Posts Tagged 'Khan Academy'

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 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 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)

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 …

Coming up for air (and spouting off)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To be continued …

It’s About Time (in Part): MOOC Planning – Part 10

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

Well, lectures have ended and the course has now switched gears. For those still left in the course (17% of the final enrollment total of 64,045), the next two weeks are focused on trying to make sense of everything they have learned, and working on the final exam — which in the case of my course involves peer evaluation.

Calibrated Peer Review is not new. A study of its use in the high school system by Sadler and Good, published in 2006, has become compulsory reading for those of us planning and giving MOOCs that cover material that cannot be machine graded. [If you want to see how I am using it, just enroll in the class and read the description of the "Peer Review system". There is no obligation to do anything more than browse around the site! No one will know you are not simply a dog that can use a computer.]

As I was working on my course, Coursera was still frantically building out their platform to support peer evaluation. There was a lot of just-in-time construction. It’s been a long time since I’ve had to go behind a user-friendly interface and dig into the underlying code to do something on a computer, and the programming languages have all changed since I last did that.

One thing I had to learn was one of the ways networked computers keep time. I now know that at the time of writing these words, 7:00AM Pacific Daylight Time on October 22, 2012,  exactly 1,350,914,400 seconds have elapsed since the first second of January 1st, 1970, Eastern Standard Time. That was the start of Unix Time.

I needed to learn to work in Unix Time in order to set the various opening times and completion deadlines for the exam process. I expect that by the time the next instructor puts together a MOOC, she or he will be greeted by a nice, friendly Coursera interface with pulldown menus and boxes to tick — which probably will come as a great relief to any humanities professors reading this, who don’t have any programming in their background.

[By coincidence, Unix was the last programming language I had any proficiency in, but I did not need to know Unix to use Unix Time. I just used an online converter. Unix was developed in 1969 at AT&T Bell Laboratories in New Jersey. Hence the 1970 EST baseline.]

In fact, time conversion issues in general turned out to be a  continuing, major headache in a course with students all over the world. One thing we will not do again is have 12:00PM Stanford Time, aka Coursera Time (i.e., PDT), as any of the course deadlines. It might seem a nice clean stopping point, and there are all those memories of Gary Cooper’s deadline in the classic Western movie High Noon, but many students missed the deadline for the first submitted assignment because they thought 12:00PM meant midnight, which in some parts of the world made them a whole day late.

The arbitrary illogicality of the AM/PM distinction is not apparent to those of us who grew up with it. But my course TA and I are now very aware of the problems it can lead to! In future, we’ll stick to unambiguous times that stay away from noon and midnight. But even then, with local computer systems usually working on local time, to say nothing of the different Summer and Winter Times, which change on different dates around the world, timing events in MOOCs is going to remain a problematic issue, just as it is for international travelers and professionals who collaborate globally over Skype and other conferencing services. (When I used the Unix Time conversion app, I had to remember that Unix thinks New Jersey is currently just two hours ahead of California, not the three hours United Airlines uses when it flies me there. Confusing, isn’t it?)

The reason why times are an issue in my course is that it is a course. At first glance, it may look little different from Khan Academy, where there are no time issues at all. But Khan Academy is really just an educational resource. (At least, that’s the part most people are familiar with and use, namely the video library that started it all. People use it as a video version of a textbook — or more precisely a video equivalent to that good old standby Cliffs Notes, which got many of us through an exam in an obligatory subject we were not particularly interested in.)

In contrast, in my case, as I’ve discussed earlier in this blog series (in particular, Part 6), my goal was to take a standard university course (one I’ve given many times over the years, at different universities, including Stanford) and make it available to anyone in the world, for free. To the degree I could make it happen, they would get the same learning experience.

That meant that the main goal would be to build a (short-lived) learning community. The video-recorded lectures and tutorials were simply tools to make that happen and to orchestrate events. Real learning takes place when students work on assignments on their own, when they repeatedly fail to solve a problem, and when they interact (with the professor and with one another) — not when they watch a lecture or read a book.

To achieve that goal, the MOOC would, as I stated in Part 6, involve admissions, lectures, peer interaction, professor interaction, problem-solving, assignments, exams, deadlines, and certification. To use the mnemonic I coined early on in this series, the basic design principle is WYSIWOSG: What You See Is What Our Students Get.

As we go forward, I intend to iterate on the course design, based on the data we collect from the students (and 64,000 students very definitely puts us into the Big Data realm). But my basic principle will remain that of offering a course, not the provision of a video library. And the reason for that should be obvious to anyone who has been following this blog series, as well as some of the posts on my other blogs Devlin’s Angle and profkeithdevlin.org. The focus is not on acquiring facts or mastering basic skills, but on learning to think a certain way (in my case, like a professional mathematician). And that requires both a lot of effort and (for most of us) a lot of interaction with others trying to achieve the same goal.

Our ancestors in the 11th Century started to develop what to this day remains the best way we know to achieve this at scale: the university, where people become members of a learning community in which learning takes place in a hothouse atmosphere that involves periods of intense interaction as deadlines loom, sustained by the rapidly formed social bonds that emerge as a result of that same pressure.

While I will likely experiment with variants of this model that allow for participation by students who have demanding, full-time jobs, I doubt I will abandon that basic model. It has lasted for a thousand years for a good reason. It works.

To be continued …

Final Lecture: MOOC Planning – Part 9

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

I gave my last lecture of the course yesterday (discounting the tutorial session that will go out next week), and we are now starting a two week exam period.

“Giving” a lecture means the video becomes available for streaming. For logistic reasons (high among them, my survival and continued sanity — assuming anyone who organizes and gives a MOOC, for no payment, is sane), I recorded all the lectures weeks ago, well before the course started.  The weekly tutorial sessions come the closest to being live. I record them one or two days before posting, so I can use them to respond to issues raised in the online course discussion forum.

The initial course enrollment of 63,649 has dropped to 11,848 individuals that the platform says are still active on the site. At around 20%, that’s pretty high by current MOOC standards, though I don’t know whether that is something to be pleased about, since  it’s not at all clear what the right definition of “success” is for a MOOC.

Some might argue that 20% completion indicates that the standards are too low. I don’t think that’s true for my course. Completion does, after all, simply mean that a student is still engaged. The degree to which they have mastered the material is unclear. So having 80% drop out could mean the standard is too high.

In my case, I did not set out to achieve any particular completion rate; rather I adopted a WYSIWOSG approach — “What You See Is What Our Students Get.” I offered a MOOC that is essentially the first half of a ten week course I’ve given at many universities over the years, including Stanford. That meant my students would experience a Stanford-level course. But they would not be subject to passing a Stanford-level exam.

In fact, I could not offer anything close to a Stanford-exam experience. There is a Final Exam, and it has some challenging questions, but it is not taken under controlled, supervised conditions. Moreover,  since it involves constructing proofs, it cannot be machine graded, and thus has to be graded by other students, using a crowd sourcing method (Calibrated Peer Review). That put a significant limitation on the kinds of exam questions I could ask. On top of that, the grading is done by as many different people as there are students, and I assume most of them are not expert mathematicians. As a result, it’s at most a “better-than-nothing” solution. Would any of us want to be treated by a doctor whose final exam had been peer graded (only) by fellow students, even if the exam and the grading had been carried out under strictly controlled conditions?

On the other hand, looking at and attempting to evaluate the work of fellow students is a powerful learning experience, so if you view MOOCs as vehicles for learning, rather than a route to a qualification, then peer evaluation has a lot to be said for it. Traditional universities offer both learning and qualifications. MOOCs currently provide the former. Whether they eventually offer the latter as well remains to be seen. There are certainly ways it can be done, and that may be one way that MOOCs will make money. (Udacity already does offer a credentialing option, for a fee.)

In designing my course, I tried to optimize for learning in small groups, perhaps five to fifteen at a time. The goal was to build learning communities, within which students could help one another. Since there is no possibility of regular, direct interaction with the instructor (me) and my one TA (Paul), students have to seek help from fellow students. There is no other way. But, on its own, group work is not enough. Learning how to think mathematically (the focus of my course) requires feedback from others, but it needs to include feedback from people already expert in mathematical thinking. This means that, in order to truly succeed, not only do students need to work in groups (at least part of the time), and subject their attempts to the scrutiny of others, some of those interactions have to be with experts.

One original idea I had turned out not to work, though whether through the idea itself being flawed or the naive way we implemented it is not clear to me. That was to ask students at the start of the course to register if they had sufficient knowledge and experience with the course material to act as “Community TAs”, and be so designated in the discussion forums. Though over 600 signed up to play that role, many soon found they did not have sufficient knowledge to perform the task. Fortunately,a relatively small number of sign-ups did have the necessary background, as well as the interpersonal skills to give advice in a supporting, non-threatening way, and they more or less  ensured that the forum discussions met the needs of many students (or so it seems).

Another idea was to assign students to study groups, and use an initial survey to try to identify those with some background knowledge and seed them into the groups. Unfortunately, Coursera does not (yet) have functionality to support the creation and running of groups, apart from the creation of forum threads. So instead, in my first lecture, I suggested to the students that they form their own study groups in whatever way they could.

The first place to do that was, of course, the discussion forums on the course website, which very soon listed several pages of groups. Some used the discussion forum itself to work together, while others migrated offsite to some other location, physical or virtual, with Skype seeming a common medium. Shortly after the course launched, several students discovered GetStudyRoom, a virtual meeting place dedicated to MOOCs, built by a small startup company.

In any event, students quickly found their own solutions. But with students forming groups in so many different ways on different media, there was no way to track how many remained active or how successful they have been.

The study groups listed on the course website show a wide variety of criteria used to bring the groups together. Nationality and location were popular, with groups such as Brazil Study Group, Grupo de Estudo Português, All Students From Asia, and Study Group for Students Located in Karachi, Pakistan. Then there were groups with a more specific focus, such as Musicians, Parents of Homeschooled Children, Older/Retired English Speakers Discussion for Assignment 1, and, two of my favorites, After 8pm (UK time) English speakers with a day job and the delightfully named Just Hanging on Study Group.

The forum has seen a lot of activity: 15,088 posts and 13,622 comments, spread across 2712 different threads, viewed 430,769 times. Though I have been monitoring the forums on an almost daily basis, to maintain an overall sense of how the course is going, it’s clearly not possible to view everything. For the most part I restricted my attention to the posts that garnered a number of up-votes. Students vote posts up and down, and once a post shows 5 or more up-votes, I take that as an indication that the issue may be worth looking at.

The thread with the highest number of up-votes (165) was titled Deadlines way too short. Clearly, the question of deadlines was a hot topic. How, if at all, to respond to such feedback is no easy matter. In a course with tens of thousands of students, even a post with hundreds of up-votes represents just a tiny fraction of the class. Moreover, threads typically include opinions on both sides of an issue.

For instance, in threads about the pace of the course, some students complained that they did not have enough time to complete assignments, and pleaded for more relaxed deadlines, whereas others said they thrived on the pace, which stimulated them to keep on top of the material. For many, an ivy-league MOOC offers the first opportunity to experience an elite university course, and I think some are surprised at the level and pace. (I fact, I did keep the pace down for the first three weeks, but I also do that when I give a transition course in a regular setting, since I know how difficult it is to make that transition from high school math to university level mathematics.)

A common suggestion/request was to simply post the course materials online and let students access them according to their own schedules, much like Khan Academy. This raises a lot of issues about the nature of learning and the role MOOCs can (might? should?) play. But this blog post has already gone on long enough, so I’ll take up that issue next time.

To be continued …

Why MOOCs Look Unprofessional: MOOC planning – Part 4

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

From an educational perspective, my goal in offering a MOOC on mathematical thinking is very modest. I have not approached the task as one of developing a whole new pedagogic model. That is a future goal — for me or for others. Rather I set out to see how much we can take current university teaching (of transition mathematics material) and make it available to a wide audience. Indeed, almost all the Stanford MOOCs currently being offered are free, online versions of regular Stanford courses, in many cases running concurrently with a physical class on campus. (As I noted in an earlier post, the technology that supports these MOOCs was actually developed at Stanford in order to facilitate flipped-classroom learning in on-campus classes.)

The underlying assumption of university education — at least at major research universities (as Stanford is) — is that the principle value for the student comes from studying with a world expert in a particular domain. Though many professors at research universities do in fact put enormous effort into their teaching, what is really being offered (sold) to students is the expertise (and reputations) of the faculty. (Other parts of the value proposition, such as the prestige of the university, stem from the faculty, both past and present.) It’s a method that works well for very bright, well-prepared, and highly motivated students, but it is not ideal for everyone.

In fact, even at less prestigious universities, where there are fewer leading research faculty, and at liberal arts colleges, where the primary focus is on undergraduate education, field-content knowledge hugely outweighs pedagogical content knowledge — how to teach the subject and how students learn it. (A Ph.D. is usually required for a faculty position.) That makes universities and colleges very different from high schools.

One of the implicit purposes of  a math transition course, such as mine (as well as many other first-year courses in different disciplines), is to help incoming students adjust to the different approach to teaching. More precisely, it is to help them adjust to not being “taught”, but having someone help them learn. This is particularly significant in mathematics — at least in the US — because of the hugely formulaic, procedures-focused nature of K-12 mathematics education in this country.

My challenge then, like that facing most of my colleagues offering their first MOOC, is to figure out how to take an existing educational model, hitherto used to teach (or help to learn) twenty-five or so students in a classroom, and make it available to thousands, spread around the world.

Since my topic is mathematical thinking, the biggest, and most obvious challenge is how to compensate for the complete absence of regular interaction between the students and me, the instructor. Sure, I give lectures when I teach a physical transition class, but the lectures are one of the least significant components. They really just set the agenda for learning. In order to help the students develop the ability for mathematical thinking, I need to see them in action at the board, to read their work, and to discuss their attempts face-to-face. Learning to think mathematically is more like learning to drive or to play tennis than soaking up knowledge. You have to do it alongside an expert or coach.

It’s a challenge I think cannot be completely overcome in a MOOC. The question is, is it possible to get part-way there? I suspect it is, but we’ll only find out for sure by making the attempt. So here we are.

One thing a MOOC does offer that is not possible in a physical class — and hence is a plus — is that all the instruction and professorial-learning-assistance can be on a one-to-one basis. Sure, it’s all one way, but if you set it up right (and if your voice/personality/whatever work over an ethernet cable), then the student can get that sense of working alongside the instructor — the expert.

Though by no means the first to discover that, Salman Khan, by virtue of his huge following at Khan Academy, demonstrated just how powerful is that sense of “working together, side-by-side”. Though I share the dismay of many of my colleagues at his less-than-expert content knowledge and his almost non-existent pedagogical content knowledge (neither of which he could be expected to have, given his background), where I seem to part company with many of them is the huge significance I attach  to the way he pulls off that human-connect. For online learning, I suspect it trumps almost all other factors.

(BTW, in developing my MOOC, I soon lost track of the number of times I made a decision based on a “suspicion” — or a “guess” or  “hunch”. MOOCs are generating enough research questions to sustain several generations of doctoral dissertations in education research.)

Based on that suspicion (admittedly a suspicion comfortingly buttressed by a Khan Academy user base that numbers in the millions), Khan’s format was my starting point, as I observed in my last post. Not just the physical aspect of “sitting alongside in a one-on-one tutorial” but the associated human connect (and with it reassurance and encouragement) that Khan delivers.

In Khan’s case, his now widely familiar format originated with him informally helping his school-age relatives (who lived a long way away) with their math homework. What the viewer gets on their computer screen is, well, just “Uncle Sal”, doing what he would have done if he were really sitting alongside one of his relatives. For my MOOC, I wanted to achieve a similar outcome. Not a slick show, not a polished, rehearsed performance. Just me doing math.

Of course, the logistics of putting together a complete course that has to run automatically, and be scalable to many thousands of students around the world, many of them not native English speakers, meant that there had to be a lot of detailed advanced planning. Everything had to be scripted. But when it comes to the bits where I explain some mathematics, I put the script to one side and just start to work through the material as if I am sitting next to a student.

You might not like it. It might not work for you. You will surely despair at my handwriting. You might hate my accent. (I did cut down drastically on my jokes and puns, in deference to a multilingual audience.) But as far as I can make it, absent being physically in the same room, it’s what you would get if you were taking the course with me here at Stanford.  [Some time spent in a campus video-editing studio made my into-camera segments look a lot smoother than they were when we recorded them! If it's digital, it's plastic. But the goal there was to reduce the length of those segments.]

Which brings me back to my starting point: seeing the extent to which we can take existing university education and make it available to the world.

Once we can do that — and it will surely take several iterations to iron out all the kinks and make an altogether better job of it — we can look at how to change the underlying model. In addition to MOOCs making accessible to the world some aspects of university education, I think that the act of designing them, mounting them, and analyzing the results, will lead to changes in the way we organize learning within our universities.

It is because the current goal is to see how well we can deliver (current) real university education to the world for free that most of the MOOCs being offered have an unpolished, unrehearsed look. By deliberate choice, to the greatest degree we can achieve, what you see is what our (on-campus) students get. (I think this WYSIWOSG philosophy — I just made up that term —  is also one of the reasons for the success of Salman Khan — including the fact that in his case, unlike university MOOCs, he does not even lesson-plan his instruction sessions.)

So much for the most visible part of the MOOC: the instruction. But instruction is still just instruction. As I’ve said before, the learning takes place elsewhere, through other mechanisms, none of which we understand very well. So where is that educational  meat?

Now we are about to really enter speculative territory.

To be continued …

COMMENTS: As always, comments are welcome, provided they remain on topic.

Khan Academy Meets Vi Hart: MOOC planning – Part 3

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

The ideal way to learn mathematical thinking (and a great many other things that involve understanding, not just doing) is in a small physical group with an expert. That provides frequent opportunities to interact one-on-one with the expert, during which the expert can observe you work in real time (on paper or at a board) and can give you direct feedback on written work you have done and handed in for evaluation. It also provides frequent opportunities to discuss what is being learned with other students at the same stage of their learning, sometimes with the expert present, other times with the expert absent.

Sometimes, the expert will provide instruction. Though there have been successful instances of mathematics professors who largely avoid instruction (R L Moore being the most notable example), most of us (i.e., university mathematics educators) find that instruction has a valuable place in mathematics education. But many of us view it as just one part of mathematics education.

Anyone who has experienced highly interactive mathematics teaching will know how different it is from mere instruction, and how much more effective. I wrote about this last March in my Devlin’s Angle column for the MAA. Unfortunately, it seems clear that a great many Americans have never experienced good mathematics teaching. If they had, you would not have thousands of Khan Academy users (including famous figures such as Bill Gates) declaring Salman Khan is the best math teacher ever. You can say a number of good things about Sal Khan (I am going to say some of them in just a moment), but being a great math teacher is not one of them. To say that he is, simply reflects on the miserable math ed diet that many millions of American have been fed, for whom Khan Academy offers something far better than they were ever exposed to.

I bring up Khan Academy for a couple of reasons, one being that it set the stage for the MOOC explosion. Indeed, former Stanford CS professor Sebastian Thrun stated publicly last January that it was Khan Academy that inspired him to give his first MOOC in fall 2011, and then to leave Stanford and launch his own MOOC service Udacity at the start of this year.

It’s not merely the wide reach that Khan Academy demonstrated. As I discussed in a recent article for the MAA, Sal Khan managed to tap into the power of the Web medium to achieve a critical element of good teaching that not all teachers can offer: a strong teacher-student bond. Moreover, he did so using just his voice and the electronic trail of a digital pen on the viewer’s computer screen. Yes, some of the math is wrong, and the pedagogy is so poor, experienced teachers tear their hair out, but the very success of Khan Academy shows how important is the teacher-student connection.

Khan Academy is not a MOOC, of course, but it does provide a model for online mathematics instruction. In starting to plan my MOOC, I began by trying variants of Sal’s approach for the instructional part. Like him, I have a voice that works on the radio (or a Web audio channel) — an accident of birth — which makes such an approach feasible.

I soon concluded that his approach would not work. It is fine for presenting short instructional mini-lectures on how to follow a particular mathematical procedure, but it is woefully impoverished for trying to help students understand a mathematics idea or a proof, and to form the right mental concepts. For that, the huge importance in mathematics teaching of physical gestures, in particular the hand(s), cannot be ignored.

There is an old challenge in which you ask someone to describe a helix while keeping their hands clasped firmly behind their back. (Try it!) But it’s not just helices. Explaining almost any mathematical concept without using at the very least hand and arm gestures, and in many cases full body motion, is difficult if not impossible. There is masses written about this topic, based on many years of research. For example, take a look at this summary, or this one, or this forthcoming book. Or Google on the terms “mathematics + learning + hand + gesture” or variants thereof to see a lot more.

Since MOOC students access the material on a wide range of devices, with different screen sizes, I felt that a full body recording of me working at (and in front of) a blackboard or whiteboard would not be ideal. Besides, I love the sense of intimacy Khan Academy offers. You get a strong sense of sitting next to a friendly relative who is personally instructing you. I wanted to create that environment.

But trying to follow an explanation of a mathematical concept or proof Khan-style, where the visual channel consists only of a digital pen trace, was impossible — at least, it was given my educational style. At the very least, I needed my writing hand to direct the student’s focus. The simplest way to achieve that was to have a video camera mounted above my desk and record me working through the material in the time-honored fashion of paper-and-pencil. That seemed to work.

Having decided on the basic modality, the next issue was one of style and tone. After playing with some variants of the basic format, I came down in favor of a very informal look, where I simply slap down a sheet of paper on the desk in front of me and the student, and work through the material. (Marking the exact position of the paper on the desk and letting it totally fill the screen looked too artificial — though at this stage the issue was largely one of taste, and this is a decision I may change based on the experience I get from this first course. I did have to tape down the paper, but the initial placement was fairly casual, and the taping was sufficiently loose that the paper could still move a little — it takes effort to create “informality” on video.)

To counter the inevitable sense of frustration when watching a pen write something out in real time, I decided to speed up a lot of the writing during the video editing phase. (Though not to the speed of the wonderful Vi Hart, whose purpose is informative entertainment.) So at that stage I found myself with a “Sal Khan meets Vi Hart” look. A great place to start, given the success both have achieved!

For standalone Web instruction, that would likely be enough, but a MOOC involves a lot more. It is, after all, a course — a structured experience over several weeks, with a professor. Regular connection to the instructor is important — at least, I think it is. (It was for me when I was a student.) To achieve that “human connection,” many of my Stanford colleagues who have given MOOCs have put a small head-and-shoulders video of themselves speaking in one corner of the screen, as the material being discussed occupies the rest of the display. I tried that, and found it did not work for me, with my material. The face was a distraction. I wanted to keep as much of the Khan Academy sense as possible — you don’t ignore success unless there is good reason! So I opted to keep video of me separate from the hand-writing part.

I’ve posted a short sample from Lecture 1 on YouTube. Given the low resolution of YouTube video encoding, this does not display well in terms of content, but the Coursera platform uses far higher resolution video.

I doubt much of this material will survive to a second iteration of the course next year. At the very least, I’d want to go back and pay more attention to lighting and audio levels and consistency.  But it does have the overall look and feel I was trying to achieve. This is live beta, folks.

But as I have already indicated in this blog series, I don’t see the video lectures as the heart of the course. They merely set the agenda for learning. The real learning takes place elsewhere. I’ll turn to that topic in a future post.

Meanwhile, my Stanford MOOC Introduction to Mathematical Thinking is scheduled to begin on September 17 on Coursera. If you want to do some preliminary reading, there is my low-cost course textbook by the same name. Though written to align to the course, it is not required in order to complete the course. (Indeed, I noted  above that I see MOOCs as replacing textbooks — though some MOOCs may have required textbooks, so it would be unwise to predict the imminent death of the printed textbook!)

To be continued …

NOTE: I mentioned Khan Academy to indicate its role in the MOOC explosion and acknowledge its role in guiding the design of the instructional videos in my MOOC. But the focus of this blog is on MOOCs in general and mathematics MOOCs in particular. Comments discussing the merits or demerits of Khan Academy are off topic and hence will not be published; there are many other venues for such discussions.


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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