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

It’s been three weeks since I last posted to this blog. The reason for the delay is I was swamped getting everything ready for the launch of my course four days ago, on Monday of this week. As of first thing this morning there are 57,592 students enrolled in the class.

The course was featured in an article on MOOCs in USA Today. It was a good article, but like every other news report I’ve seen on MOOCs, the focus was on the video lectures. Those certainly take a fair amount of time on the part of the instructor (me, in this case), and are perhaps the most visible feature of a MOOC, just as the classroom lecture is the most visible part of many on-campus courses.

For some subjects, lectures, either in-person or on a computer screen, may be a major part of a course. But for conceptual mathematics, which is what my course is about, they are one of the least important features.

Learning to think mathematically is like learning to swim, to ride a bicycle, to ski, to play golf, or to play a musical instrument. You can probably get some idea by having someone explain it to you, but you won’t learn how to do it that way. The key words in that last clause are “learn” and “do”. There is really only one way to learn how to do something, and that is by doing it. Or, to put it more bluntly, the only way to achieve mastery is by repeated failure. You keep trying until you get it. The one thing that can help is having someone who already has mastery look at your attempts and give you constructive feedback.

In fact, failing in attempting to do something new isn’t really failure at all in the sense the word is usually used. Rather, a failed attempt is a step towards eventual success. Edison put it well when asked how he felt about his many failures to make a light bulb. He replied, “I have not failed. I’ve just found 10,000 ways that don’t work.”

After just one week of my course, I’ve seen a lot of learning going on, but it wasn’t in the lectures. Even if I’d been able to see each student watching the lecture, I would not have seen much learning going on, if any.  Rather, the learning I saw was on the discussion forums, primarily the ones focused on the assignments I gave out after each lecture. As I explained to the students, the course assignments and the associated forum discussions are the heart of the course.

So what is my part in all of this? Well, first of all, I have to admit I am uncomfortable with the title “instructor,” since that does not really reflect my role, but it’s the name society generally uses. “Course designer, conductor (as for an orchestra), and exemplar” would be a much better reflection of what I have been doing. Once the course was designed, the lectures recorded, and all the ancillary materials prepared, my task was to set the agenda, provide motivation and context for the various topics, and give examples of mathematical thinking.

The rest is up to the students. It has to be. (At least, I don’t know of any other way to learn how to think mathematically.) To be sure, in a physical class, the instructor (and or the TAs) can interact with the students, and (if it occurs) that can be a huge factor. But that simply helps the students learn by repeated failure, it does not eliminate the need for that learning-by-trying-and-failing process. Let’s face it, if you are not failing at something, you have already learned it, and should move on to the next step or topic. (With understanding, once you get it, you don’t need to practice!)

In a MOOC, that regular contact with the instructor and or the TAs is missing, of course. That means the students have to rely on one another for feedback. This is where the Coursera platform delivers. Here are some recent stats from my course website:

Total Registered Users	57592
Active Users Last Week	32123
Video Lectures
Total Streaming Views	77415
Total Downloads	19491
# Unique users watching videos	21712
Discussion Forums
Total Threads	641
Total Posts	5414
Total Comments	3823
Total Views	119489

Though I’d like to see a lot more students posting to the forums, with almost 120,000 views (after just one lecture and one course assignment!), it’s clear that that is where a lot of the action is.

As I surmised in an early blog-post, I don’t think it was the widespread availability of video technology and sites like YouTube that set the scene for MOOCs. To my mind, Facebook opened the floodgates, by making digitally-mediated social networking a mainstream human activity. (I’d better add Skype, since there are already several Skype-based study groups for my course. And of course, students who live close together can do it the old-fashioned way, by getting together in person to work through the assignments.)

One feature of the course that did not surprise me was the sense of feeling lost some students reported (and I’m sure many more felt), in some cases maybe being accompanied by panic. For most students, not only does my course present a side of mathematics they have never seen before (the world of the professional mathematicians), on top of that, none of the strategies they were taught to succeed in high-school math work any more.

Because the focus of the course is on mathematical thinking, I can’t provide the students with a list of rules to follow, templates to recognize, or procedures to follow. The whole point is to help them develop the ability to solve novel problems for which no  rules are known.

Of course, at this stage, the problems I give them are ones that have been solved long ago, and which have been shown to provide good learning material. But to the student, they are new, and that’s what matters in terms of learning. Unless, of course, they look for the solution on the Web, which defeats the whole purpose. But in a voluntary course where the focus is on process, not “getting answers,” and which provides no college credential, I hope that does not occur. In fact, one of the things that attracted me to free MOOCs was that the students would enroll because they wanted to learn, not because they were forced to learn or simply in need of a diploma. (We mathematicians get a lot of students like that! But we get paid to teach those classes. So far, no one is paying MOOC faculty for their efforts.)

Most US students have a particularly hard time with this “there are no templates” approach, because of the way mathematics is typically taught in American schools.  Instead of helping students to learn mathematics by figuring it out for themselves, teachers frequently begin by providing instruction and following it up with examples. Michael Pershan has a nice summary of this on YouTube. (His initial focus is on Khan Academy, but Khan is simply providing a service that is molded on, and fits into, the US system. The crucial issue Pershan’s video addresses is the system.)

The pros and cons of the two approaches, instruction based or guided discovery, remains a topic of debate in this country, but in the case of my course, there can be no debate. The goal is to develop the ability to encounter a novel problem and eventually be able to figure it out. Providing instruction in such a course would be like giving a golf cart to someone who wants to walk to lose weight! It might get them to their destination with less effort, but it would defeat the real goal.

Having thought at length about how to structure this first version of the course, and played around with some approaches, I ended up, as I thought I probably would, going minimal.  Virtually no instruction, and what little there is presented as examples of mathematical thinking in action, not by way of a carefully planned lesson. I was pretty sure I’d do that, because that’s how I’ve always conducted classes where the goal is student learning (as opposed to passing a standardized test).

There are a number of studies pointing out the dangers of over-planned lessons, one of the most famous and influential being Alan Schoenfeld’s 1988 paper in Educational Psychologist (Vol 23(2), 1988), When Good Teaching Leads to Bad Results: The Disasters of “Well Taught” Mathematics Courses. Still, as I said, I did play around with alternatives, since I was worried how students would fare without having regular access to the instructor and the TAs. I may have to re-visit those other approaches, if things go worse this time than I fear.

But this time round, what the student gets is as close a simulation as I can produce of sitting next to me as I work through the material. The result is not perfect. It’s not meant to be. There are minor errors in there. It’s meant to provide an example of how a professional mathematician sets about things. Definitely not intended as something to be perceived as an entry in an instruction manual.

After those work sessions were video-recorded, they were edited, of course, but only to cut out pauses while I thought, and to speed up the handwriting in places. I found that on a screen, watching the handwriting in real time looked painfully slow, and rapidly became irritating, particularly in places where I had to write out an entire sentence. So I took a leaf out of Vi Hart‘s wonderful repertoire. The speed ramping ended up being the only place that modern digital technology actually impinged on the lecture. Everywhere else it merely provided a medium. The approach would be familiar to Euclid if he were somehow to come back and take (or give) the class.

To be continued …

You may be interested in two recent videos featuring the founders of the two Stanford MOOC platforms that started the current explosion of interest in these courses. In one, Sebastian Thrun talks about Udacity. In the other Daphne Koller discusses the creation of Coursera.