The fact is, a student taking my MOOC can make a closer connection with me than if they were in a class of more than 25 or so students, and certainly more than in a class of 250.

So let’s take stock of what  can be delivered to the students in a MOOC.

Certainly, the streamed lecture video of a MOOC delivers more than they would get if they were sitting in a large lecture hall with me doing my thing at the front. The lecture video delivers me in a way the student has complete control over, making it self-evidently better.

And in a large class, the student is not going to get my individual attention, so there is no loss there in learning in a MOOC.

So a MOOC seems to offer more of me than a student would get in a regular, large class.

But they also get a version of that close, one-on-one instruction that they absolutely do not get in a regular class of any size.

Absent being able to speak back to me – something many students have insufficient confidence to do (unfortunately) – I think there is good reason to believe that human connection through social media may be enough to have whatever effect is provided by the real thing.

For sure, for some students, it may be important to have frequent real contact with someone to work with, especially someone who knows enough about the subject to provide constructive feedback. But that can often be arranged locally on the receiving end.

(Equally, shy students can perform much better in an online environment.)

The bottom line then is this. Though I do not know that the modalities in a MOOC are enough to help people learn how to think mathematically, I have yet to encounter any reason that it cannot be made to work.

Mathematics, with its intrinsic figure-out-able nature, may be a special case.

It would be ironic indeed if the subject that has historically been the one that most people find impossibly difficult, turns out to be the one most suited to MOOC learning. (Again, let me stress that I am at not talking about procedural problem solving.)

I doubt that large numbers of students can become mathematicians by taking a MOOC, and the same is true for physical classes. But I see no reason why a great many cannot gain useful mathematical thinking skills from a MOOC, nor that there is an insurmountable obstacle to people with the talent and the motivation using a MOOC to take the first crucial step towards a professional mathematical career.

In any case, I no more am discouraged by recent media articles claiming the death of the MOOC than I was encouraged by those same writers’ breathless hype just twelve months ago. (The only MOOC death associated with the story the New York Times ran on December 10, 2013 was the demise of its own over-hyped and under-informed coverage of a year earlier.) America, in particular, has a strikingly naive perception of education that would be its undoing were it not for a continuing supply of J1 and H1 visas. I plan on moving ahead.

My total spend so far? Forget all those media stories about MOOCs costing hundreds of thousands of dollars. After an initial outlay from Stanford of, I think, around $40,000, to cover initial video recording and editing and student TA support for the first version, and $9,000 to cover the cost of a course TA in the second version (TA-ships being a form of student financial aid, of course), everything since has been on a budget of $0.

VE

The “video editing suite” in my home where I edit all my instructional videos

In particular, as I noted above, I now do all my own recording (cheap consumer camcorder) and video editing (cheap consumer editing package) at my home in Palo Alto.

Of course, Stanford does pay my salary, but developing and giving my MOOC is on top of my regular duties, and is essentially viewed as research into teaching methods. So when Oklahoma Senator Tom Coburn looks into me for fodder for his annual Wastebook (see Section 63 if you think innovative mathematics education could not possibly be in his sights), I will be able to counter by saying that no taxpayers were harmed in the making of my MOOC.

By the way, the two panel lights  I use when I record my handwriting segments (shown in the earlier photograph) have historical significance in the world of MOOCs. I was given them by Google’s Peter Norvig after he had finished using them to record the first Stanford-Google Artificial Intelligence MOOC that generated all the current interest in the medium. A contemporary equivalent of the Ishango Bone?

THE END

About these ads

8 Responses to “MathThink MOOC v4 – Part 10”


  1. 1 mgozaydin January 8, 2014 at 10:47 am

    You should be paid for your online course development job too .

  2. 2 Kathryn Johns January 8, 2014 at 12:10 pm

    I completed the 3rd version of your Mathematical Thinking MOOC and agree with you totally on the ability of social media to bring people together in a useful way. For me this worked in two ways. Firstly I was part of a study group based on a commonality of language and time zone so we were able to provide each other with immediate feedback and support while doing the unmarked assignments. Because we typed and posted our feedback several people could offer their view at more or less the same time without being influenced by the others. This process greatly improved our ability to talk about mathematical thinking which at first was totally unnatural. We many times commented that we knew what we thought but didn’t know how to express it. Gradually our confidence improved and we got quite adept at arguing our corner if necessary.
    Secondly there were the much larger class forums where there were threads covering everything imaginable from home schooling to recreational math and logic problems as well as course related topics. For me it was a place to go at first to get input from the TA’s and prof as they answered other students’ questions and participated in discussions. As the course went on I grew enough in confidence to ask my own questions and even offer my own opinions. Being what you describe in your blog as ‘the shy student’ this was progress indeed and back in the day when I was at university this was something I would have been very uncomfortable with even in a tutorial of maybe only 4 students and lecturer
    The success of these forums for me was in part because of the generosity of time and openness given by some of the most frequent and interesting posters and secondly because they were well run by yourself and the TAs who kept things on track when they could very easily have gone off the rails.

  3. 4 Jim Humelsine January 8, 2014 at 1:56 pm

    I agree with your assessment. I find the MOOC experience more intimate than the large lecture hall – but then again, I am a child of the TV generation. (I took one MOOC where the instructor only recorded his voice. He did not include head-shot videos of himself. The course was a dud for several reasons, but I feel the lack of visual contact with the students was a contributing factor.)

    Even if instructor/student is virtual one-to-one, the “Massive” student body allows for many-to-many relationships on the discussion forums. We have access to the student “crowd source” body of knowledge and an experience that I never had in college. Small classroom cliques usually formed in classes when I was in college, but they pale in comparison to the discussion forum resource.

    I’ve met and interacted with students on every continent except for Antarctica, and I’m still hoping for that encounter.

    • 5 Keith Devlin January 8, 2014 at 2:38 pm

      Jim, Though it is interesting how Sal Khan succeeds without appearing on the screen. He manages to convey that intimacy using just his voice. That’s unusual, I think, and my oft repeated critique of Khan Academy is because I think that ability to connect and overcome fear ought to be matched by an educationally and mathematically better product.

      • 6 Jim Humelsine January 8, 2014 at 7:49 pm

        Keith – Excellent non-visual example with Khan. Part of the difference is in the speaker’s voice and the quality of the audio. Sal has an engaging voice, and the audio sounds like he’s right there with you. For the above mentioned MOOC, the instructor basically read his view graphs verbatim and he sounded like he was recorded in a mens room.

  4. 7 Alain Rouleau January 8, 2014 at 3:06 pm

    Thanks for the insights into how you record the handwriting segments and of your so-called “video recording studio”. Very interesting.

    • 8 Keith Devlin January 8, 2014 at 7:32 pm

      Alain, With what I know now, I could create the same MOOC at almost no cost beyond purchase of a $900 camcorder, a tripod, a couple of lighting panels like the ones Peter Norvig gave me, and a $90 consumer video editing package – I use Adobe Premiere Elements. The only other thing I would pay for is six hours use of a good TV studio for recording the green screen face-into-camera segments. (I originally did them for the entire course in one six hour session.)

      BTW, that “home studio” is my living room. Because I am beneath one of the approach paths to San Francisco International Airport, and close to the main Peninsula commuter railway line, I can record only between midnight and 5:00AM. I have to turn of my fridge in order to record! :)


Comments are currently closed.



I'm Dr. Keith Devlin, a mathematician at Stanford University. I gave my first free, open, online math course in fall 2012, and have been offering it twice a year since then. This blog chronicles my experiences as they happen.

Twitter Updates

New Book 2012

New book 2011

New e-book 2011

New book 2011

January 2014
M T W T F S S
« Dec   Sep »
 12345
6789101112
13141516171819
20212223242526
2728293031  

Follow

Get every new post delivered to your Inbox.

Join 574 other followers

%d bloggers like this: