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 …