Archive for January, 2014

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

MathThink MOOC v4 – Part 9

In Part 9, I admit that my interest in MOOCs is driven by a very Selfish Gene.

Why do I devote so much (unpaid) time working on my MOOC? And it is, to be sure, a lot of time, little of it factored in to my official Stanford workload.

According to least one very good, and highly respected (by me no less than many others) educational writer, it is the prospect of fame, as she recently tweeted thus.

WojcickiTweet

I suppose there may be a professor or two somewhere who sees MOOCs as a pathway to fame, but if so, they should definitely take my Mathematical Thinking MOOC to develop good numerical sense. A globally distributed, ten week class of maybe 40,000 students, half of whom will watch at most one video and many of whom would not be able to tell you the name of their MOOC instructor if you asked them (the same is true for regular, physical classes, by the way), is hardly fame.

Fame is epitomized by @KimKardashian, with almost 20 million Twitter followers. If that’s your goal, devoting many years of your life to get a PhD ain’t the optimal path!

What academics tend to seek is peer recognition. And, believe me, giving a MOOC will, if anything, reduce the status of any scholar within the Academy, possibly to an even greater extent than writing books and magazine articles “for the general reader”. (I’ve done both. As an academic, I was doomed long ago.)

The danger of stepping outside the walls of Academia has been recognized ever since The National Academy of Sciences denied entry to Carl Sagan. As a recipient of the Carl Sagan Award for Science Popularization, I am thus doubly doomed.

No wonder I felt I had nothing to lose by jumping onto the MOOC bandwagon – though at the time I started work on my first MOOC it was not so much a bandwagon as a small Stanford wheelbarrow, yet to be discovered by  New York Times columnist Thomas Friedman. (He soon made up for missing the start. Just google “Thomas Friedman MOOC” and you will uncover a host of Massively Over-hyped Outrageous Claims.)

Why do academics give MOOCs? While I surely cannot speak for all MOOC instructors, I can probably speak for the many I have talked with, and by and large they all give the same answer. It comes in two parts.

The first part is educational research. (This is the reason why Stanford, my university, provides some – very modest – support for MOOC development.) The process of designing and giving a MOOC provides a wonderful opportunity for an instructor to find ways to improve their teaching craft, and provides educational researchers with massive amounts of data to help us better understand the learning process. For just one illustration of this, check out this article from a MOOC instructor at Vanderbilt University.

ChrisChristie

New Jersey governor Chris Christie showing his opinion of teachers

The second part is the same answer you will get if you ask someone why they went into K-12 teaching, a profession that not only pays poorly, but ranks so low in the US psyche that a savvy State governor contemplating a run for President will regard you as fair media game for a finger-wagging, photo-opp tongue-lashing:

Teachers are not seeking fame, or wealth. They do it because they have this deep-seated urge to change lives by teaching.

When I joined the tiny band of Stanford faculty who were designing the first wave of MOOCs, our motto was “Let’s Teach the World”, a slogan that I took for the subtitle to this blog. This is what it is about.

It wasn’t a desire to be famous that we found attractive. Heavens, if you are at Stanford, you probably already have all the academic “fame” you could ever want. Rather, the hook was an opportunity to take something we had been providing regularly to a privileged few and make it available to anyone in the world who had access to the Internet.

It was, in short, an idealistic dream. How to operationalize that dream was another question, and there were at least as many approaches as MOOC instructors.

The Stanford-MOOC-pioneering computer science professors Thrun, Koller, and Ng set their initial sights on large numbers of students around the world being able to take CS courses, 100,000 or more (maybe a lot more) at a time.

Recognizing that (introductory-level) computer science is almost certainly a special case – because it is suited to instruction-based learning and a lot of what is being taught is, by its very nature, machine gradable – instructors in other disciplines set different expectations for their courses.

In my case, I had two clear teaching goals in mind, one very much focused on “the world”, the other “egalitarian elitist”.

As a mathematician who has devoted a lot of my career to community outreach, through public talks, newspapers, general-audience books, magazines, radio, television, movies (occasionally), blogs, and podcasts, I saw MOOCs as yet another medium to “spread the gospel of mathematics”, moreover a medium that offered the possibility of taking my audience a lot further down the mathematical path than any of those other media.

Broadly speaking, the first six weeks of my Mathematical Thinking MOOC attempt to cater to that general audience. I very definitely want to capture and sustain the interest of as many individuals as possible. Massive (the M of MOOC) is the goal. My focus is not so much on getting my students to learn mathematics – there is precious little of it in those first six weeks – but to raise their awareness of the nature and power of mathematics, and to help them come to realize that they actually do have a (creative) mathematical mind, it just needs to be unlocked from the panic-inducing prison that traditional K-12 math education so often drives it into.

[Time for another Ken Robinson video. This one is a doozy. It’s the one that made him world famous – unlike MOOCs, TED talks can make you famous. For the evidence that what Sir Ken says applies to mathematics, see my own book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip.]

In the final weeks of my MOOC, I slowly shift attention to my second audience. That audience is a lot smaller. I am looking for people who, in certain key ways, are very much like I was as a teenager.

Hull

Alexander Dock in the 1950s, about half a mile from my childhood home

Growing up in a working class family in post-Second-World-War England, in the grimy, Northern industrial city and port of Hull, with no ready access to quality education (let alone higher education), and no role models for learning in my family or my neighborhood, my innate talent for mathematics would likely have gone forever un-realized.

(Through to my early teens, my school teachers advised me to focus on writing, since they felt I had no mathematical abilities, as evidenced by the fact that I was always the last person to master each technique, and kept asking pesky “What?” and “Why?” questions when “everyone knew” that doing math was all about “How”. “Our’s not to reason why, just invert and multiply.”)

Fortunately, at high school I encountered a math teacher who recognized something else in me, and pulled me out of his regular math class to teach myself, with his occasional guidance, from his own college textbooks.

I also started to pore through every available “popular mathematics book.” (There weren’t many back then, but most were available as cheap paperbacks.)

That got me started on a rewarding and fulfilling mathematical journey I have been following ever since.

I am certainly not unique in having stumbled my way into mathematics through chance. For most of my professional career I have been surrounded by people who are a lot better mathematicians than me, and a lot more accomplished, and many of them can tell similar “humble origins” stories. But they come from all around the world. Not many of them, if any, come from where I grew up. Similar places, but not the same place. (It’s a density issue.)

In fact, I was surprised to discover a few years ago that the official listing of “Famous People of Hull” includes just two mathematicians, John Venn (of Venn diagram fame) and yours truly.

That may or may not be a comprehensive listing (I never knew John Venn was from Hull until I saw that entry), but it does suggest that you may have to extend access to quality mathematical learning to populations in the hundreds of thousands (Hull’s population was about 300,000 when I was growing up there, it’s considerably less today), in order to connect with just one or two who have talent.

I want to do just that. Citizen Devlin wants to provide mathematical outreach to millions around the world. Keith Devlin the grown-up kid from Hull, wants to reach those few individuals who have talent for mathematics but neither learning role models nor access to good education, and provide an educational opportunity analogous to the one that changed my life.

If the “Famous People of Hull” data is even remotely correct, I need to reach many hundreds of thousands, and perhaps millions, around the world, to stand any chance of connecting to those talented few who currently do not have a seat at the educational table.

(It’s probably not an issue of raw talent density. I am sure there are many people will significant mathematical ability in every part of the world. Rather the challenge is the density of talented individuals you are able to connect with, and as a result recognize and bring out their talent.)

Large dropout rates in MOOCs? Though I work hard to try to keep everyone in my course for the first half, and put considerable effort into keeping as many as possible through to the end of the Basic Course (see earlier posts), as far as my second motivator is concerned, those dropout rates are not a problem at all. They are part of the filtering process.

I’m looking for “me” – that talented young person with no access, and probably no hope – to give them a similar opportunity to the one that chance brought my way all those years ago.

MOOCs have given me that dream.

In each of the three iterations of my MOOC I have given, I have seen a small number of students who I think may be such individuals. They are the ones for whom I have made an exception to my (obviously essential) rule of not communicating individually to MOOC students. That’s reason enough to continue.

In other words, my involvement in MOOCs is in large part driven by my own educational Selfish Gene. Not to replicate me, but to replicate what happened to me. Now you know.


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.

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