Posts Tagged 'Stanford MOOC'

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 …”

MathThink MOOC v4 – Part 3

In Part 3, I describe some aspects and origins of the basic course pedagogy, and how they relate to student expectations.

This post continues the previous two in this series.

Expectations. So far I’ve talked about two expectations many students bring to my MOOC that cause problems:

(1) a perception that learning is a cycle of

instruction –> worked examples –> student exercises

(a process that’s better described as training, not learning), and

(2) a belief that failure is something to be avoided (rather than the essential part of learning that it is).

A third problematic expectation many students bring is based on the assumption that mathematics is a body of knowledge to be absorbed, rather than a way of thinking that has to be learned/acquired/developed. That belief is what can lead to the erroneous, and educationally debilitating, perception of mathematics that what makes it hard to learn is the sheer number of different rules and tricks that have to be learned, as described in the article about Jo Boaler’s work I cited in Part 1 of this series.

The view of mathematics as a large collection of procedures can get you quite a way, which explains the huge success of Khan Academy, which shows you all those rules – thousands of them! But it won’t get you to the stage of thinking like a mathematician. Mastering an array of procedures is fine if you are (1) willing to invest the time to keep learning new tricks and (2) prepared to end up working for someone who can do the latter (i.e., think mathematically). Because, increasingly, in the western world, it is that latter that is the valuable commodity. (I wrote about this back in 2008.) My use of the term “mathematical thinking”, rather than just “mathematics”, to title my course was designed to highlight the distinction, but many students nevertheless come to my MOOC expecting a mathematics course (in the sense they have come to understand that term), and are disappointed to discover that it is nothing of the kind. (Some have even asked why I don’t make it more like Khan Academy, a bizarre request which leaves me wondering why they don’t just enter the KA URL in their browser rather than navigate to my MOOC.)

Based on the kinds of issues I’ve been discussing regarding mathematical thinking, in designing my MOOC (and the classroom course that came earlier), I drew on a number of established pedagogies. Most notably among them is Inquiry-Based Learning. For a general background on this powerful and effective learning method, check out this 21-minute video.

Do please watch this video. The focus of much of the video is producing professional mathematicians, and that reflects a common use of the IBL method in mathematics majors classes. In my course, however, with its focus on general mathematical thinking skills for use in many life situations, I don’t ask the students to act as those in a regular IBL class – that would be impossibly hard to pull off in a MOOC in any case. But I believe the general learning principles apply (perhaps even more so), and some of the comments in the video from people who pursued careers in industry address that aspect.

Another pedagogic strategy I adopt is one that has been used in mathematic education since the time of the ancients, which I usually refer to as the Mr Miyagi Method, after the Japanese martial arts expert in the hit 1984 movie The Karate Kid. Having promised to teach karate to the young American Daniel Larusso, Mr Myagi makes his young student paint a fence, wax a floor, and polish several cars. Only with great reluctance does Daniel acquiesce, but in due course he discovers the value of all that effort, as you see from this brief clip.

As I say, this form of teaching has been used in mathematics for centuries. The reason is that in many cases it is impossible to appreciate how mathematics can be applied in a particular situation until enough of the relevant mathematics has been learned. So you design small, self-contained exercises to develop the individual component abilities. Mathematics textbooks have been doing this since they were written on clay tablets five thousand years ago. It’s what most people experience as “mathematics education.”

An attractive alternative is project-based learning. (Again, please do watch this short video.) Unfortunately, whereas PBL is fine for a regular course, in a MOOC that is designed to be of value both to students working on their own, with few if any additional resources, and to students who just participate in a part of the course, it is not an option. That leaves the Miyagi Method as the only game in town.

Even is a regular classroom, and for sure in a MOOC, I would however strongly recommend not adopting Mr Miyagi’s method of delivery. It would surely have been better (as an educational strategy, though not as a movie scene) if he had first explained to Daniel what those chores had to do with learning karate. If a student has to ask, “Why am I learning this?”, the teaching has failed. Why not tell the student from the start?

But remember, times change, and skills and abilities that were valuable in one era sometimes become far less significant, as we are reminded by another Hollywood blockbuster character, Indiana Jones. So you’d better be sure that when you tell a student why a particular topic is important, the reason you give is plausible. (Note: In today’s world, no one balances checkbooks any more – heavens, most people no longer have a checkbook – and no householder uses geometry to figure out how much carpet to order for a room.)

Turning the failing-as-part-of-learning meme on my own journey of learning how to design and give a MOOC, I think that so far I have definitely failed to make sufficiently clear to my MOOC students (1) the basic goals of the course, (2) the approach I am taking to try to achieve those goals, and (3) how those goals lead to adopting the methods I have just outlined above.

To be sure, I laid everything out in detail in the guide-notes I posted on the course website, and in some of my earlier posts to this blog, that I link to from the course site. The problem was, many students never read everything on the site; indeed, some appear not to have read any of the site information.

Now, you might say, they had an obligation to do so. It’s their education, after all, not mine. But MOOCs are about taking learning to a much wider audience than is reached by traditional higher education, and if a MOOC instructor does not manage to connect to that audience, then that is a failure of mission.

As a result, one change I am making with the new version of the course in February is that one of the first things the students will encounter is a video of me explaining the course pedagogy.

[From the very first offering of the course, I posted video discussions between me and my then course TAs, in which we discussed the course design, but those discussions really only made sense after a student had spent some time in the course. So from the second run onwards I cut them into short segments that were released on the site throughout the course. I suspect those discussions were perceived more as "Charlie Rose type" television conversations, rather than providing key information about how to take the course. (In the second of the two discussions, I even asked a professional television and radio host I know to moderate the discussion.) In any case, they did not have the effect I hope will be achieved by a face-to-face explanation by me, as the instructor, of the course goals and structure, given before the course starts. You can view those two earlier videos at: Team Discussion (8mins), What's New in Number Two (10min 45sec).]

Will my new introductory video solve the problem? I don’t know. For sure, MOOC students do watch (almost) all the videos. Indeed, if there is a problem, it is that some seem to perceive the videos as the most important component of the course, a perception the news media seem to share. Why is that a problem? Because video instruction (i.e., direct instruction) in fact-based, science disciplines does not work. Indeed, instructional videos do actual harm by re-enforcing any prior-held false beliefs, as Derek Muller explains in this video. (Yup, putting math and science education out as a MOOC is hard!)

My guess is that my new introductory video will have an effect, but it will be limited, and many will still be left feeling confused as the course moves ahead. Unfortunately, since the only tools we have at our disposal in a MOOC are video, text, and social media, I don’t see what more I can do, so my gut feeling at this stage is that with the new video I will have gone as far as the medium allows. Nothing works for everyone. All we can do is design for a feasible maximum.

I’ll say (yet) more on this theme of recognizing, anticipating, and dealing with student expectations in my next post. Based on giving three successive versions of my MOOC now, I think the student expectations issue is much more significant in a MOOC than in a regular class. The reason is that in a MOOC, because you have no direct contact with the students, you have very limited ability to counter or correct or allow for those expectations. Your only real strategy is to identify them, and pre-emptively try to lessen their impact on the student.

great-expectations-posterTRAILER (LOOKS GOOD)

MathThink MOOC v4 – Part 2

In Part 2, I reveal that I share with Steve Jobs, J K Rowling,  Sebastian Thrun, Thomas Edison, and a successful Finnish video-game studio head, a strong belief in the power of failure.

This post continues the one posted two days ago about the expectations students being to my MOOC.

One of the problematic expectations many students bring to my course is that I will show them how to solve certain kinds of problems, work through a couple of examples, and then ask them to solve one or two similar ones. When I don’t do that, some of them complain, in some cases loudly and repeatedly.

There are several reasons why I do not simply continue to serve up the pureed (instructional) diet they are familiar with, and instead offer them some raw meat to chew on.

Most importantly, the course is not about mastering yet more, specific procedures; rather the goal is to acquire a new way of thinking that can be used whenever a novel situation is encountered. Tautologically, that cannot be “taught.” It has to be learned. The role of the “instructor” is not to instruct, but to offer guidance and feedback – the latter being feasible in a MOOC by virtue of most beginners having broadly similar reactions and making essentially the same mistakes.

To progress in the course, the student has to grow accustomed to the way professional mathematicians (to say nothing of engineers, business leaders, athletes, and the like) make progress: learn by failing. That’s the raw meat I serve up: failure.

Not global failure that debilitates and marks an end to an endeavor; rather repeated local failures that lead to eventual success. (Though the distinction is really one of our attitude toward a failure – I’ll come back to this in a moment.)

Most of us find it difficult making the adjustment to regarding failing as an integral part of learning, in large part because our school system misguidedly penalizes (all) failures and rewards (every little) success.

Yet, it is only when we fail that we actually learn something. The more we fail, the better we learn; the more often we fail, the faster we learn. A person who tries to avoid failure will neither learn nor succeed. If you take a math test and score more than 75%, then you are taking a test that is too easy for you, and hence does not challenge you to learn. A score of 75% or more says you did not need to take the test! You were not pushing the frontiers of your current abilities.

I should add that I am not talking about tests and exams designed to determine what you have learned, rather those that are an integral part of the learning process – which in my case, giving a course that offers no credential, means all the “graded” work.

In my course, the numbers the system throws out after a machine-graded Problem Set, or the mark assigned by peer evaluation, are merely indicators of progress. A grade between 30% and 60% is very solid; above 60% means you are not yet at the threshold where significant (for you) learning will take place, while a score below 30% tells you either that you need to put more time and effort into mastering the material, or slow down, perhaps working through the remainder of the course at your own pace then trying again the next time it is offered. (Another great advantage of a free MOOC.)

What is important is not whether you fail, but what you do as a result. As I was working on this post, I came across an excellent illustration in an article in FastCompany about the Finnish video game studio Supercell. Though the young company has only two titles in the market – Clash of Clans and Hay Day – it grossed $100 million in 2012 and $179 million in the first quarter of 2013 alone.

Supercell’s developers work in autonomous groups of five to seven people. Each cell comes up with its own game ideas.  If the team likes it, the rest of the employees get to play. If they like it, the game gets tested in Canada’s iTunes App store. If it’s a hit there it will be deemed ready for global release.

This approach has killed off several games. But here is the kicker: each dead project is celebrated. Employees crack open champagne to toast their failure. “We really want to celebrate maybe not the failure itself but the learning that comes out of the failure,” says Ilkka Paananen, the company’s 34-year-old CEO.

It’s not just in the PISA scores where Finland shows the world it knows a thing or two about learning; you can find it manifested in the App Store download figures as well!

(And let’s not forget that another Finnish game studio, Rovio, produced over a dozen failed games before they hit the global App Store jackpot with Angry Birds.)

Where I live, in Silicon Valley, one of the oft-repeated mantras is, “Fail fast, fail often.” The folks who say that do pretty well in the App Store too. In fact, some of them own the App Store!

One of my main goals in giving my MOOC is helping people get comfortable with failing. You simply cannot be a good mathematical thinker if you are not prepared to fail – frequently and repeatedly. Failing is what professional mathematicians do maybe 99% of the time. Responding appropriately to failure is a key part of mathematical thinking.

And not just mathematical thinking. It’s definitely true of engineering as well. Remember Thomas Edison, who on being asked how he motivated himself to continue his efforts to build an electric light bulb when a thousand attempts had failed, replied (paraphrase), “They were not failures, I just found a thousand ways it won’t work.”

The metaphor I use regularly in my MOOC is learning to ride a bike. If you think about it, you don’t learn to ride a bike; you learn how not to fall off a bike. And you do that by repeatedly falling off until your body figures out how to avoid falling.

Incidentally, the fact that you really did not learn to ride a bike by learning how to is indicated by the fact that almost no one can correctly answer the question, What direction do you turn the handlebars in order for the bike to turn to the right? Your conscious mind, the one that would have been involved if you had learned how to ride a bike, says you twist the handlebars to the right in order to turn the bike to the right. But, if you are able to ride a bike, your body knows better. You turn the handlebars to the left in order to make the bike turn to the right. Your body figured that out when it learned how not to fall down.

Don’t believe me? Go out and try. Make a conscious attempt to turn right by twisting the handlebars to the right. Most likely, your body will prevent you carrying through. But if you manage to over-ride your body’s instinct, you will promptly fall off. So please, do this on grass, not the hard pavement.

Not surprisingly, six weeks in a MOOC is woefully little to adjust to the professionals’ view of failure. The ones who breezed through my course, unfazed by seeing the system return a grade of 30% on a Problem Set, were in most cases, I suspect (and in a fair number of cases that suspicion was confirmed), professional engineers, business people, or others with a fair bit of post-high-school education under their belts. Those for whom the course was one of their first ventures into collegiate education, often had a hard time of it. (Not a few gave up and dropped the course, sometimes leaving an angry, departing post on the class forum page.)

It’s not called a “transition course” for nothing.

I’ll continue this theme of dealing with student expectations in my next post.

Meanwhile, I’ll leave you with three more examples about the power of failing in the learning process.

The first is Steve Jobs’ 2005 commencement address at Stanford.

The second is J. K. Rowling’s 2008 commencement address at Harvard.

Finally, and very close to home, is Sebastian Thrun’s recent business pivot of his MOOC delivery company Udacity, which I discussed in a commentary in the Huffington Post. Though I would agree with the many commentators that his initial attempt had “failed,” where the tone of many was dismissive, I saw just another instance of someone on the pathway to (for him, yet another) success. It’s all about how you view failure and what you do next.

I’ll continue the theme of dealing with student expectations in my next post.

MathThink MOOC v4 – Part 1

In Part 1 of a series, I focus on the distinction between high school math and university-level mathematics, suggesting they are effectively different subjects that are best learned in different ways.

One of the biggest obstacles in giving an online course on mathematical thinking, which my MOOC is, is coping with the expectations students bring to the course – expectations based in large part on their previous experience of mathematics classes. To be sure, prior expectations are often an issue for regular, physical classes. But there the students have an opportunity to interact directly with the instructor on a regular basis. They also have the benefit of a co-present support group of others taking the same class.

But in a massive open online class, apart from locally configured support groups and text-based discussions on the MOOC platform discussion forum, each student is pretty much on her or his own.

The situation is particularly bad for a course like mine, designed to help students transition from high school mathematics to university-level mathematics. For one thing, the two are so different as to be in many ways completely distinct subjects.

School mathematics tends to be almost exclusively procedural, mastering established methods to solve artificially constructed problems designed to be amenable to such an approach. The student who best masters all the techniques in the syllabus and becomes skillful in pattern-matching problems to solution methods, does well. (I know that first hand; it’s how I got to university to study mathematics!)

In contrast, university mathematics is about learning how to deal with a novel situation of a kind you have not encountered before. (If no one else has encountered it, we call it mathematics research.) Though it certainly can involve pattern matching and the application of established, standard procedures, it usually does so only as components of a novel solution you develop to deal with that particular situation. Moreover, at university level, the problems are typically of a “prove that this is true (or false)” variety, rather than “solve this equation” or “compute the value of that formula.”

What is more, while a school math problem typically has a right answer, university mathematics generally involves much more than mere correctness. Indeed, there may not be a unique “right answer.”

Not only is the subject matter different, so too is the pedagogy. Almost all students’ experience of mathematics learning in school is teacher instruction. The teacher describes a method, does a few worked examples, and then asks the students to do a few similar ones. Rinse and repeat.

It’s a very efficient way to cover a lot of ground when the goal is pattern matching and procedure application. It works for school mathematics. Unfortunately, it does not prepare the graduates for the other kind of mathematics. (It also leaves them without ever having a satisfactory answer to their question “What is this good for?”, a question that leaves anyone versed in mathematics astounded. “What is it not good for?” is a more interesting question. It does not have a simple answer, by the way. It’s a very nuanced question.)

It’s like teaching someone the elements of bricklaying, carpentry, plumbing, and electrical wiring, and then asking them to go out and design and build a house. You need all of those skills to build a house, but on their own they are not enough. Not even close.

In deciding, almost two years ago now (before the New York Times had heard of MOOCs) to develop a MOOC to help people learn the other kind of mathematics, what I call mathematical thinking, I knew I was taking on a big challenge. I’d found it hard to teach that kind of course in a physical classroom with just 25, carefully selected students at elite colleges and universities.

On the other hand, most people go through their entire mathematics education without ever encountering what I and my colleagues would call “real mathematics,” and many of them eventually find they need to be able to handle novel situations that involve – or may involve – or could productively be made to involve – mathematical thinking. So I felt there was a need to have a resource publicly available to help them acquire this valuable ability.

The huge dropout rates in MOOCs did not really bother me. For a mathematical thinking course, it’s possible to gain value from dropping into the course for just a few days – and to keep coming back at future times if required. The focus was not on credentialing, it was developing a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.

That way of thinking can be utilized profitably in many other courses that do yield a certified credential, so students could approach the course as a low-stress, no-risk way of preparing for subsequent learning.

The course is structured as course for those students who seek an encapsulated experience, and in many ways that yields the greatest benefits, in large part because of the interactions with other students working on the same stuff. But the majority of students who have taken it the three times I have offered it have just taken a part of the course.

Each time I gave the course, I changed it, based on what I had learned. When it launches again in February, it will be different again. This time, in some fairly significant ways. In the coming days, I’ll describe those changes and why I made them.

First out of the gate, I’ll describe what exactly were the problems caused by those expectations many students brought to the course, and  how did I try to deal with them. Also, what am I changing in the coming version of the course to try to help more people make what is a very difficult transition: from being taught (i.e., instructed) to being able to learn. The reward for making that one transition is huge. It opens up all of mathematics, and in the process makes it much, much easier.

The traditional, instructional way of teaching procedural mathematics frequently leaves students with the impression (dramatically documented by my Stanford colleague Jo Boaler) that mathematics consists of a large number of rules to be learned. But at the risk of sounding like those weird web advertisements (you know, the ones with a drawing or photo of a strange looking person) promising to teach that “one great trick” that will change your life, let me leave you by telling you the one great trick that all mathematicians learn:

You just have to master, once, a particular way of thinking, and you no longer need all those rules.

That’s what my course focuses on. Stay tuned.

The MOOC will soon die. Long live the MOOR

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

The second running of my MOOC (massive open online course) Introduction to Mathematical Thinking ended recently. The basic stats were:

Total enrollment: 27,930

Number still active during final week of lectures: ca 4,000

Total submitting exam: 870

Number of students receiving a Statement of Accomplishment: 1,950

Number of students awarded a SoA with Distinction: 390

From my perspective, it went better than the first time, but this remains very much a research project, and will do for many more iterations. It is a research project with at least as many “Can we?” questions as “How do we?”

From the start, I took the viewpoint that, given the novelty of the MOOC platform, we need to examine the purpose, structure, and use of all the familiar educational elements: “lecture,” “quiz,” “assignment,” “discussion,” “grading,” “evaluation,” etc. All bets are off. Some changes to the way we use these elements might be minor, but on the other hand, some could be significant.

For instance, my course is not offered for any form of college credit. The goal is purely learning. This could be learning solely for its own sake, and many of my students approached it as such. On the other hand, as a course is basic analytic thinking and problem solving, with an emphasis on mathematical thinking in the second half of the course, it can clearly prepare a student to take (and hopefully do better in) future mathematics or STEM courses that do earn credit – and I have had students taking it with that goal in mind.

Separating learning from evaluation of what has been learned is enormously freeing, both to the instructor and to the student. In particular, evaluation of student work and the awarding of grades can be devoted purely to providing students with a useful (formative) indication of their progress, not a (summative) measure of their performance or ability.

To be sure, many of my students, conditioned by years of high stakes testing, have a hard time adjusting to the fact that a grade of 30% on a piece of work can be very respectable, indeed worth an A in many cases.

My typical response to students who lament their “low” grade is to say that their goal should be that a problem for which they struggle to get 30% in week 2 should be solvable for 80% or more by week 5 (say). And for problems they struggle with in week 8 (the final week of curriculum in my course), they should be able to do them more successfully if they take the course again the next time it is offered – something else that is possible in the brave new world of MOOCs. (Many of the students in my second offering of the course had attempted the first one a few months earlier.)

Incidentally, I think I have to make a comment regarding my statement above that the MOOC platform is novel. A number of commentators have observed that “online education is not new,” and they are right. But they miss the point that even this first generation of MOOC platforms represents a significant phase shift, not only in terms of the aggregate functionality but also the social and cultural context in which today’s MOOCs are being offered.

Regarding the context, not only have many of us grown accustomed to much of our interpersonal interaction being mediated by the internet, the vast majority of people under twenty now interact far more using social media than in person.

We could, of course, spend (I would say “waste”) our time debating whether or not this transition from physical space to cyberspace is a good thing. Personally, however, I think it is more productive to take steps to make sure it is – or at least ends up – a good thing. That means we need to take good education online, and we need to do so for the same reason that it’s important to embed good learning into video games.

The fact is, we have created for the new and future generations a world in which social media and video games are prevalent and attractive – just as earlier generations created worlds of books and magazines, and later mass broadcast media (radio, films, television) which were equally as widespread and attractive in their times. The media of any age are the ones through which we must pass on our culture and our cumulative learning. (See my other blog profkeithdevlin.org for my argument regarding learning in video games.)

Incidentally, I see the points I am making here (and will be making in future posts) as very much in alignment with, and definitely guided by, the views Sir Ken Robinson has expressed in a series of provocative lectures, 1, 2, 3.

Sir Ken’s thoughts influenced me a lot in my thinking about MOOCs. To be sure, there is much in the current version of my MOOC that looks very familiar. That is partly because of my academic’s professional caution, which tells me to proceed in small steps, starting from what I myself am familiar with; but in part also because the more significant changes I am presently introducing are the novel uses I am making (or trying to make) of familiar educational elements.

The design of my course was also heavily influenced by the expectation (more accurately a recognition, given how fast MOOCs are developing) that no single MOOC should see itself as the primary educational resource for a particular learning topic. Rather, those of us currently engaged in developing and offering MOOCs are, surely, creating resources that will be part of a vast smorgasbord from which people will pick and choose what they want or need at any particular time.

Given the way names get assigned and used, we may find we are stuck with the name MOOC (massive open online course), but a better term would be MOOR, for massive open online resource.

For basic, instructional learning, which makes up the bulk of K-12 mathematics teaching (wrongly in my view, but the US will only recognize that when virtually none of our home educated students are able to land the best jobs, which is about a generation away), that transition from course to resource has already taken place. YouTube is littered with short, instructional videos that teach people how to carry out certain procedures.

[By the way, I used the term “mathematical thinking” to describe my course, to distinguish it from the far more prevalent instructional math course that focuses on procedures. Students who did not recognize the distinction in the first three weeks, and approached the material accordingly, dropped out in droves in week four when they suddenly found themselves totally lost.]

By professional standards, many of the instructional video resources you can find on the Web (not just in mathematics but other subjects as well) are not very good, but that does not prevent them being very effective. As a professional mathematician and mathematics educator, I cringe when I watch a Khan Academy video, but millions find them of personal value. Analogously, in a domain where I am not an expert, bicycle mechanics, I watch Web videos to learn how to repair or tune my (high end) bicycles, and to assemble and disassemble my travel bike (a fairly complex process that literally has potential life and death consequences for me), and they serve my need, though I suspect a good bike mechanic would find much to critique in them. In both cases, mathematics and bicycle mechanics, some sites will iterate and improve, and in time they will dominate.

That last point, by the way, is another where many commentators miss the point. Something else that digital technologies and the Web make possible is rapid iteration guided by huge amounts of user feedback data – data obtained with great ease in almost real time.

In the days when products took a long time, and often considerable money, to plan and create, careful planning was essential. Today, we can proceed by a cycle of rapid prototypes. To be sure, it would be (in my view) unwise and unethical to proceed that way if a MOOC were being offered for payment or for some form of college credit, but for a cost-free, non-credit MOOC, learning on a platform that is itself under development, where the course designer is learning how to do it, can be in many ways a better learning experience than taking a polished product that has stood the test of time.

You don’t believe me? Consider this. Textbooks have been in regular use for over two thousand years, and millions of dollars have been poured into their development and production. Yet, take a look at practically any college textbook and ask yourself is you could, or would like to, learn from that source. In a system where the base level is the current college textbook and the bog-standard course built on it, the bar you have to reach with a MOOC to call it an improvement on the status quo is low indeed.

Again, Khan Academy provides the most dramatic illustration. Compared with what you will find in a good math classroom with a well trained teacher, it’s not good. But it’s a lot better than what is available to millions of students. More to the point, I know for a fact that Sal Khan is working on iterating from the starting point that caught Bill Gates’ attention, and has been for some time. Will he succeed? It hardly matters. (Well, I guess it does to Sal and his employees!) Someone will. (At least for a while, until someone else comes along and innovates a crucial step further.)

This, as I see it, is what, in general terms, is going on with MOOCs right now. We are experimenting. Needless to say – at least, it should be needless but there are worrying developments to the contrary – it would be unwise for any individual, any educational institution, or any educational district to make MOOCs (as courses) an important component of university education at this very early stage in their development. (And foolish to the point of criminality to take them into the K-12 system, but that’s a whole separate can of worms.)

Experimentation and rapid prototyping are fine in their place, but only when we all have more experience with them and have hard evidence of their efficacy (assuming they have such), should we start to think about giving them any critical significance in an educational system which (when executed properly) has served humankind well for several hundred years. Anyone who claims otherwise is probably trying to sell you something.

A final remark. I’m not saying that massive open online courses will go away. Indeed, I plan to continue offering mine – as a course – and I expect and hope many students will continue to take it as a complete course. I also expect that higher education institutions will increasingly incorporate MOOCs into their overall offerings, possibly for credit. (Stanford Online High School already offers a for-certificate course built around my MOOC.) So my use of the word “die” in the title involved a bit of poetic license

But I believe my title is correct in its overall message. We already know from the research we’ve done at Stanford that only a minority of people enroll for a MOOC with the intention of taking it through to completion. (Though that “minority” can comprise several thousand students!) Most MOOC students already approach it as a resource, not a course! With an open online educational entity, it is the entire community of users that ultimately determines what it primarily is and how it fits in the overall educational landscape. According to the evidence, they already have, thereby giving us a new (and more accurate) MOOC mantra: resources, not courses. (Even when they are courses and when some people take them as such.)

In the coming posts to this blog, I’ll report on the changes I made in the second version of my MOOC, reflect on how things turned out, and speculate about the changes I am thinking of making in version 3, which is scheduled to start in September. First topic up will be peer evaluation – something that I regard as key to the success of a MOOC on mathematical thinking.

Those of us in education are fortunate to be living in a time where there is so much potential for change. The last time anything happened on this scale in the world of education was the invention of the printing press in the Fifteenth Century. As you can probably tell, I am having a blast.

To be continued …

How are MOOCs organized?

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

With exactly one week to go before the second edition of my MOOC Introduction to Mathematical Thinking goes live, my TA and I have been working feverishly to get everything ready — a task far more complex and time consuming than preparing for a traditional (physical) course. (If you have been following this blog since I launched it last summer, when I started to plan my first edition of the course, you likely have some idea of the complexities involved.)

MOOCs continue to be in the news. Just last week, NBC-tv used my course as an illustration in a news story (4 min 21 secs) they ran about the American Council on Education’s recommendation that some Coursera MOOCs be considered eligible to receive college credit.

But what exactly is a MOOC and how are they organized? The easiest way to find out is to simply sign up for one or more and take a look. They are all free (at least, all the ones everyone is talking about are free), and there is no requirement to do any more than hang around online and see what is going on. If you do that, you’ll find that they all exhibit some differences from one another, as well as many similarities. Moreover, almost everyone giving a MOOC approaches it as an experiment, so they often change from one edition to the next.

Taking my own MOOC as an illustration, when the course website opens to registered students next weekend (Saturday March 2), they will initially find themselves in a website populated with several pages of information about the course structure, together with a bit of background information relevant to the course content, but none of the lectures, assignments, quizzes, problem sets, or tutorials will be available. Those are released at specified times throughout the ten weeks the course will run, starting with Lecture 1 on March 4.

For a sample of a lecture, see this short clip (7min 16 sec) from Lecture 1 on YouTube. (But note that Coursera videos are much higher resolution than YouTube, so the YouTube video is hard to follow — it’s purely an illustration of the overall format of the lectures.)

One of the main informational pages the students will see describes the various components of the course. Here, verbatim, are the contents of that page.

Basic elements of the course

Consult the Daily timetable (see link on left) on a regular basis to see what is due at any one time.

1. Lectures – videos presented by the instructor.
2. In-lecture quizzes – simple multiple-choice questions that stop the lecture, designed to assist you in pacing and monitoring your progress.
3. Assignment sheets (one for each lecture) – downloadable PDF files to work through in your own time at your own pace, ideally in collaboration with other students. Not graded.
4. Problem sets (one a week for weeks 1 through 8) – in-depth problems like those on the assignment, but with a deadline for submitting your answers (in a multiple choice format). Machine graded.
5. Tutorial sessions – the instructor provides (video) comments and answers to some of the previous week’s assignment problems.
6. Reading assignments – downloadable PDFs files providing important background information.
7. Final exam – a downloadable PDF file that you will have one week to complete before participating in a peer review process. Required to be eligible for a grade of completion with distinction.

Lectures

Lecture videos are released at 10:00AM US-PDT on Wednesdays. (Weeks 1 and 2 are slightly different, with lectures released on Monday and Wednesday.) Each lecture comprises one or two videos, with each video of length 25 to 35 minutes if played straight through. Completing the embedded progress quizzes will extend the total duration of a video-play by a few minutes, and you will likely want to stop the playback several times for reflection, and sometimes you will want to repeat a section, perhaps more than once. So you can expect to spend between one and two hours going through each lecture, occasionally perhaps more.

The lecture videos are not carefully crafted, heavily edited productions. If you want a polished presentation of the course material, you can read the course textbook. My goal with the lectures is to provide as best I can the experience of sitting alongside me as we work through material together. And, guess what, I often make mistakes, and sometimes mis-speak. I want to dispel any misconception that mathematicians are people who generate perfect logical arguments all the time. We’re not. We just keep going until we get it right.

In-lecture quizzes (Ungraded)

Each lecture is broken up by short multiple-choice “progress quizzes”. The vast majority of these in-lecture quizzes are essentially punctuation, providing a means for you to check that you are sufficiently engaged with the material.

Slightly modified versions of the quizzes will also be released as standalones at the same time as the lecture goes live, so if you do not have a good broadband connection and have to download the lecture videos to watch offline, you can still take the quizzes. In which case, you should do so as close in time to viewing the lecture as possible, to ensure gaining maximim benefit from the quizzes in monitoring your progress. The standalone quizzes are grouped according to lecture.

Completion of all the quizzes is a requirement (along with watching all the lectures) for official completion of the course, but we do not record your quiz scores, so quiz performance does not directly affect your final grade. If you complete the quizzes while watching the lecture (the strongly preferred method, as it helps you monitor your progress in mastering the material), you do not need to complete the standalone versions.

BTW, you may notice that it is possible to speed up video replay up to a factor of double speed. This can be a useful device when watching a video a second or third time. Going beyond 1.50 speed, however, can sometimes lead to problems with the display of the quizzes (besides making me sound like a chipmunk (though some may find that an enhancement).

Course assignments (Self graded)

An assignment will be released at the end of each lecture, as a downloadable PDF file. The assignment is intended to guide understanding of what has been learned. Worked solutions to problems from the assignments will be demonstrated (video) or distributed (PDFs) in a tutorial session released the Monday following the lecture (so in Weeks 2 through 9). The tutorial sessions will be released at 10:00AM US-PDT.

Working on these assignment problems forms the heart of the learning process in this course. You are strongly urged to form or join a study group, discuss the assignment problems with others in the group, and share your work with them. You should also arrange to assess one another’s answers. A structured form of peer review will be used for the final exam, when you will be graded by, and grade the work of, other students, randomly (and blindly) assigned, so it will help to familiarize yourself beforehand with the process of examining the work of others and providing (constructive) feedback.

Problem Sets (Machine graded)

Each Wednesday (in weeks 1 thtough 8), following the lecture, a for-credit Problem Set will be posted, with submission due by 9:00AM US-PDT the following Monday. The scores on these problem sets will count toward the course grade. Though the Problem Set has a multiple-choice quiz format, these questions are not the kind you can answer on the spot (unlike most of the in-lecture quizzes). You will need to spend some time working on them before entering your answers.

Though you are strongly encouraged to work with others on understanding the lecture material and attempting the regular assignments, the intention is that you work alone on the Problem Sets, which are designed to give you and us feedback on how you are progressing.

Tutorial sessions

The tutorial sessions are more than mere presentations of solutions to the previous week’s assignments and problem session. They are really lectures based on problems that the student has already attempted. You can expect to expand your knowledge of the course material beyond the lectures. Not all questions on the assignments sheets and problem set will be considered in the tutorial session.

Final exam (Peer graded)

Though the lectures end after week 8 (apart from a tutorial on the final assignment), the final two weeks are intended to be highly active ones for any students seeking a grade of distinction, with considerable activity online in the various forums and discussion groups. This is when you are supposed to help one another make sense of everything.

At the start of week 9, an open-book exam will be released, to be completed by the end of the week. Completed exams will have to be uploaded as either images (or scanned PDFs) though students sufficiently familiar with TeX have an option of keyboard entry on the site. The exam will be graded during week 10 by a calibrated peer review system. The exam will be based on material covered in the entire course.

As with the weekly Problem Sets, the intention is that you work alone in completing the final exam.

NOTE: The process of peer reviewing the work of others (throughout the course, not just in the final exam) is intended to be a significant part of the learning experience and participating in the formal peer review procedure for the final exam is a requirement for getting a grade of distinction. In principle, it is during week 10 that stronger students will make cognitive breakthroughs. (Many of today’s professors really started to understand mathematics when, as graduate student TAs, they first helped others learn it!)

Course completion and final grade

There are two final course grades: “completion” and “completion with distinction”. Completion requires viewing all the lectures and completing all the (in-lecture) quizzes and the weekly problem sets. Distinction depends on the scores in the problem sets and the result of the final exam.

Pacing

The pacing of the lecture releases is designed to help you maintain a steady pace. At high school, you probably learned that success in mathematics comes from working quickly (and alone) and getting to the right answer as efficiently as possible. This course is about learning to think a certain way – the focus is on the process not the product. You will need time to understand and assimilate new ideas. Particularly if you were a whiz at high-school math, you will need to slow down, and to learn to think and reflect (and ideally discuss with others) before jumping in and doing. A steady pace involving some period of time each day is far better than an all-nighter just before a Problem Set is due.

Keeping track

Consult the Daily timetable on the website on a regular basis to see what is due.

SO NOW YOU KNOW!


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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