Archive for September, 2014

Here we go again

This blog has been quiet for the past few months, as other activities took all my available time, among them spending the first half of the year as a Visiting Professor at Princeton University, where I used the Spring session of the MOOC in flipped classroom mode as part of a course I gave there. But with the fifth session of my MOOC Introduction to Mathematical Thinking starting in a week’s time, it’s time to bring this sleeping blog back to life. (One should not let sleeping blogs lie for too long.)

Having made changes to the course on sessions 2, 3, and 4, this time round I have made only very minor tweaks. Session 4 was, I felt, more or less what I wanted it to be. Sure, I could re-do the entire thing with better video, better sound, and slicker graphics. But I’d prefer to wait another year or two before embarking on what would be considerable expense and a fairly significant amount of work. I think the jury is still out as to whether there will continue to be significant interest in MOOCs (at least as they are at present), in particular a MOOC like mine, which goes against some of the common wisdom.

For one thing, my MOOC is very definitely a course, with regular submission deadlines, and the videos are long by MOOC standards, averaging around half an hour each.

The former (the deadlines) are designed to try to ensure that as many students as possible are working on a particular topic or assignment at the same time, thereby facilitating fruitful discussions on the course Discussion Forum or on social media. Only very unusual students are able to master mathematical thinking on their own. Everyone else needs constant interaction with others, either with an instructor familiar with the material (something not possible in a MOOC) or with other students working on the same issues.

The longer videos reflect the fact that mathematical thinking cannot be broken down into bite-sized chunks – indeed, mathematical thinking demands the very opposite of morselization. It’s not about individual steps, rather the construction and carrying out of an overall strategy. To put it bluntly, working in intensive, thirty-minute chunks is the absolute minimum required to solve almost any mathematical problem of merit, and in general it takes a fair number of such half hour sessions, if not more sustained efforts.

Of course, there is nothing to prevent someone from working their way through the course materials in their own time, or from pausing the videos whenever they want. Depending on the individual, that could prove more or less beneficial. But they would then be using my materials to create their own learning experience. The course as I designed it is intended to be experienced in a cohort group, with much of the actual learning emerging during, or as a result of, discussions with other students.

Details aside, though, why am I in the MOOC business at all? I still get asked this from time to time.

I articulated my reasons for originally creating the MOOC in the early posts to this blog, starting with my first post in May 2012. Subsequent, modified sessions of the course were driven by a desire to try to “get it right”. Not in the sense of creating “the perfect course”. There is no such thing. Rather, my goal was to create a MOOC that represented what I felt was my best effort to put into MOOC format a course by me. What I wanted to create was the closest I could get in a MOOC format to taking a regular, physical class with me.

But what of now? Why am I offering this course for a fifth time? Well, with 20,000 students already enrolled, a full week before the course opens, there is  clearly still considerable demand. But that is only part of my rationale. The fact is, with the initial MOOC euphoria now (thankfully) a thing of the past – I never bought into the hype and said so at the time – I still see MOOCs as offering some benefits over traditional, classroom teaching.

One significant benefit of MOOCs over traditional classroom courses is that they offer the possibility to deliver personal, non-threatening, side-by-side, one-on-one education. The course presenter simply has to design it that way. I believe the huge early success of Khan Academy comes from that one factor. Khan’s pedagogic model is poor (though typical of a lot of classroom teaching) and in some instances his content is flat wrong, but his delivery is superb and he puts people at their ease. The guy has charisma, and it flows at you through the audio channel on your computer. What is more, for many people, what he offers is a lot better than they experienced, or are enduring, in a more traditional education setting. (Disclaimer: I know Sal slightly, and like him a lot, but we are not close friends.)

So, seeing what he had done well, I modeled, as best I could, the videos in my MOOC on Sal’s delivery, modified to work for more advanced, less-procedural mathematics.

The second benefit of a MOOC, for those who can take advantage of it, is that it puts the student in full control of their learning. Timing, pace, number of repeats (of items or of the whole course). True, many students cannot handle that. But for the ones who can, it is wonderfully freeing and empowering.

Certainly, the students at Princeton who took my MOOC as part of their course said they preferred accessing the instructional lectures part of the course in video format rather than actual lectures by me, precisely because they could control the pace and “rewind the tape” whenever they needed to.

Neither of those MOOC pluses has anything to do with the Massive Open part, of course. What is the upside for me to having thousands of students? Well, my major satisfaction on that front is that, by being totally open on a global scale, MOOCs can reach a relatively small number of talented individuals, in various parts of the world, who crave and can benefit from a good education, but have no other access to one. I’ll happily tolerate massive dropout from my MOOC in order to reach those few whose lives I really can change.

Of course, I am hardly alone in seeking my reward in my successes with a few. It’s what motivates math teachers the world over.

How do I know I actually am changing some lives? Some have told me. Like all MOOC instructors, in every course I have given, I have e-chatted with a small number of students whose forum posts catch my eye, and some of them eventually tell me I have absolutely transformed their lives.

So, perhaps 75,000 of my 80,000 registrants drop out, as happened with the first session I gave. Before they pull the plug, they may have gotten something of benefit. It may have just been conformation that they really don’t like math, though I suspect that most gain more benefit than that. Be that as it may, however, what really inspires me, is being able to reach 10, 20, 100 – or maybe only 1 or 2 – students for whom my MOOC was the thing that changed their lives.

I hardly ever have an opportunity to do that in a Stanford or a Princeton classroom. The most I can do there is polish a jewel. Maybe.


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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