Posts Tagged 'flipped classroom'

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.

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 …


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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