Posts Tagged 'Big Data'

Answering the 64,000-Students Questions

A real-time chronicle of a seasoned professor who has just completed giving his first massively open online course.

With the “instructional” part of the course finished and the remaining students working on the Final Exam (it will be peer graded next week), at last I can sit back and take a short breather. The next step will be to debrief and reflect with my two course assistants (both PhD students in the Stanford Graduate School of Education) and decide where to ride the MOOC beast next.

For sure I’ll offer another version of this course next year, with changes based on the huge amounts of data you get with a global online class of 64,000 students. Despite the enormous effort in designing, preparing, and running such a massive enterprise, there are three very good reasons to pursue this.

First, and this I believe is one of the main reasons why Stanford is supporting the development of MOOCs (I am not part of the central, policy-making administration), designing, running, and analyzing the learning outcomes of MOOCs is a tremendous research opportunity that will almost certainly result in new understandings of how people learn, and as a result very likely will enable the university to improve the learning experience of our regular on-campus students. After just five weeks, my two graduate assistants have enough data to write several dissertations, in addition to the one they need to get their doctorates.

Second, there is a huge, overall, feel-good factor for those of us involved, knowing that we can help to provide life-changing opportunities for people around the world who would otherwise have no access to quality higher education. Is what they get as good as being at Stanford? I very much doubt it, though the scientist in me says we should keep an open mind into the eventual outcomes of what is at present a very novel phenomenon. But if you compare a Stanford MOOC with the alternative of nothing at all, then already you have an excellent reason to continue.

Third, and this is something that anyone in education will acknowledge makes up for our earning a much lower salary than our (often less formally qualified) friends in the business and financial worlds, there is the pleasure of hearing first-hand from some of our more satisfied customers. The following is one of many appreciative emails and forum posts I have received as my course came to and end:

Mr. Devlin and all members of the Introduction To Mathematical Thinking team, I just wanted to say Thank You for everything that you have done to share your knowledge and giving your time and great effort to help others learn. I imagine that this is not an easy project to lead and sustain on a continuous basis. However, you have done a wonderful job in relaying your message. Through your efforts, you have helped many people in the process; especially me. Until this class, I hated math. I hated the idea of learning math or thinking in mathematically analogous methods that are applicable to real world situations. I just didn’t get it. I’m still a little confused about why I am able to comprehend your lessons as effectively as I am (which is saying a lot considering how much I hated math) when I have not been able to do so in the past. Now, I find myself looking forward to your classes everyday! I look forward to using what I have learned from the last video lectures or assignments and using those lessons in situations I did not think possible. And now, I love math! Your instruction has helped me to think more logically and to draw more concise conclusions with issues that I am trying to handle. This is indeed a skill. This is also a skill that you can build upon throughout your lifetime if one chooses to do so. Though I may not be at the level of learning that I should be at, I have learned more in the past three weeks than I have learned throughout my life; and I will continue to learn. I am very serious about this statement. So, thank you All. Thank you, Mr. Devlin. Great Job and Cheers!


To be sure, there were trolls on the course discussion forum, for whom nothing we did was right. But one of the benefits of having tens of thousand of students is that within at most an hour of a flame post appearing, tens of others jumped on the offending individual, and within a short while all that was left was a “This comment has been deleted” notice. As the course wore on, the trolls simply dropped away.

Though there was the one individual who, in week four, posted a comment that he hated my teaching style and was learning nothing. Given that this was a free course that no one was under any compulsion to take, and for which no official credential was awarded, one wonders why this person stuck around for so long!

That example provided no more than an amusing anecdote to tell when I start to give talks on “What’s it like to teach 64,000 students?” (Invitations are already coming in.) But there is a somewhat closely related issue that I find far more significant.

Like almost all current MOOCs, there was no real credentialing in my course, so the focus was entirely on learning for its own sake. (As a lifelong math professor, used to teaching classes where many of the students were there because they needed to fulfill a mathematics requirement, having a class of students who were there purely voluntarily added appeal to my giving a MOOC.) To be sure, there were in-lecture quizzes, machine-graded assignments, and a peer evaluated final exam, but the only people who had access to any student’s results were myself, my two course assistants, and the student. Moreover, there was no official certification to back up a good result (the course offered two levels, Completion and Completion with Distinction), and turn it into a form of credential.

Yet many students had an ongoing obsession with their grades, and indeed pleaded with me from time to time to re-grade their work. (Clearly not possible in a 64,000 student MOOC. Besides, I never saw their work. How could I?) As a competitive person myself, I can appreciate the desire to do well. But with literally nothing at stake, I was at first surprised by the degree to which it bothered some of them. When I figured out what was probably going on, I found something that bothered me.

Unlike most MOOCs, mine, being at first-year university level, can be taken by high school students. Indeed, since my primary target audience comprised students entering or about to enter university to study mathematics or a math-related subject, I expected to get high school seniors, and designed my course as much as possible to accommodate them.

I’m guessing that the majority of students who were obsessed with grades were still at high school – indeed, most likely a US high school. That grade obsession I observed is, I suspect, simply a learned behavior that reflects the way our K-12 system turns the learning of a fascinating subject – one of humankind’s most amazing, creative, intellectual achievements – into a seemingly endless sequence of bite-sized pieces that are fed to the student in a mandated hamster-wheel.

No wonder they could not relax and enjoy learning for its own sake. Any natural curiosity and desire to learn – something all humans are born with – had been driven out of them by the very institution that is supposed to encourage and develop that trait. In its place was mere grade hunting.

Do I know this for a fact? No. That’s why I used those hedging words “guess” and “suspect”. But something has to explain that grade obsession in my course, and it certainly brought to mind Paul Lockhart’s wonderful essay A Mathematician’s Lament, which I had the privilege to bring to a wider audience some years ago.

But now I digress. Time to wrap up and check the dashboard on the course website see how many students have submitted the Final Exam so far.

Though this post has dropped the title “MOOC Planning”, I am going to keep posting here, as the project goes forward. Stay tuned.

To be continued …

It’s About Time (in Part): MOOC Planning – Part 10

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

Well, lectures have ended and the course has now switched gears. For those still left in the course (17% of the final enrollment total of 64,045), the next two weeks are focused on trying to make sense of everything they have learned, and working on the final exam — which in the case of my course involves peer evaluation.

Calibrated Peer Review is not new. A study of its use in the high school system by Sadler and Good, published in 2006, has become compulsory reading for those of us planning and giving MOOCs that cover material that cannot be machine graded. [If you want to see how I am using it, just enroll in the class and read the description of the "Peer Review system". There is no obligation to do anything more than browse around the site! No one will know you are not simply a dog that can use a computer.]

As I was working on my course, Coursera was still frantically building out their platform to support peer evaluation. There was a lot of just-in-time construction. It’s been a long time since I’ve had to go behind a user-friendly interface and dig into the underlying code to do something on a computer, and the programming languages have all changed since I last did that.

One thing I had to learn was one of the ways networked computers keep time. I now know that at the time of writing these words, 7:00AM Pacific Daylight Time on October 22, 2012,  exactly 1,350,914,400 seconds have elapsed since the first second of January 1st, 1970, Eastern Standard Time. That was the start of Unix Time.

I needed to learn to work in Unix Time in order to set the various opening times and completion deadlines for the exam process. I expect that by the time the next instructor puts together a MOOC, she or he will be greeted by a nice, friendly Coursera interface with pulldown menus and boxes to tick — which probably will come as a great relief to any humanities professors reading this, who don’t have any programming in their background.

[By coincidence, Unix was the last programming language I had any proficiency in, but I did not need to know Unix to use Unix Time. I just used an online converter. Unix was developed in 1969 at AT&T Bell Laboratories in New Jersey. Hence the 1970 EST baseline.]

In fact, time conversion issues in general turned out to be a  continuing, major headache in a course with students all over the world. One thing we will not do again is have 12:00PM Stanford Time, aka Coursera Time (i.e., PDT), as any of the course deadlines. It might seem a nice clean stopping point, and there are all those memories of Gary Cooper’s deadline in the classic Western movie High Noon, but many students missed the deadline for the first submitted assignment because they thought 12:00PM meant midnight, which in some parts of the world made them a whole day late.

The arbitrary illogicality of the AM/PM distinction is not apparent to those of us who grew up with it. But my course TA and I are now very aware of the problems it can lead to! In future, we’ll stick to unambiguous times that stay away from noon and midnight. But even then, with local computer systems usually working on local time, to say nothing of the different Summer and Winter Times, which change on different dates around the world, timing events in MOOCs is going to remain a problematic issue, just as it is for international travelers and professionals who collaborate globally over Skype and other conferencing services. (When I used the Unix Time conversion app, I had to remember that Unix thinks New Jersey is currently just two hours ahead of California, not the three hours United Airlines uses when it flies me there. Confusing, isn’t it?)

The reason why times are an issue in my course is that it is a course. At first glance, it may look little different from Khan Academy, where there are no time issues at all. But Khan Academy is really just an educational resource. (At least, that’s the part most people are familiar with and use, namely the video library that started it all. People use it as a video version of a textbook — or more precisely a video equivalent to that good old standby Cliffs Notes, which got many of us through an exam in an obligatory subject we were not particularly interested in.)

In contrast, in my case, as I’ve discussed earlier in this blog series (in particular, Part 6), my goal was to take a standard university course (one I’ve given many times over the years, at different universities, including Stanford) and make it available to anyone in the world, for free. To the degree I could make it happen, they would get the same learning experience.

That meant that the main goal would be to build a (short-lived) learning community. The video-recorded lectures and tutorials were simply tools to make that happen and to orchestrate events. Real learning takes place when students work on assignments on their own, when they repeatedly fail to solve a problem, and when they interact (with the professor and with one another) — not when they watch a lecture or read a book.

To achieve that goal, the MOOC would, as I stated in Part 6, involve admissions, lectures, peer interaction, professor interaction, problem-solving, assignments, exams, deadlines, and certification. To use the mnemonic I coined early on in this series, the basic design principle is WYSIWOSG: What You See Is What Our Students Get.

As we go forward, I intend to iterate on the course design, based on the data we collect from the students (and 64,000 students very definitely puts us into the Big Data realm). But my basic principle will remain that of offering a course, not the provision of a video library. And the reason for that should be obvious to anyone who has been following this blog series, as well as some of the posts on my other blogs Devlin’s Angle and The focus is not on acquiring facts or mastering basic skills, but on learning to think a certain way (in my case, like a professional mathematician). And that requires both a lot of effort and (for most of us) a lot of interaction with others trying to achieve the same goal.

Our ancestors in the 11th Century started to develop what to this day remains the best way we know to achieve this at scale: the university, where people become members of a learning community in which learning takes place in a hothouse atmosphere that involves periods of intense interaction as deadlines loom, sustained by the rapidly formed social bonds that emerge as a result of that same pressure.

While I will likely experiment with variants of this model that allow for participation by students who have demanding, full-time jobs, I doubt I will abandon that basic model. It has lasted for a thousand years for a good reason. It works.

To be continued …

The Crucible: MOOC Planning – Part 8

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 …

The “C” in “MOOC”: MOOC planning – Part 6

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

A few days ago, I went into our campus TV studio with the two course assistants for my upcoming MOOC, to record a short video introducing them to the students.  The students will see a lot of me, but my two TAs will be working behind the scenes, and the students will encounter them only through their contributions to the forum discussions. The videos were intended to compensate for that lack of human contact.

During the course of recording that video, the three of us got into a discussion about our backgrounds, our motives in giving the MOOC, and our views on mathematics, science, education, and our expectations for the MOOC format. The camera was rolling all the time, and we were able to select a few parts of that discussion and create a second video that I think will help our students understand some of our thinking in putting this course together.  I posted copies of both videos on YouTube.  (They are much lower resolution than the videos the registered students will see on the course website when it goes live on September 17 — the “first day of classes”.) I think the two videos provide an insight into our thinking as we designed this course.

The fact that the current round of MOOCs have a “first day of class” at all has been a matter of some debate. The C in MOOC stands for “course”, but is this the best way to go?  For example, see this blogpost from a graduate student at Berkeley, who argues for a more open framework of learning resources. He makes some good points that all of us involved in this initiative have thought about and discussed, but I’m not sure the kind of thing he advocates can work for disciplines and subjects that depend heavily on student-faculty and student-student interaction, as mine does.

In fact, I’m not sure the MOOC will work sufficiently well at all in such cases; this is very much an experiment that I anticipate will continue for several years before we get good answers either way. For the first iteration, it makes sense to start with a model we know does work. And important (we think!) elements of that model are, to repeat Sebastian Thrun’s list, as quoted in the Berkeley student’s blog: admissions, lectures, peer interaction, professor interaction, problem-solving, assignments, exams, deadlines, and certification. To use the mnemonic I coined earlier in this series, our basic design principle is WYSIWOSG: What You See Is What Our Students Get.

Since these courses are free, we can, of course, do a lot of A/B testing in future years, to see which of these truly are crucial, which can be changed and how, and which can be dropped. I suspect the answers we get will vary from discipline to discipline, and possibly from course to course.

All of us involved in this MOOC movement are trying to find out the best way that works for our particular discipline and is consistent with our own style as instructors. As I indicated in Part 4 of this diary, I think it makes sense to begin by trying to implement in a MOOC as much of our tried-and-trusted classroom-based teaching as we can (as Thrun did with Udacity), and then iterating in the light of what we learn.

This is why, instead of hiring a mathematics graduate student to TA my course, which is what I would have done for an on campus class, I brought onto my team two graduate students from Stanford’s School of Education with several years of experience in learning design and the use of technology in education. In addition to helping me with the design and running of the course, they will conduct research into the course’s efficacy and try to understand how learning occurs in a MOOC. (Other than a brief, non-compulsory questionnaire at the start and finish of the course, all their research will be based on data gathered on the Coursera course platform and human monitoring of the forum discussions. One huge benefit of MOOCs is that they facilitate Big Data research.)

It’s live beta, folks.

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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