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.
MOOCtalk 
I am taking the course, and have ‘taken’ some other MOOCs. I think that this approach addresses many of the issues with on-line learning.
I am sure that technology will get a handle on evaluating non-multile guess quizzes. I am hopeful that the peer-review process for evaluation will be helpful. In some other classes, I have taken part in the discussion fora, but many of the discussions quickly degenerated into the blind leading the blind. If I can figure out how to be effective as a TA (along with other people like me), the discussions could be quite useful. When I was in school, there wasn’t even the concept of a study group — at least for maths.
The book is good, and I suppose that I could learn the material by just reading the book and going through the exercises. ( This is not the first time I’ve seen the material.) However, seeing and hearing the discussions helps to re-enforce the learning.
Thanks for all the extra work that you have done planning this course. I hope that others who are planning similar moocs will pay attention.
George, Thanks for the feedback. I think the future of courses like this is to build up, over time, a cadre of experienced TAs who volunteer every year. It’s a great way of taking the learning some of us are privileged to acquire and make it available to benefit those who are not so fortunate. KD.
I think you got the speed on the handwriting just right. It didn’t even occur to me when watching that it might have been sped up, yet it matches the speed of the explanation well.
Crowbeak, I’m glad to hear that. I’ve had one comment in another blog from someone who does not like it. We just took the video and sped it up to match the soundtrack of my voice! Pretty low-tech really. 🙂
I’m one of your TAs and I’m super happy to be of any help to the students who need some sort of guidance or simply have a quick question.
A couple of us, TAs, have come together in the study room and it is super exciting to see how hundreds of students come in to simply discuss the assignments, help each other and meet each other 🙂
Emerson, Glad to have you on the team. Yes, this is a tremendous experience!
Hi KD,
Really I am feeling great to get so much from your this blog post along with the course. Being one of TAs in your MOOC really made me thinking everything differently than older days as I also need to let me help others & learning along side. Being from India, I would like to make you clear that such courses are very much useful for the students as per need here who really want to learn. Also,I w’d love to learn as much as possible in your ways to enhance the skills up to an effective TA for your future course(s), least but not the last.
Thanks a ton for showing & Guiding a different way of THINKING in this digital era!! Wonderful Experience!!
Just wanted to mention that I’m one of your students taking the MOOC.
Thanks for your latest blog post and all your efforts. I really appreciate the course and how it has opened up a whole NEW way of thinking for me.
I’m from Canada and we have the same so-called “template” problem that the U.S. has in terms of just memorizing equations and doing procedures. As you have mentioned many times, just learning procedures will only take you so far and eventually you will hit the wall.
Prior to your MOOC, I always thought that doing math was just more of what I learned in high school. Boy was I wrong, LOL.
Now I understand why so many people fail various math courses. It’s simply because they’re not taught properly to begin with. If you ask me, we really, really should be teaching our kids how to “think” mathematically instead of just solving equations. No doubt some countries actually understand that while others don’t.
Don’t stop.
Very good idea in such elegant presentation.
A saw yours the last lectures. Very impressed by the presentation. Especially by thoughts that you wanted to convey.
I’m interested to see mathematicians from other universities. To compare how they teach math. I know a lot of students from mathematics faculty of our university who watch these lectures too.
I am enrolled on the course. The first week is a bit like the first week at a new university (in my past have worked at 4 universities; 2 UK (BSc & PhD), 1 Canadian (MSc), 1 US (part of UK BSc) ). Firstly, everyone is trying to find out who everyone else is relative to themselves. secondly, 50k international students try to group themselves into clans/peer groups etc. Thirdly, realisation of what the course is about starts to hit home and the effort required. There are many upsides to this means of teaching a subject which have pretty much been covered above. The upside for me is an opportunity to fit the course around my life and learn ( relearn). I think KD is correct in that i would expect the majority of the people attending the course want to learn the material. I expect drop outs will be down to two reasons; (1) realisation that time is required and fitting it in, (2) feeling left out when forming a study group(if i am reading some of the posts correctly). I think there is a big learning here about how do people form their study groups when everything is remote and has to happen quicky. It has been fascinating to watch as well as participate.
This is so great and exciting!
I just watched the binary tree video by Vi Hart, I love it! I could spend all day watching videos (I know, we’re supposed to exchange thoughts with real people, will do!)
I must admit that this subject matter is quite new to me, and I really had a hard time answering the first quiz (and I got a real bad result 🙂 because I rushed it. Nevermind, it was a challenge – but even if I fail this course, nothing will happen to me!! 😉
I can feel it is so good for the brain to do some THINKING.
The video lectures with the possibility of stopping the tape are fantastic, because you can go back and forth several times and stop it – cool!
I also like the assignments which are very much language-focused. (I come from the linguistic side).
Congrats on this course, I’m proud to be in!
Best regards from Central Europe,
Andrea
Hi Keith, Unfortunately i have dropped out of your course. Currently registered for 4 on coursera, 1 on EdX & Another on venturelab, so dont think i will have the time to dedicate to this. Hopefully it will be run again, and i can follow along and dedicate enough time.
However, can you comment on Mooc (Video Lectures in particular) format of Coursera/Udacity vs EdX, EdX seems to have a much better interface, however their video seem to be just recordings of lectures given on campus. I prefer The method you use (talking direct to camera), and the use of other aids writing on paper etc. Would love to see an article addressing this.
I’m a student in your MOOC (along with my wife…this should get interesting before we’re done) and enjoying it immensely. I like the handwriting component, and frequently pause the video to digest what you’ve written without the explanation, just as if I said, “Wait a second before you go on” if we were sitting side by side. Good presentation.
I also did not notice the handwriting had been sped up; good touch.
One observation regarding the problem sets: I’m not a fan of the resort of the ‘answers’ on question 8 when saving my answers. I’d rather see the order maintained, so that I know which I have worked through when I come back to the set. I was successful in confusing myself that I had evaluated a statement that I had not, and left it false when I should not have.
Outstanding work, though. I’m really enjoying the course.
I am enjoying the mathematical thinking class and very grateful for the opportunity to learn to think mathematically, while its quite challenging and I am struggling, I love it. Thank You
Hi,Keith I am student in your MOCC. And really be so grateful for a terrific course even know this is my first time taking classes on line I am enjoying learning to think mathematically.
Thanks for this wonderful experience.
The concept of a MOOC is strangely intuitive. It marries what I have found to be the most fertile learning environment (a strange form of compassionate neglect.) Being left to struggle with the ideas I find more difficult allows me to organically invest more time where it is most needed. Having someone with a degree of mastery over the topic provide direction and examples keeps me moving in a straight line while having others struggle alongside me in a common pursuit keeps me motivated.
Having taken many classes in both an online and on campus format (I am currently working on my masters degree in a mostly online setting), I feel this new approach returns the emphasis of education back to the learning and mastery of new ideas. That said, it is my sincere hope that this method would grow and begin to permeate into mainstream learning modes.
Let me speak for many in saying that I appreciate your effort and share in your excitement for this class. Keep going.
Best,
J Sanders
I’m very glad to be taking this course. I’m taking it along side two other courses on the coursera platform. I’m one of many other students enrolled at the Open University of West Africa studying from Ghana.
Most if not all of us registered a little bit late and this presents a challenge of some sorts as we have to play catch up in three different courses, nonetheless we’re working hard, our facilitators are also encouraging.
It’s amazing what the human race is about to achieve with this much quality tuition made available on such a large scale.
I’m hopeful that I will gratefully improve my problem solving capabilities with this course. Thank you very much for this opportunity.
I’m taking this course and loving the experience! It’s hard and one gets insights all the time: while watching the lecture for the first time, then during the quizzes, in the forums, with the second time around the lecture and with the additional readings and recommendations.
Thanks, Keith, for a real learning experience!
Best,
guadalupe
Your enthusiasm and commitment are contagious. Thank you so much for doing this.