Posts Tagged 'higher education'

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.

MathThink MOOC v4 – Part 8

In Part 8, I explain why I believe MOOCs cannot and will not lead to cost savings in higher education – at least in a nation that values its standard of living.

As I’ve noted in previous posts to this blog, for the first version of my Introduction to Mathematical Thinking MOOC, I took the first part of a course I had given many times in regular classroom settings, and ported it to a MOOC platform in what I thought was the most sensible way possible. In particular, I changed only things that clearly had to be changed. It was always going to be an iterative process, whereby each time I gave the course I would make changes based on what I had learned from previous attempts.

Given the significant differences between a physical class of 25 entry-qualified students at a selective college or university and a distributed class of 80,000 students around the globe (the size of my first MOOC class in Fall 2012), of widely different educational backgrounds and ability levels, for whom the only entrance criterion was being able to fill in a couple of personal information boxes in a Website, it made sense to maintain – for the first version – as much as possible the contents and structure of the original classroom course. That way, I could focus on the MOOC-specific issues.

After the first session was completed (survived more accurately describes my sensation at the time), all bets would be off, and I would follow where the experience led me. I felt then, and continue to feel now, that there is no reason why a MOOC should resemble anything we are currently familiar with.

I watched as Sebastian Thrun quickly moved Udacity away from his original conception of a highly structured, programmed traditional course – with all that entails – to offering more a smorgasbord of mini-courses, built up from what can be viewed as stand-alone lectures. I asked myself then, and continue to do so, if I should hang on to the central notion of a course, and maybe just tweak it.

So far I have decided I should, the main reason being, as I tried to explain in my last post, the kind of experience I feel best results in the kind of learning I want to provide.

In particular, the primary goal of my course was, and is, to help develop a particular way of thinking – certain habits of mind. That is best achieved, I believe, by focusing on particular “content”.

I used the quotation marks there, because I think it is not accurate to view learning experiences (for experiences are what produce learning) as a certain volume of “content” that is “contained” is some sort of container or vessel. But it seems that everyone else knows what the term (educational) content means – a shared understanding that provides Silicon Valley entrepreneurs with a nice story to raise investment for developing “platforms” to “deliver” that “content” – so I’ll go with it. (I used the word five times in my last post, and no one wrote in to object or say they did not understand what I meant.)

Anther reason for maintaining a course structure (the indefinite article is intentional) is that I want my course to function as a transition course, to help students make the shift from high school to university. And for the foreseeable future, I think universities will continue to carve up “content” into delivery packages called “courses”.

The third reason for having a course is our old friend, student expectations. Many of my full-term students tell me that they signed up because they want a course, with all that entails: commitment, deadlines, testing, and community.

That third reason likely reflects the self-selection implicit in students who sign up for a MOOC, fully 80% of whom (according to recent MOOC research) already have a college degree, and hence are adapted to – and good at – learning that way.

This implies that, by offering a course, I may be reinforcing that emergent trend of primarily providing further college education to individuals who already had one.

That may, in fact, be where MOOCs will end up. For sure, Udacity’s recent pivot appears to reflect Sebastian Thrun’s having decided to direct his (investors’) money toward that audience/market.

If the provision of continuing higher education  for college graduates does turn out to be the main benefit that MOOCs provide, that will surely be something for we MOOC developers to be proud of, particularly in a world in which everyone will need to learn and re-tool throughout their lives. (Major innovations rarely land where the innovators thought they would, or do what was originally intended.)

But in that case, MOOCs won’t yield the massive cost savings in first-pass, higher education that many politicians and education-system administrators have been thinking they offer.

In fact – and here I am probably about to bring the wrath of Twitter onto me – I think the current goal of “solving the problem” of the rising cost of higher education by finding ways to reduce it, misunderstands what is going on. I suspect the costs of providing first-pass higher education will continue to rise, because quality higher education is becoming ever more important for life in the Twenty-First Century.

Just as the introduction of the automobile meant society had to adjust to the new – and ever rising – expense of gasoline, so too the shift to knowledge work and the knowledge society means we have to adjust to the cost (high and rising) of a first-pass higher education (the fuel for the knowledge society) that stays in synch with society’s needs.

What MOOCs and other forms of online education have already been shown to be capable of – and it is huge – is provide lifelong educational upgrades at very low cost.

But based on what I and many of my fellow MOOC pioneers have so far discovered – or at least have started to strongly suspect – the initial “firmware” required to facilitate those continual “software” upgrades is not going to get any cheaper. Because the firmware installation is labor intensive and hence not scalable – indeed, for continuously-learning-intensive Twenty-First Century life, not effectively scalable beyond 25-student class-size limits.

The world we have created simply entails those (new and rising) educational costs every bit as much the growth of the automotive society meant accepting the (new and ever-after rising) cost of automotive fuel.

(Oh, and by the way, we in the US need to realize that the knowledge society requires better teacher preparation in the K-12 system as well. Well-educated humans are the new fuel, and they neither grow on trees nor are found underground.)

Okay, that’s enough editorializing for one post. At the end of my last report, I promised to describe how I structure my course so that, while designed primarily to provide a framework for a community learning experience, it can still be useful to folks who want to use it as a resource.

First, what do I mean by “resource”? I decided that for mathematical thinking, it was not possible to produce Khan Academy style “online encyclopedia” materials, where someone can dive in to a single video or narrowly focused educational resource. You simply have to devote more than ten minutes to gain anything of value in what I am focusing on.

So I set my sights on people who come in and complete one or two “Lectures”, a Lecture in my case comprising a single thirty-minute video and some associated problem-solving assignments. So I am not delivering “bite-sized learning.” I am serving up meals. (Restaurant meals, where you have time to savor the food and engage in conversation.)

To facilitate such use, the earlier Lectures focus on everyday human communication, ambiguity resolution, logical reasoning, and very basic mathematical ideas (primarily elementary arithmetic – though in a conceptual way, not calculation, for which we have cheap and efficient machines).

Only in Weeks 7 and 8 do I cover more sophisticated mathematical ideas. (Weeks 9 and 10 comprise my new Test Flight process, which I described in Part 6 of this series. That part is specifically for advanced mathematics seekers.)

Thus, Weeks 1 through 6 can be accessed as a resource by someone not strongly interested in mathematics. At least, that is my current intention.

Admittedly, someone who delves into, say, Week 4 might find they need to go back and start earlier; but that’s true of Khan Academy as well, and is surely unavoidable.

By making the awarding of a Statement of Accomplishment dependent on completion of the Basic Course (first eight weeks), not the achievement of a particular grade, I hope to be able to maintain and reward the participation of someone who begins by just “trying out the course” and gets hooked sufficiently to keep going.

To cater for this dual use as much as possible, in addition to changing the course structure, the upcoming new session has four new videos, and I modified four existing ones. (All the time keeping that magic ingredient “content” the same.)

Well, that’s where I am at present. As I noted earlier, this blog series is essentially my lab book – complete with speculative reflections – made public in real time. (I am already deviating from things I said in this blog just a year ago.)

Ah yes, last time I also promised I would say “what motivated me to give a MOOC in the first place – and still does.” The answer is, “Reaching students who do not currently have access to quality higher education.”

That probably seems very much at odds with everything I’ve said above. It’s not. I’ll explain why in my next post.

MathThink MOOC v4 – Part 7

In Part 7, I ask myself (yet again) does it need to be a course?

One issue I keep returning to is whether my MOOC should be a course. Or, to put the question a more useful way, what features of a classroom course do I want or need to carry over to a MOOC, what features should I jettison, and what new features should I add?

I raised the issue in my blogpost of August 31, 2012, just before my MOOC launched for the first time. Since then, students’ expectations (as expressed in emails to me and in the discussion forums) have continued to confirm my initial instinct that there are good reasons to carry over a lot of  traditional course structure.

Still, the question is not going to go away. I brought it up again in June of 2013 after completing the second version of my MOOC, noting that the majority of my students treated the course as a resource rather than a course.

In those early posts, I made a number of references to Khan Academy, an educational resource I now have very mixed feelings about. (In particular, I think Sal’s enthusiasm and undeniable – and hugely valuable – ability to project his personality through his voice, and thereby to remove much of the fear that many of his followers may have toward mathematics, fall well short of what he could achieve, due to poor pedagogy and way too many elementary – but educationally important – factual mistakes.) I made several key choices based on what could be learned from his endeavors.

One thing I did not do was go the route of turning my MOOC into a collection of Khan-like, standalone, bite-sized snippets. Indeed, deliberately ignoring the current buzz that the audience will drop precipitously if your videos run more than seven minutes, I decided to aim for half-hour chunks. Hey, if thirty-minutes works for Seinfeld and Thirty Rock, why not for Mathematical Thinking? (Remember, I’m looking at a highly selective audience who have voluntarily chosen to enroll in an online math course! I haven’t completely lost it – just enough to keep trying to make this free online course thing work in the first place.)

My decision was largely because the material simply cannot be broken up in that way. Unless you are a mathematical genius, when it comes to mathematical thinking, most of us find that thirty-minute chunks is the absolute minimum time commitment to make any progress at all, and a lot is lost if you cannot arrange for much longer periods. The very last “lecture” of the course actually lasts an hour and a half, with the original video cut up into three segments of roughly equal, thirty-minute lengths. And students who have completed the course say they wished I had spent even more time on the one (capstone) topic I covered in that last lecture.

Since approximately 5,000 students have, on average, stayed with the course to the end each time, I definitely want to continue to provide the learning experience they have clearly been looking for. (In my next post I’ll say how, at the same time, I try to cater for those seeking a resource.)

A significant part of that experience is, I believe, being part of a community, where everyone is working toward the same goal, with regular pressure points (deadlines) that force them to keep sufficiently in lockstep so that they can exchange ideas and express community reactions in real time. Though many of them do not post regularly on the community discussion forums, they do (I assume) follow them, finding answers to their questions and surely being encouraged to learn that they are not alone in finding something particularly difficult or confusing.

That sense of community is, to my mind, an important part of my course. In the (necessarily) simplistic terminology introduced to try to explain the conceptual difference between the original Canadian MOOCs originating from Athabasca University and the unrelated MOOCs coming out of Stanford some years later, my course is a c-MOOC in x-MOOC clothing. (See the Wikipedia article for the tangled history.)

From the very first lecture, I recommend repeatedly that students try to form small learning communities to work through the weekly problem assignments that are the heart of the course.

And there we have another reason why I have not carved my course into bite-sized instructional videos. It’s not about instruction! The expressed goal is not “teaching mathematics” but guiding folks on a process of learning how to think a certain way. In particular, learning how to set about solving a novel problem that perhaps only partially resembles one encountered before.

In other words, in my course the devil is very much not in the details. It’s in the overall flow of ideas, the swirling cloud that hovers above all those details.

The key for making that transition from “template recognizer and applier of known techniques” to “creative problem solver” is to rise above the details and grasp the meta-cognitive aspects of good problem solving.

Having myself made that transition by sitting next to my senior tutor (a professor) in my senior undergraduate year and then my doctoral adviser for the subsequent three years, and watching and listening to them as they worked through problems with me (a very one-sided “with”!), I knew first-hand that the process works. I also know of no other way that does.

It’s a slow process, to be sure. Many students in my regular classes over the years, and far greater numbers of students in my MOOCs, have not been prepared, and in some cases not willing, to adjust to that different pace.

I lost count of the number of MOOC students who expressed frustration (and more) at how slowly I was moving, how I “rambled” and “repeated myself,” and how “unprepared” I had been when I sat down to record those videos.

My approach was, of course, carefully thought out and deliberate. I never intended to give a slick, prepared presentation. (I do many of them, and there are videos all over the Web. But those presentations are about infotainment, not learning to think a different way.)

My approach was always about providing a window into one person’s (mine) thought processes. Not to mimic me. That would make no sense in terms of learning how to think creatively.  Rather, to gain sufficient insight to be able to develop that capacity in themselves.

Of course, I can provide just one example – me. But one example is enough. Because the capacity for original thought is in every one of us. It just has to be unleashed.

Evolution by natural selection has made all of us creative problem solvers. That is Homo sapiens’ great survival trick. Unfortunately, an educational system developed in the industrial age to turn innately creative humans into compliant cogs in organizations, suppresses that innate creativity, rewarding fast acquisition and retrieval of facts and rapid execution of procedures, a sad turn of events for today’s world, as summarized brilliantly by the provocative and always entertaining Sir Kenneth Robinson in the animated talk I will leave you with.

Creativity is in all of us. You see it in every small child. Despite systemic education’s efforts to suppress it, it remains eager to break out. (Google dopamine.) It does not take much of a stimulus to make it (start to) happen. A ten week MOOC may seem very short. But it may be enough to initiate the process. (Google “Prison Break”.)

* * *

Next time I’ll describe how I structure the course so that, while designed primarily to provide a framework for a community experience, it can still be useful to folks who want to use it as a resource. I’ll also say what motivated me to give a MOOC in the first place – and still does. Meanwhile, here is Sir Ken:

MathThink MOOC v4 – Part 6

In Part 6, I talk about the new Test Flight process.

In the past, when students enrolled for my MOOC, they essentially had three options. One was not to take it as a course at all, but just regard it as a resource to peruse over time or to pick and choose from. A second was to take the entire course, but do so on their own time-scale. Or they could take it as a course, and go through it at the designated pace.

As do many MOOC designers, I tried to make sure my course could be used in all three ways. Though the vast majority of MOOC students fall into the first category, the other two are the ones that require by far the greatest effort by the course designer. They are the learners who have significant ambitions and will put in a lot of effort over several weeks.

The students in the last category will surely gain the most. In particular, they move through the course in lockstep with a cohort of several thousand other students who can all learn from and support one another, as they face each course deadline at the same time. Those students form the core community that is the heart of the course.

When the new class enrolls at the start of February, the ones intending to take an entire course as scheduled will have a new choice. They can take what I am calling the Basic Course, which lasts eight weeks, or the Extended Course, which lasts ten. As I described in my last post, those extra two weeks are devoted to a process I am calling Test Flight.

In the previous two versions of the course, the final weeks nine and ten had been devoted to a Final Exam, one week for completion of the (open book) exam itself, the following week to peer evaluation. In peer evaluation, which started as soon as the class had completed and submitted their exam solutions, each student went through a number of activities:

1. Using a rubric I supplied, each student evaluated three completed examination scripts assembled by me, and then compared their results to mine. (Those three samples were selected by me to highlight particular features of evaluation that typically arise for those problems.)

2. Having thus had some initial practice at evaluation, each student then evaluated three examination scripts submitted by fellow students. (The Coursera platform randomly and anonymously distributed the completed papers.)

3. Each student then evaluated their own completed examination.

This was the system Coursera recommended, and for which they developed their peer evaluation module. (Actually, they suggested that each student evaluated five peer submissions, but at least for my course, that would have put a huge time requirement on the students, so I settled for three.)

Their original goal, and mine, was to provide a means for assigning course grades in a discipline where machine evaluation is not possible. The theory was that, if each student is evaluated by sufficiently many fellow students, each of whom had undergone an initial training period, then the final grade – computed from all the peer grades plus the self-grade – would be fairly reliable, and indeed there is research that supports this assumption. (Certainly, students who evaluate their own work immediately after evaluating that of other students tend to be very objective.)

As far as I could tell, the system worked as intended. If the goal of a MOOC is to take a regular university course and make it widely available on the Internet, then my first three sessions of the course were acceptably successful. But MOOCifying my regular Mathematical Thinking (transition) class was always just my starting point.

Since I was aware from the outset that the MOOC version of my regular classroom course was just a two-dimensional shadow of the real thing, where I interact with my class on a regular basis and give them specific feedback on their work, my intention always was to iteratively develop the MOOC into something that takes maximum advantage of the medium to provide something new of value – whatever that turns out to be.

I expected that, as MOOCs evolve, they would over time come to be structured differently and be used in ways that could be very different from our original design goals. That, after all, is what almost always happens with any new product or technology.

One thing I observed was that, while students often began feeling very nervous about the requirement that they evaluate the work of fellow students, and (justifiably) had significant doubts about being able to do a good job, the majority found the process of  evaluating mathematical arguments both enjoyable and a hugely beneficial learning process.

Actually, I need to say a bit more about that “majority” claim. My only regular means of judging the reactions of the class to the various elements of the course was to read the postings on the course discussion forums. I spent at least an hour every day going through those forums, occasionally posting a response of my own, but mostly just reading.

Since the number of regular forum posters is in the hundreds, but the effective (full-term) class was in excess of 5,000 in each of the sessions, forum posters are, by virtue of being forum posters, not representative. Nevertheless, I had to proceed on the assumption that any issue or opinion that was shared (or voted up) by more than one or two forum posters was likely to reflect the views of a significant percentage of the entire (full-term) class.

Since I made gradual changes to the course based on that feedback, this means that over time, my course has been developing in a way that suits the more active forum posters. Arguably that is reasonable, since their level of activity suggests they are the ones most committed, and hence the ones whose needs and preferences the course should try to meet. Still, there are many uncertainties here.

To return to my point about the learning and comprehension benefits evaluators gained from analyzing work of their peers, that did not come as a surprise. I had found that myself when, as a graduate student TA, I first had to evaluate students’ work. I had observed it in my students when I had used it in some of my regular classes. And I had read and heard a number of reports from other instructors who noted the same thing.

It was when I factored the learning benefits of evaluating mathematical arguments in with my ongoing frustration with the degree to which “grade hunting” kept getting in the way of learning, that I finally decided to turn the whole exam part on its head.

While some universities and some instructors may set out to provide credentialing MOOCs, my goal was always to focus on the learning, drawing more on my knowledge of video games and video-game learning (see my blog profkeithdevlin.org) than on my familiarity with university education (see my Stanford homepage).

Most of what I know about giving a university-level course involves significant student-faculty interaction and interpersonal engagement, whereas a well-designed video game maintains the player’s attention and involvement using very different mechanisms. With a MOOC of necessity being absent any significant instructor-student interaction, I felt from the outset that the worlds of television and gaming would provide the key weapons I needed to create and maintain student attention in a MOOC.

[A lot of my understanding of how TV captures the viewer’s attention I learned from my close Stanford colleague, Prof Byron Reeves, who did a lot of the groundbreaking research in that area. He subsequently took his findings on television into the video game business, co-authoring the book Total Engagement: Using Games and Virtual Worlds to Change the Way People Work and Businesses Compete.]

So from the outset of my foray into the world of online education, I was looking to move away from traditional higher-education pedagogic models and structure, and towards what we know about (television and) video games, hopefully ending up with something of value in between.

The idea of awarding a Statement of Accomplishment based on accumulated grade points had to go sooner or later, and along with it the Final Exam. Hence, with Session Four, both will be gone. From now on, it is all about the experience – about trying (and failing!).

The intention for the upcoming session is that a student who completes the Basic Course will have learned enough to be able to make useful, and confident use of mathematical thinking in their work and in their daily lives. Completion of the Test Flight process in the Extended Course will (start to) prepare them for further study in mathematics or a mathematically-dependent discipline – or at least provide enough of a taste of university-level mathematics to help them decide if they want to pursue it further.

At heart, Test Flight is the original Final Exam process, but with a very different purpose, and accordingly structured differently.

As a course culmination activity, building on but separate from the earlier part of the course – and definitely not designed to evaluate what has been learned in the course – Test Flight has its own goal: to provide those taking part with a brief hands-on experience of “life as a mathematician.”

The students are asked to construct mathematical arguments to prove results, and then to evaluate other proofs of the same results. The format is just like the weekly Problem Sets that have met throughout the course, and performance level has no more or less significance.

The evaluation rubric, originally employed to try to guarantee accurate peer grading of the exam, has been modified to guide the evaluator in understanding what factors go into making a good mathematical argument.  (I made that change in the previous session.)

After the students have used the rubric to evaluate the three Problem Set solutions supplied by me, they view a video in which I evaluate the same submissions. Not because mine provides the “correct” evaluations. There is usually no single solution to a question and no such thing as the “right” one. Rather, I am providing examples, so they can compare their evaluations with mine.

After that, they then proceed to evaluate three randomly-assigned, anonymously-presented submissions from other students, and finally they evaluate their own submission.

Procedurally, it is essentially the same as the previous Final Exam. But the emphasis has been totally switched from a focus on the person being evaluated (who wants to be evaluated fairly, of course) to the individual doing the evaluation (where striving for a reliable evaluation is a tool to aid learning on the part of the evaluator).

Though I ran a complete trial of the process last time, the course structure was largely unchanged. In particular, there was still a Final Exam for which performance affected the grade, and hence the awarding of a certificate. As a consequence, although I observed enough to give me confidence the Test Flight process could be made to work, there was a square-peg-in-a-round-hole aspect in what I did then that caused some issues.

I am hoping (and expecting) things will go smoother next time. For sure, further adjustments will be required. But overall, I am happy with the way things are developing. I feel the course is moving in the general direction I wanted to go when I set out. I believe I (and the successive generations of students) are slowly getting there. I just don’t know where “there” is exactly, what “there” looks like, and how far in the future we’ll arrive.

As the man said, “To boldly go …”

The MOOC Express – Less Hype, More Hope

A real-time chronicle of a seasoned professor just about to launch the fourth edition of his massively open online course.

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Last week, I headed off to Arlington, Texas, to participate in a large, international conference on MOOC education, part of the Gates Foundation funded MOOC Research Initiative (MRI). While the founders of the big, massively-funded American MOOC (“MFAM”) platforms Coursera, edX, Udacity, and Novo Ed capture most of the media’s attention, this conference was led by the small band of far less well known Canadian online-education pioneers who actually developed the MOOC concept some years earlier, in particular George Siemens and Stephen Downes who organized and ran the first MOOC in 2008, and David Cornier who forever has to live with having coined the name “MOOC”.

(There were so many Canadians in Arlington, they brought their own weather with them, as you can see from the photograph. The conference ended with participants having to change flights and book additional nights in the conference hotel, as a severe ice storm hit the area. With a return flight that happened to lie within a brief lull in the storm, I managed to get out on time, though only after a slip-sliding taxi ride at a snail’s pace to get to DFW Airport. Others had it a lot worse.)

While teams of engineers in Silicon Valley and Cambridge (MA) are building out MOOC platforms that provide huge opportunities for massive scale-up, the two hundred or so researchers and educators who came together in Texas represent the vanguard of the educational revolution that is underway. If you wanted to know what MOOC learning might look at in a few years time, you would have better spent your time at the University of Texas in Arlington last week rather than in Silicon Valley. In his October announcement of the conference, organizer Siemens described it as “the greatest MOOC conference in the history of MOOCs,” a bit of satirical hype that is almost certainly true.

You need both, of course, the technology to reach millions of people and the appropriate, quality pedagogy. For example, the movie industry required a series of major advances in motion picture technology, but fancy film cameras alone are not what gave us Hollywood. As the technology advanced, so too did the art and craft of motion picture writing, acting and directing. Similarly with MOOCs. The focus in Arlington was on the educational equivalent of the latter, human expertise factors.

To pursue the movie analogy a bit further (and with that great spoof movie poster as a visual aid, how could I resist?), the MOOC action that gets reported in the Chronicle of Higher Education and the breathless (but hopelessly off-base and over-hyped) prose of Thomas Friedman in the New York Times is the equivalent of taking an early movie camera into a theater and recording what happens on the stage.

If you want to see the future of MOOCs, you need to hang around with the instructors in the lesser known, small universities and community colleges who, for many years, have been experimenting with online learning. Most of the leaders of that loosely knit band could be found in a large, cavernous room in Arlington for two days last week – along with key figures from such new-MOOC, Ivy League players as Stanford, MIT, and Georgia Tech.

What was the take-home message? In my case, and I suspect everyone else’s, confirmation that we really don’t know where the MOOC train is taking us. The problem is not an absence of good ideas or useful leads; rather the opposite. Don’t expect a “Conference Proceedings” volume any day soon. The best summary you will find is probably the conference Twitter stream (hashtag #mri13).

The fact is, there isn’t even a clear definition of what a MOOC is. The common classifications of c-MOOC (for the original, Canadian, connectionist animal) and x-MOOC (for the later, scalability-focused, Stanford version) don’t help much, since many (most?) of the MOOCs being developed now have elements of both. Commenting on the lack of a generally accepted definition in his welcoming remarks, conference organizer George Siemens opined that it may be that no agreed definition will emerge, and that the term “MOOC” will be similar to “Web 2.0″, remaining an undefined term that “reflect[s] a mess of concepts that represent foundational changes that we don’t yet understand, can barely articulate, but that will substantially impact the system.”

Actually, I should modify my remark above that Stanford is a MOOC player. That’s not really accurate. Some Stanford scholars (including me) are developing and offering MOOCs, but the main focus at my university is research into learning in a digital age, including online learning. There is a lot of such research, but MOOCs are just one part of it. And those MOOC platform providers you keep reading about, Udacity, Coursera, and Novo Ed? They are all private companies that span out of Stanford. They are now (and  were from their creation) Silicon Valley entities, outside the university. Stanford’s original, in-house MOOC platform, eventually called Class2Go, was recently folded into edX, to be run by MIT and Harvard as an open source platform.

As the MOOC research train goes forward, don’t expect the big, Ivy League universities to exclusively dominate the leading edge of the research. The reason so many participants in the Arlington conference came from far less wealthy, and often smaller institutions is that they have been developing and using online education for years to cater to their geographically-diverse, economically-diverse, and education-preparedness-diverse student bodies. The connections made or strengthened at the Arlington conference are likely to result in many collaborations between institutions both big and small, from the wealthy to the impoverished. The Digital World is like that. When it comes to expertise, today’s academic world is just as flat as the economic one – as Siemens clearly realized in drawing up his conference invitation list.

Expect to see MOOC pioneer Stephen Downes leading a lot of the action, as the head of a new, $19 million, 5-year R&D initiative for the Canadian National Research Council. Keep your eyes too on Siemens himself, who at the conference announced his move from Athabacsa University in Canada to be a professor in, and executive director of, the  University of Texas at Arlington’s new Learning Innovations & Networked Knowledge (LINK) Research Lab. (So new, it doesn’t have a website yet!) Track conference keynoter Jim Groom, who whiled away the time holed up at snowed-in DWF Airport to draft this summary of the gathering.  And don’t overlook the University of Prince Edward Island, where Dave Cormier and Bonnie Stewart brave the weather of the far North East. There are a whole host more. Check the list of recipients of MRI grants for other names to follow, and remember that this is just the tip of, dare I say it under the circumstances, the iceberg.

And never, ever forget to read the excellent (and highly knowledgable) ed tech commentator Audrey Watters, who was invited to attend the Arlington conference but had a scheduling conflict. New readers interested in MOOCs, start here.

Recent headlines may have given the impression that MOOCs were a short-lived bubble, and the experiment has largely failed. Nothing could be further from the truth. For one thing, even the much reported business pivot of Udacity was a familiar event in Silicon Valley, as I argued in a commentary in the Huffington Post.

As Siemens put it in his conference welcome, “the ‘failure’ of MOOCs is a failure of hype and an antiquated notion of learning,  not a failure of open online learning.”

Overcoming the legacy of prior education

A real-time chronicle of a seasoned professor who is giving his second massively open online course.

We’re now into the third week of the course. The numbers are down on the first edition, almost certainly because the six months that have passed have seen the appearance of hundreds of other MOOCs students have to choose from. But the numbers are still huge. As of today:

Total registration: 27,014

Active students last week: 9,608

Total number of streaming views of lectures: 120,925

Total number of lecture downloads: 35,888

Number of unique videos watched: 87,155

Number of students submitting homework assignments: 5,552

Based on what we (my TA, Paul, and I) learned when I gave the course the first time last fall, I made some changes this time round. Paul and I discussed those changes in a video-recorded discussion we had with media host Angie Coiro just before edition 2 launched, that I referred to in my last blog.

Although the overall numbers are down by about 60%, the profile of the class activity is very similar. The most obvious one, the huge drop in numbers from the total number of enrollments to the number who are still active in week three, has been discussed ad infinitum, often being referred to as “a big problem with MOOCs.” As I observed in a recent blog in the Huffington Post, I don’t think there is a problem at all. The drop off is just a feature of what is a very new form of human experience. Old metrics are simply not appropriate, “retention rate” being one such. (Unless you pay attention to the base for the retention computation, in which case MOOC “retention” is not that different from retention in traditional college education.)

Some of the early research into MOOC participants that has been carried out by my colleagues at Stanford (including studies of my first MOOC) has already demonstrated what we suspected about why so many drop out of MOOCs: many people who register for a MOOC never have any intention of completing the course, or even getting beyond sampling one or two lectures and perhaps attempting one or two of the assignments. Some are motivated by pure curiosity into this new phenomenon, others just want to get a flavor of a particular discipline or topic, and doubtless others have different reasons.

For example, one reason some students enroll that I had not anticipated, reflects the fact that a MOOC offers a large number of eyeballs to be accessed. A very  small number of students enrolled for my course in order to advertise products. (At least, that was one reason they enrolled; they may also have wanted to learn how to think mathematically!) In the long run, this may or may not turn out to be a positive thing. Certainly, the products advertised in the discussion forums for my course (at least the ones I saw) were all education related and free. (Moreover, I also included my own course-related textbook in my short list of suggested – but not required – resources.)

Still, the very wide reach of MOOCs means we are likely to see new kinds of activities emerge, some of them purely commercial. The example I cite above, though right now a very isolated one, may be a sign of big things to come – which is why I mention it. There is, after all, a familiar pattern. The Internet, on which MOOCs live, began as a military and educational network, but now it is a major economic platform. And textbooks grew from being a valuable educational support to the present-day mega-profit industry that has effectively killed US K-12 education.

Talking of which (and this brings me to my main focus in this post), the death – or at least the dearth – of good K-12 mathematics education becomes clear when you look through the forum posts in a MOOC such as mine, which assumes only high school knowledge of mathematics.

To be sure, generalizing is always dangerous, particularly so when based on comments in an online forum, which always attracts people with something to complain about. (Case in point: See my Twitter feed when it comes to banks, United Airlines, and bigoted politicians.) But with that caveat in mind, some themes become clear.

First, many forum posters  seem to view education as something done to them, by other people who are in control. This is completely wrong, and is the opposite of what you will find in a good university (and a very small number of excellent K-12 schools).  “To learn” is an active verb. The focus should be creating an environment where the student can learn, wants to learn, and can obtain the support required to do so. There is no other way, and anyone who claims to do anything more than help you to learn is trying to extract money from you.

Second, there is a common view of education as being primarily about getting grades on tests – generally by the most efficient means (which usually means by-passing real learning). In education, tests are metrics to help the student and the instructor gauge progress. That does not prevent tests being used to assess achievement and provide credentials, but that is something you do after an educational experience is completed. Their use within the learning process is different, and everyone involved in education – students, instructors, parents, bureaucrats, and politicians – needs to be aware of the distinction.

Even worse, is the belief that a test grade of less than 90% is an indication of failure, often compounded by the hopeless misconception that activities like mathematics depend mostly on innate talent, rather than the hours of effort that those of us in the business know is the key. (Check out Carol Dweck’s Mindset research or read Malcolm Gladwell’s book Blink. Better still, read both.)

This is compounded by the expectation that a grade of 90% is possible within just a few days of meeting something new. For example, here is one (slightly edited) forum post from a student in my class:

Right now I want to quit this class. I don’t understand ANY of it. Hell I don’t understand anything regarding to math except basic equations and those barely. When asked to give a theorem on why something (let’s say a right angle) is that way my answer always was “it is because it is”). So now I don’t know what to do. I got 14 out of 40 … 14, and the perfectionist in me is saying might as well give up … you gave it a shot … there is no way to catch up now. The person in me who wants to learn is saying to keep trying you never know what will happen. And the pessimist in me says it doesn’t matter – I dumb and will always be dumb and by continuing I am just showing how dumb I am.

In this case, I looked at other posts from this student and as far as I can tell (this is hard when done remotely over the Internet) she is smart and shows every indication she can do fine in mathematics. In which case, I take her comment as an indication of the total, dismal failure of the education system she has hitherto been subjected to. No first-line education system should ever produce a graduate who feels like that.

Certainly, in learning something new and challenging, getting over 30% in the first test, less than a week after meeting it for the first time, is good. In fact, if you are in a course where you get much more than that so quickly, you are clearly in the wrong course – unless you signed up in order to fine-tune something you had already learned. Learning is a long, hard process that involves repeated “failure”. And (to repeat a point I made earlier) anyone who says otherwise is trying to extract money from you.

Turning to the third theme emerging on the course forums, there is a perception that the most efficient way to learn is to break everything down into the smallest possible morsels. While an important component of learning – if the breaking down is done by, and not for, the student – it is just the first part of a two-part process. The second part, which is by far the most important, and is in fact where the actual learning takes place, is putting it back together into a coherent whole. Textbooks and YouTube videos can provide morselized edubits (I just made that word up), and they do so by the bucketload. What they cannot do, is deliver real learning.

Suitably designed, I see no reason why MOOCs cannot be made to provide good learning, at least up to sophomore college level in many, if not most, disciplines. But a key to doing that is to leverage the power, not of machines, but of people. For fairly well understood evolutionary reasons, human learning is a social activity. We learn best from and with other people. That is how we are built!

Part of the benefit from learning in a social context is that it can offer the learner not just feedback, but also the – at a fundamental level, more important – human support that people need to succeed in education. You can find both of these in a MOOC. Within a short time of the student above posting her feelings, another student responded with this:

Hi. Don’t be discouraged. This course will give you the opportunity to think in a different way. I took the course last year and struggled with most of it. I am taking the course again as I find the subject of mathematical thinking fascinating. My scores this time round are better than the last time which indicates that given enough time even the most mathematically challenged can improve! Only have one caveat for you. If you don’t enjoy the struggle in trying to comprehend and feel that it is not worth the effort then maybe this course is not for you.

With that comment we can see one huge benefit of MOOCs. (At least, all the time they are free.) You can take them as many times as you need or want.

The one essential ingredient in order to take advantage of the huge opportunity MOOCs offer, is knowing how to learn. That should be the main ability graduates of the K-12 system get from their education. Unfortunately, with the current US (and elsewhere) system built around “being taught” and “being tested,” only a few students emerge with that crucial ability, and the ones who do usually say it is in spite of their school education.

The problem, by the way, is not the teachers. Certainly, most of the ones I meet agree with me, and are very clear as to what the problem is: a system that simply does not give them the freedom and support that is necessary for them to really help students learn. (See Jo Boaler’s excellent, well researched book What’s Math Got To Do With It? for a distressing account of how the current, overly micro-regulated system fails our students in the case of mathematics.)

Okay, that’s enough ranting for one post. Let me finish with a couple of examples where MOOCs are already working well. One student in my MOOC posted the following comment:

I have taken this course on a whim to get myself back in gear to return to school in the fall. I always despised the math classes that I was forced to attend in high school and early college. I was frustrated with the endless formulas and cookie cutter style problem solving. If you can solve one you can solve them all so being forced to endlessly solve these equations and proofs over and over seemed to be a futile act of nonsense.

Heading into week three three of this class, my mind has been completely changed. I not only enjoy this more logic based math, but have, in the course of some personal reading and problem solving, discovered i have a knack for it. I have found the challenge of solving more and more difficult problems from a few books i have purchased much more gratifying and interesting than any other area of previous study.

I would like you know that I now plan to switch majors to mathematics. I would like to thank you and your team for an eye-opening experience.

Oh, all right, I admit that included more ranting about US K-12 education. But, heavens, it is bad, and it is likely to remain so all the time that real, knowledgable educators are not part of the conversation, with all the important decision being made by people whose primary interests are profits or political career advancement. (BTW, I have nothing against the profit motive. Heavens, I have two for profit companies of my own and am talking with colleagues about launching a third. But financial ROI is not the same as educational ROI – and again, anyone claiming otherwise, as one head of a major textbook publisher did not long ago, is motivated by the former. I do have something against many politicians, but then I am an American citizen, so after what we have experienced in the past four years, I would.*)

Here’s the other example, this one sent to me in an email, rather than posted on the course discussion forum.

I am enrolled in your course “Introduction to Mathematical Thinking.” It is incredible. You have alleviated my fears that my college professors will have the same attitude towards mathematics that my high school teachers do. Mathematics is beautiful and certainly emotional. I am surrounded at school by people who believe mathematics is systematic. Through all of the videos you have posted so far and your archived NPR clips, I am now confident that mathematics is the direction I want to pursue. I am excitedly awaiting next week’s lectures. 

With tears in my eyes and more gratitude than I know how to express,

It’s that kind of feedback that makes teaching one of the most rewarding professions in the world. It’s why people become teachers. If society would just get off teachers’ backs and let them get on with what they were trained to do, what they know how to do,  and what they want to do, we’d all be a lot better off. (Check out Finland.)

To be continued …

*ADDED LATER IN RESPONSE TO A QUERY FROM AN OVERSEAS READER: The problem is the complete refusal of the Republican Party to cooperate with a now twice-elected President of the US, in governing the country as they are all elected and paid from public funds to do, choosing instead to drive the country, and with it most of the world, to the brink of financial and thence  social disaster.

 

MOOC reflections – and Coursera’s Business Model

A real-time chronicle of a seasoned professor who has just completed giving his first massively open online course.

Two of my most recent reflections on MOOCs were in many ways reflections about mathematics education in general, so instead of burying them here, where only the MOOC-curious would see them, I submitted them to the Mathematical Association of America as articles in my monthly series “Devlin’s Angle”, and that’s where you will find them.

The first, titled MOOC lessons, focused on the kind of learning that can take place in a MOOC.

In the second, The Darwinization of Higher Education, I looked at the likely effect of MOOCs on the higher education landscape. I originally submitted a shorter, “less-personal-blog” version as a post to my blog in The Huffington Post (Education Section), but much to my surprise, after sitting on it for over a week, they rejected it. Either I am way ahead of the HuffPost’s education editors or else they think I’m off my rocker (maybe both). It probably reflects on the massive uncertainty about where MOOCs are going, that I think there is a 5% chance I am off my rocker on this issue. A week ago I would have put that figure at 10%, but just this morning (a scant week after I had submitted my thoughts to HuffPost, and a mere 24 hours after I had sent the piece instead to the MAA) I received an email Coursera sent out to all past and present students.

It began thus:

Career Services: Finding great job opportunities

Coursera has begun Career Services with the goal of helping Coursera students find great jobs! Meeting great companies just got easier. Just go to <Coursera web page URL> and fill in your profile to opt-in to the service. After you opt-in, we will share your resume and other information you provide with selected partner companies who will introduce themselves if there’s a match.
We’re excited to connect you with great companies and new opportunities! Complete your profile here!

Remember, you read it first here. (As they say.)

Is this really Coursera’s business model (in the sense of the business model)? I am in no position to know. I suspect they don’t yet know either, how (and maybe if) they, or any other MOOC platform, will eventually make sufficient revenue to sustain their activities. Calling it “Coursera’s business model” in my title indicates only that it is a business model that the company has now announced. From my second article listed above, you will gather I think it is a smart move on their part. On the other hand, I can think of at least half a dozen others ways to monetize MOOCs, and at least as many ways for others to build businesses around the MOOC phenomenon.

I know many of my academic colleagues feel uneasy when education is discussed as a for-profit enterprise, but it has never been anything else. Someone has to pay. Usually, it is the student or the student’s family, either directly or indirectly. The novel aspect of the Ivy League MOOCs that I hope those colleagues see as positive is that the one person who does not pay is the student — at least on entry, which means that MOOC education is entirely free.

While on the topic of MOOC upsides, I had lunch recently with three of my fellow pioneer MOOC-instructors, and one substantial student demographic we all noticed was moms with young children (in many cases single moms, without the means to afford child care while they study). Hard to fault that.

We are entering a very different world in terms of access to higher education.

To be continued …

Coming up for air (and spouting off)

A real-time chronicle of a seasoned professor who has just completed giving his first massively open online course.

Almost a month has passed since I last posted to this blog. Keeping my MOOC running took up so much time that, once it was over, I was faced with a huge backlog of other tasks to complete. Taking a good look at the mass of data from the course is just one of several post-MOOC activities that will have to wait until the New Year. So readers looking for statistics, analyses, and conclusions about my MOOC will, I am afraid, have to wait a little bit longer. Like most others giving these early MOOCs, we are doing so on the top of our existing duties; the time involved has yet to be figured into university workloads.

One issue that came up recently was when I put on my “NPR Math Guy” hat and talked with Weekend Edition host Scott Simon about my MOOC experience.

In the interview, I remarked that MOOCs owed more to Facebook than to YouTube. This observation has been questioned by some people, who believe Kahn Academy’s use of YouTube was the major inspiration. In making this comment, they are echoing the statement made by former Stanford Computer Science professor Sebastian Thrun when he announced the formation of Udacity.

In fact, I made my comment to Scott with my own MOOC (and many like it) in mind. Though I have noted in earlier posts to this blog how I studied Sal Khan’s approach in designing my own, having now completed my first MOOC, I am now even more convinced than previously that the eventual (we hope) success of MOOCs will be a consequence of Facebook (or social media in general) rather than of Internet video streaming.

The reason why I felt sure this would be the case is that (in most disciplines) the key to real learning has always been bi-directional human-human interaction (even better in some cases, multi-directional, multi-person interaction), not unidirectional instruction.

What got the entire discussion about MOOCs off in the wrong direction – and with it the public perception of what they are – is the circumstance of their birth, or more accurately, of their hugely accelerated growth when a couple of American Ivy League universities (one of them mine) got in on the act.

But it’s important to note that the first major-league MOOCs all came out of Stanford’s Computer Science Department, as did the two spinoff MOOC platforms, Udacity and Coursera. When MIT teamed up with Harvard to launch their edX platform a few months later, it too came from their Computer Science Department.

And there’s the rub. Computer Science is an atypical case when it comes to online learning. Although many aspects of computer science involve qualitative judgments and conceptual reasoning, the core parts of the subject are highly procedural, and lend themselves to instruction-based learning and to machine evaluation and grading. (“Is that piece of code correct?” Let the computer run it and see if it performs as intended.)

Instructional courses that teach students how to carry out various procedures, which can be assessed to a large degree by automatic grading (often multiple choice questions) are the low hanging fruit for online education. But what about the Humanities, the Arts, and much of Science, where instruction is only a small part of the learning process, and a decidedly unimportant part at that, and where machine assessment of student work is at best a goal in the far distant future, if indeed it is achievable at all?

In the case of my MOOC, “Introduction to Mathematical Thinking,” the focus was the creative/analytic mathematical thinking process and the notion of proof. But you can’t learn how to think a certain way or how prove something by being told or shown how to do it any more than you can learn how to ride a bike by being told or shown. You have to try for yourself, and keep trying, and falling, until it finally clicks. Moreover, apart from some very special, and atypical, simple cases, neither thinking nor proofs can be machine graded. Proofs are more like essays than calculations. Indeed, one of the things I told my students in my MOOC was that a good proof is a story, that explains why something is the case.

For the vast majority of students, discussion with (and getting feedback from) professors, TAs, and other students struggling to acquire problem solving ability and master abstract concepts and proofs, is an essential part of learning. For those purposes, the online version does not find its inspiration in Khan Academy as it did for Thrun, but in Facebook, which showed how social interaction could live on the Internet.

When the online version of Thrun’s Stanford AI class attracted 160,000 students, he did not start a potential revolution in global higher education, but two revolutions, only the first of which he was directly involved in. The first one is relatively easy to recognize and understand, especially for Americans, who for the most part have never experienced anything other than instruction-based education.

For courses where the goal is for the student to achieve mastery of a set of procedures (which is true of many courses in computer science and in mathematics), MOOCs almost certainly will change the face of higher education. Existing institutions that provide little more than basic, how-to instruction have a great deal to fear from MOOCs. They will have to adapt (and there is a clear way to do so) or go out of business.

If I want to learn about AI, I would prefer to do so from an expert such as Sebastian Thrun. (In fact, when I have time, I plan on taking his Udacity course on the subject!) So too will most students. Why pay money to attend a local college and be taught by a (hopefully competent) instructor of less stature when you can learn from Thrun for free?

True, Computer Science courses are not just about mastery of procedures. There is a lot to be learned from the emphases and nuances provided by a true expert, and that’s why, finances aside, I would choose Thrun’s course. But at the end of the day, it’s the procedural mastery that is the main goal. And that’s why that first collection of Computer Science MOOCs has created the popular public image of the MOOC student as someone watching canned instructional videos (generally of short duration and broken up by quizzes), typing in answers to questions to be evaluated by the system.

But this kind of course occupies the space in the overall educational landscape that McDonalds does in the restaurant business. (As someone who makes regular use of fast food restaurants, this is most emphatically not intended as a denigratory observation. But seeing utility and value in fast food does not mean I confuse a Big Mac with quality nutrition.)

Things are very, very different in the Humanities, Arts, and most of Science (and some parts of Computer Science), including all of mathematics beyond basic skills mastery – something that many people erroneously think is an essential prerequisite for learning how to do math, all evidence from people who really do learn how to do math to the contrary.

[Ask the expert. We don’t master the basic skills; we don’t need them because, early on in our mathematic learning, we acquired one – yes, just one – fundamental ability: mathematical thinking. That’s why the one or two kids in the class who seem to find math easy seem so different. In general, they don’t find math easy, but they are doing something very different from everyone else. Not because they are born with a “math gene”. Rather, instead of wasting their time mastering basic skills, they spent that time learning how to think a certain way. It’s just a matter of how you devote your learning time. It doesn’t help matters that some people managed to become qualified math teachers and professors seemingly without figuring out that far more efficient path, and hence add their own voice to those who keep calling for “more emphasis on basic skills” as being an essential prerequisite to mathematical power.]

But I digress. To get back to my point, while the popular image of a MOOC centers on lecture-videos and multiple-choice quizzes, what Humanities, Arts, and Science MOOCs (including mine) are about is community building and social interaction. For the instructor (and the very word “instructor” is hopelessly off target in this context), the goal in such a course is to create a learning community.  To create an online experience in which thousands of self-motivated individuals from around the world can come together for a predetermined period of intense, human–human interaction, focused on a clearly stated common goal.

We know that this can be done at scale, without the requirement that the participants are physically co-located or even that they know one another. NASA used this approach to put a man on the moon. MMOs (massively multiplayer online games – from which acronym MOOCs got their name) showed that the system works when the shared goal is success in a fantasy game world.

Whether the same approach works for higher education remains an open question. And, for those of us in higher education, what a question! A question that, in my case at least, has proved irresistible.

This, then, is the second MOOC revolution. The social MOOC. It’s outcome is far less evident than the first.

The evidence I have gathered from my first attempt at one of these second kinds of MOOC is encouraging, or at least, I find it so. But there is a long way to go to make my course work in a fashion that even begins to approach what can be achieved in a traditional classroom.

I’ll pursue these thoughts in future posts to this blog — and in future versions of my Mathematical Thinking MOOC, of which I hope to offer two variants in 2013.

Meanwhile, let me direct you to a recent article that speaks to some of the issues I raised above. It is from my legendary colleague in Stanford’s Graduate School of Education, Larry Cuban, where he expresses his skepticism that MOOCs will prove to be an acceptable replacement for much of higher education.

To be continued …

The Crucible: MOOC Planning – Part 8

A real-time chronicle of a seasoned professor embarking on his first massively open online course.

Well, I have survived the initial three weeks of my first MOOC. Though the bulk of the work (and I mean “bulk”) came before the course launched, it has still taken my TA and me a lot of time to keep things ticking over. There are the in-flight corrections of the inevitable errors that occur in a new course, together with the challenges presented by a completely new medium and a buggy, beta release platform, still under very rapid development.

The course website shows 61,846 registered students, but I suspect many of those have long stopped any kind of connection to the course, and another large group are simply watching the lecture videos. The really pleasing figure is that the number of active users last week (week 3) was 19,298. Based on what I hear about other MOOCs, retaining one student in three is a good number.

Both my hands-on TA, Paul, and the course Research Associate, Molly, are graduate students in Stanford’s School of Education, and besides helping me with aspects of the course design, they are approaching the project as an opportunity to carry out research in learning, particularly mathematics learning. Given the massive amount of data a MOOC generates, the education research world can expect to see a series of papers coming from them in the months ahead.

I’m not trained in education research, but some observations are self-evident when you look over the course discussion forums – something I’ve spent a lot of time doing, both to gauge how the course is going and to look for ways to improve it, either by an in-course modification of for a future iteration of the course.

I’ve always felt that the essence of MOOC learning is community building. There is no hope that the “instructor” can do more than orchestrate events. Without regular close contact with the students, the video-recorded lectures and the various course notes and handouts are like firing off a shotgun on a misty Scottish moor. The shot flies out and disperses into the mist, and you just hope some of it hits a target. (I haven’t actually fired a shotgun on a Scottish moor, or anywhere else for that matter, but I’ve seen it on TV and it seems the right metaphor.) With 60,000 (or 20,000) students, I can’t allow myself to respond to a forum post or an email from any single student. I have to rely on the voting procedure (“Like/Dislike”) of the forums to help me decide which questions to address.

This means the student body has to resolve things among themselves. It was fascinating watching the activity on the discussion forums take shape and develop a profile over the first couple of weeks.

One huge benefit for the instructor is the virtual elimination of the potentially disruptive influence – present in almost any class with more than twenty or so students – of the small number of students for whom nothing is good enough. Even in a totally free course, put on by volunteers, for which no college credential is awarded, there were a few early posts of that kind. But in each case the individual was rapidly put in his or her place by replies from other students, and before long stopped posting, and very likely dropped the course.

(An interesting feature of this was that each time it occurred, a number of students emailed me in private – rather than on the public course forum – to say they did not agree with the complainer, and to tell me they were enjoying the course. Clearly, even with the possibility of anonymous forum posts, which Coursera allows, at least for now, some people prefer to keep their communication totally private.)

Of far greater interest, at least to me, was how the student body rapidly split into two camps, based on how they reacted to the course content. As I’ve discussed in earlier posts to this blog, my course is a high-school to university transition course for mathematics. It’s designed to help students make the difficult (and for most of us psychologically challenging) transition from high school mathematics, with its emphasis on learning to follow procedures to solve highly contrived “math problems”, to developing an ability to think logically, numerically, analytically, quantitatively, and algebraically (i.e., in aggregate, mathematically) about novel problems, including often ill-defined or ambiguous real-world problems.

When I give this kind of course to a traditional class of twenty-five or so entering college students, fresh out of high school, the vast majority of them have a really hard time with it. In my MOOC, in contrast, the student body has individuals of all ages, from late teens into their sixties and seventies, with different backgrounds and experiences, and many of them said they found this approach the most stimulating mathematics class they had ever taken. They loved grappling with the inherent ambiguity and open-ended nature of some of the problems.

Our schools (at least in the US), by focusing on one particular aspect of mathematics – the formal, procedural – I think badly shortchange our students. They send them into the world with a fine scalpel, but life in that world requires a fairly diverse toolkit – including WD40 and a large roll of duct tape.

The real world rarely presents us with neat, encapsulated problems that can be solved in ten minutes. Real world problems are messy, ambiguous, ill-defined, and often with internal contradictions. Yes, precise, formal mathematics can be very useful in helping to solve such problems. But of far broader applicability is what I have been calling “mathematical thinking”, the title of my course.

I suspect the students who seemed to take to my course like ducks to water were people well beyond high school, who had discovered for themselves what is involved in solving real problems. Judging by the forum discussions, they are having a blast.

The others, the ones whose experience of mathematics has, I suspect, been almost entirely the familiar, procedural-skills learning of the traditional K-12 math curriculum, keep searching for precision that simply is not there, or (and I’ve been focusing a lot on this in the first three weeks) where the goal is to learn how to develop that precision in the first place.

The process of starting with a messy, real world problem, where we have little more than our intuitions to guide us, and then slowly distilling some precision to help us deal with that problem, is hugely valuable. Indeed, it is the engine that powered (and continues to power) the entire development of our science and our technology. Yet, in our K-12 system we hardly ever help students to learn how to do that.

Done well, the activities of the traditional math class can be great fun. I certainly found it so, and have spent a large part of my life enjoying the challenges of pure mathematics research. But a lot of that fun comes from working within the precise definitions and clear rules of engagement of the discipline.  To me mathematics was chess on steroids. I loved it. Still do, for that matter. But relatively few citizens are interested in making  a career in mathematics. An education system that derives its goals from the ivory-towered pursuit of pure mathematics (and I use that phrase in an absolutely non-denigrating way, knowing full well how important it is to society and to our culture that those ivory towers exist) does not well serve the majority of students.

It requires some experience and sophistication in mathematics to see how skill in abstract, pure reasoning plays an important role in dealing with the more messy issues of the real world. There is an onus on those of us in the math ed community  to help others to appreciate the benefits available to them by way of improved mathematical ability.

As I have followed the forum discussions in my MOOC, I have started to wonder if one thing that MOOCs can give to mathematics higher education in spades is a mechanism to provide a real bridge between K-12 education and life in the world that follows. By coming together in a large, albeit virtual community, the precision-seeking individuals who want clear rules and guidelines to follow find themselves side-by-side (actually, keyboard-to-keyboard) with others (perhaps with weak formal mathematics skills) more used to approaching open-ended, novel problems of the kind the real world throws up all the time. If so, that would make the MOOC a powerful crucible that would benefit both groups, and thus society at large.

To be continued …


I'm Dr. Keith Devlin, a mathematician at Stanford University. In fall 2012, I gave my first free, open, online math course. I repeated it in spring 2013, then in fall 2013, and in February I am giving it a fourth time, each time with changes. This blog chronicles my experiences as they happen.

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