Posts Tagged 'Stanford MOOC'



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.

How Facebook Made MOOCs Viable: MOOC planning – Part 2

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

One obvious, but huge distinction between planning a physical course and planning a MOOC is that for the former, it is generally fairly easy to make changes — even major ones — once the course is underway. But MOOCs are different. It requires an enormous amount of time to put a MOOC together (video recording/editing and implementing all the online course materials are just two elements not present in a physical course, or if they are, those materials can usually simply be omitted if a mid-course adjustment is required). As a result, once the course launches, you are pretty well committed to running it through largely as planned.

If I were putting together a MOOC for which Stanford would charge (and offer credit), by now I would be getting decidedly nervous. But that is not how things stand at present. Everyone sees this sudden MOOC explosion purely as an experiment to see what the medium can offer. The courses are free, and since there is no credential at stake, there is no worry about unmotivated students or of cheating. An unmotivated student is not going to continue with the course beyond the first week or so, and the only person who loses by student cheating is the student. Presumably both will change if this experimental phase is a success, and MOOCs take their place alongside other forms of higher education, where there are payments and credentials.

My own view, as I’ve noted elsewhere, is that MOOCs are not a replacement of the traditional bricks-and-mortar university, rather they are the twenty-first century version of the textbook.

Widespread availability of textbooks did not replace universities. Indeed, they did not change university education very much at all. In theory, once every student could purchase a textbook, there should have been little need for professors to give mainstream content lectures — particularly if the professor had written the course textbook — but the basic content lecture continued to remain the dominant model.  Early in my professorial career, I tried to adopt a flipped classroom approach, based on giving students reading assignments from a book I had written, and using the class time to discuss the material. It proved to be a disaster; hardly any of the student read the assigned reading, and of those that had, few really knew how to read a mathematics text and learn by so doing. I soon ended up having to give classical lectures on the material that was expressed far better in my textbook — far better because I had spent time putting my thoughts onto the page and the resulting manuscript had been professionally edited.

I am not sure that, on their own, video-recorded instructional material will lead to much of a change in university education either. Video-lectures are not really very different from textbooks. At least, for most university-level material that is the case. For learning how to carry out maintenance around the house, to change a bicycle tire, to assemble a piece of furniture, etc., video is far better than text. But those are all simple procedural learning — the goal is to learn how to do something, and for that purpose, showing is more efficient than describing in words. In contrast, the main focus of much university education is understanding; the student is supposed to learn how to think differently. That is very hard to do at arm’s length, regardless of whether the arm involves a textbook or a video. It is by direct interaction with an instructor and with other learners that we can gain understanding and learn how to think a certain way. That is why I don’t see MOOCs as a threat to the existence of universities.

MOOCs may, however, do what textbooks and instructional-videos failed to do. They may finally give rise to flipped classrooms — a mere six centuries after the invention of the printing press give rise to textbooks. The reason is, MOOCs are far more than video-recorded instruction. In fact, video lectures are one of the least significant elements of a MOOC. The key to the educational potential of MOOCs are human-computer and human-human interaction —  the latter especially so for most subjects. In particular, social media are what make MOOCs possible, and it is the widespread familiarity with, and acceptance of, human-human interaction over an ethernet cable that led to the sudden explosion of interest in MOOCs. In short, MOOCs are a direct consequence of the growth of Facebook, which made interaction-by-social-media global.

[I should add that I don’t see the degree of human-human interaction offered by social media in a MOOC being as educationally powerful as direct fact-to-face interaction. The unavoidable limitation in a MOOC is not the medium per se, rather is the scalability factor. In a physical class, the students get to interact with the professor — the expert, the domain professional. In a MOOC, that crucial part is missing. I think good course design can get a lot out of social media, but that one factor means that we’ll always need physical universities.]

The challenge facing a professor setting out to design and offer a MOOC, then, is to figure out how to take advantage of the (human-computer and) human-human interaction made possible on a global scale by social media, in order to provide students with a valuable learning experience.

In this regard, the experiment really begins with (many of) the 117 MOOCs currently offered by the MOOC platform Coursera. Coursera is a spin-off from a Stanford project in Computer Science to develop a platform to support flipped classrooms at the university. The first wave of Stanford MOOCs were basic level computer science courses, where there is a heavy focus on procedural learning and less dependency on reflection and peer interaction. (Those features come later in CS, and when they do, not a few Stanford CS students drop out and start their own companies, occasionally becoming millionaires within a few years!) But many of the second wave of courses now underway are in humanities and other areas, where the primary focus is on thinking and understanding, not doing.

To take just one instance of course design, in a basic-level computer science MOOC, it is possible to give machine-graded assignments. It would be possible to offer a math MOOC a similar way, provided the focus was on mastering basic computational procedures.  But in my case, where my goal is to develop mathematical thinking, I realized from the start that the key to making it work would be the social media factor. Just as it is for humanities courses.

That impacted how I would design, structure, and present the core material, as I’ll describe in my next post.

To be continued …

The Challenges of Online Education: MOOC planning – Part 1

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

I’ve been pretty quiet on this blog since launching it on May 5.

Partly that is due to summer vacation and the start of great cycling weather. But a lot of my time got swallowed up planning and developing my fall MOOC. It’s now scheduled to start on September 17, and the registration page just went live on Coursera, the Stanford spin-off MOOC platform now offering online courses from a number of the nation’s best universities.

All my Stanford colleagues who gave courses in the first round earlier this year reported how much time it takes to create such a course, no matter how long you have been teaching at university level. Knowing that you won’t be in the same room as the students, where there is ongoing interaction and constant, instant feedback, means that the entire course has to be planned down to the finest detail, before the first day. In addition to the usual course planning, lectures have to be recorded written materials prepared, and interactive quizzes constructed well in advance, with the knowledge that for some students, you may be their only connection to the material.

In my case, my fall term was already pretty full, before counting the MOOC, so I knew I could not rely on having the opportunity to record material once the course begins. That meant I had to try to anticipate well before the course launch, the difficulties the students might have.

Of course, I would not have chosen my topic (introduction to mathematical thinking) if I had not taught it many times before. Many colleges and universities ask their incoming mathematics students to take a “transition course” to develop the all-important skill of mathematical thinking. I helped pioneer such courses back in the 1970s. So I did start out with a good idea of the kinds of difficulties students would encounter on meeting the material for the first time.

But the challenges I faced (and still face) in trying to provide such a course in a MOOC format were, and are, formidable. To be honest, I am not sure it can really be done, but the only way to find out is to try – and not just once either. (Like the Coursera platform itself, my fall MOOC will be very much a beta release.)

An obvious problem is that learning to think like a mathematician, which is what transition courses are about, is not something that can be achieved by instruction. In that respect, the learning process is similar to learning to ride a bicycle. There is no avoiding a lengthy, and often painful process of trying and failing (i.e., falling) until, one day everything drops into place and you find you can ride. At that point, you wonder why it took you so long. Instruction helps, though only in retrospect can you see how. During the learning period, riding seemed impossible – something others could miraculously do but that you were not capable of.

(As someone who came to serious road biking and mountain biking later in life, I can recall vividly that the same is true for “advanced cycling.” For instance, being instructed – many times – how to corner fast on a downhill did not prevent me having to go through a lengthy process of learning how to do it. And while the broken collarbone I sustained in the process was a result of a rear-tire blowout on a sharp corner descending Mt Hamilton outside San Jose, California, it is possible that with more experience I could have kept control. But I am getting off track, which is what happened on Mt Hamilton as well.)

The challenge facing anyone trying to help students learn how to think mathematically by way of a MOOC, is that the communication channel is one way, from the instructor to the student. The sheer number of students (likely into the thousands) prevents any reliance on even the highly impoverished forms of student-faculty interaction that are possible with distance education for a class of no more than thirty students.

The only option (at least the only one I could see) is to try to create an environment where the students can help one another, by forming small study-groups and working together. In particular, I felt the students in my transition mathematics MOOC would benefit greatly by having regular transition course instructors use my MOOC in a flipped classroom model, so that my MOOC students working alone would be able to interact with other MOOC students who in turn were interacting in-person with a professor in a regular class, and perhaps on occasion interact directly with one of those professors online.

This is why I decided to offer my MOOC at the same time (the start of the US academic year) as many US colleges and universities offer their own transition courses. If instructors of those courses get their students to take my MOOC as part of their own learning process, their participation in study groups and the online discussion forums could ensure that every student in the MOOC is at most just one step removed from an expert. For the students in regular transition courses, using my MOOC in a flipped classroom experience, there is the added benefit that we all learn very efficiently when we try to teach others.

Another advantage of trying to involve instructors and students from regular transition classes, is that those instructors could critique my teaching in their class. Contrary to popular belief, “experts” are not infallible beings who know everything. They are just regular people who have more experience in a particular domain than most others. Analyzing and critiquing expert performance is another powerful way to learn. (So feel free to tear me apart. I can take it; I brought up two daughters through childhood and adolescence to adulthood, and after that I was a department chair and then a dean.)

To make my course attractive to regular transition course instructors, I had to make it very short, and focus on the very core of such courses, so those instructors would have plenty of time to take their own courses in whatever direction they choose.

Once I made that decision, I decided to write a companion book for the course. My Stanford colleagues who were giving the first MOOCs reported that some students wanted a physical book to read to support the online learning. People learn in different ways, and we instructors should accommodate them as much as possible.

There are many transition mathematics textbooks on the market, but they are all fairly pricey (ranging from $60 to $140) and cover much more ground than was possible in a mere five weeks of MOOC instruction. Definitely outside the spirit of free learning for all. I decided to write a companion book rather than a textbook (insofar as there is a distinction), since my view is that MOOCs are actually twenty-first century replacements of textbooks.

(I don’t think there is any chance that MOOCs can effectively replace regular university education, by the way, and a school district, state, or nation that decides to go that route will be just a single generation away from becoming a new third-world economy. But if I were a major textbook publisher, I would see MOOCs as the impending end of that business.)

To remain close to the ideal of free education, I decided to make my text a cheap, print-on-demand book. I typeset it myself in LaTeX, paid for an experienced mathematics textbook editor to edit the manuscript, and sent it off as a PDF file to Amazon’s self-publishing CreateSpace service to turn it into a book that can be ordered from Amazon. It’s called Introduction to Mathematical Thinking, and it should be available by August 1. It costs $9.99 and comes in at 102 pages. (There is no e-book option. Given the necessity of mathematical typesetting, an acceptable e-book not possible – at least for e-books that can display on any e-reader. Besides, as I mentioned already, to my mind, the MOOC itself is the true digital equivalent of a textbook.)

Incidentally, the process of self publication on CreateSpace is so simple and efficient, I suspect that low-cost, print-on-demand publishing is the future of academic textbooks.

So add writing a book to the other tasks involved in creating a MOOC.

Still, the book-writing part was easy. Though many of my colleagues find writing books a major challenge – an insurmountable challenge for some of them – I have always found it relatively painless, indeed pleasurable.

In any event, books are an ancient medium that academics and teachers have long been familiar with. Pretty well everything else about the MOOC process was new. I wrote the book before I designed the course; indeed, the book constituted the curriculum. The only new twist for me was that in writing the book I was conscious of using it as the basis for a MOOC.

With the book written, the next question was, how do I present the lectures? After experimenting with a number of formats, I finally settled on the one I’ll use this fall. It’s not the one Sal Khan uses for Khan Academy. Given his success, I started out trying his format, but I found it just did not work for the kind of material I was dealing with. I’ll say more in my next posting. There were other surprises ahead as well.

To be continued …

Podcast-talk about MOOCtalk

The Pulse Project recently podcast an informative and entertaining ten-minute discussion of my upcoming Stanford MOOC between Peter Rowlett in the UK and Samuel Hansen in the USA. The part focusing on MOOCs is available here. The full hour-long discussion is available at Math/Maths 95.

A couple of days later, Steve Hargadon interviewed me for an hour in his excellent Web 2.0 series, and MOOCs formed a substantial part of our wide ranging discussion. The complete discussion can be accessed here.

Thanks to Peter, Samuel, and Steve for their interest.


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

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