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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To be continued …