Posts Tagged 'Daphne Koller'

MathThink MOOC v4 – Part 9

In Part 9, I admit that my interest in MOOCs is driven by a very Selfish Gene.

Why do I devote so much (unpaid) time working on my MOOC? And it is, to be sure, a lot of time, little of it factored in to my official Stanford workload.

According to least one very good, and highly respected (by me no less than many others) educational writer, it is the prospect of fame, as she recently tweeted thus.

WojcickiTweet

I suppose there may be a professor or two somewhere who sees MOOCs as a pathway to fame, but if so, they should definitely take my Mathematical Thinking MOOC to develop good numerical sense. A globally distributed, ten week class of maybe 40,000 students, half of whom will watch at most one video and many of whom would not be able to tell you the name of their MOOC instructor if you asked them (the same is true for regular, physical classes, by the way), is hardly fame.

Fame is epitomized by @KimKardashian, with almost 20 million Twitter followers. If that’s your goal, devoting many years of your life to get a PhD ain’t the optimal path!

What academics tend to seek is peer recognition. And, believe me, giving a MOOC will, if anything, reduce the status of any scholar within the Academy, possibly to an even greater extent than writing books and magazine articles “for the general reader”. (I’ve done both. As an academic, I was doomed long ago.)

The danger of stepping outside the walls of Academia has been recognized ever since The National Academy of Sciences denied entry to Carl Sagan. As a recipient of the Carl Sagan Award for Science Popularization, I am thus doubly doomed.

No wonder I felt I had nothing to lose by jumping onto the MOOC bandwagon – though at the time I started work on my first MOOC it was not so much a bandwagon as a small Stanford wheelbarrow, yet to be discovered by  New York Times columnist Thomas Friedman. (He soon made up for missing the start. Just google “Thomas Friedman MOOC” and you will uncover a host of Massively Over-hyped Outrageous Claims.)

Why do academics give MOOCs? While I surely cannot speak for all MOOC instructors, I can probably speak for the many I have talked with, and by and large they all give the same answer. It comes in two parts.

The first part is educational research. (This is the reason why Stanford, my university, provides some – very modest – support for MOOC development.) The process of designing and giving a MOOC provides a wonderful opportunity for an instructor to find ways to improve their teaching craft, and provides educational researchers with massive amounts of data to help us better understand the learning process. For just one illustration of this, check out this article from a MOOC instructor at Vanderbilt University.

ChrisChristie

New Jersey governor Chris Christie showing his opinion of teachers

The second part is the same answer you will get if you ask someone why they went into K-12 teaching, a profession that not only pays poorly, but ranks so low in the US psyche that a savvy State governor contemplating a run for President will regard you as fair media game for a finger-wagging, photo-opp tongue-lashing:

Teachers are not seeking fame, or wealth. They do it because they have this deep-seated urge to change lives by teaching.

When I joined the tiny band of Stanford faculty who were designing the first wave of MOOCs, our motto was “Let’s Teach the World”, a slogan that I took for the subtitle to this blog. This is what it is about.

It wasn’t a desire to be famous that we found attractive. Heavens, if you are at Stanford, you probably already have all the academic “fame” you could ever want. Rather, the hook was an opportunity to take something we had been providing regularly to a privileged few and make it available to anyone in the world who had access to the Internet.

It was, in short, an idealistic dream. How to operationalize that dream was another question, and there were at least as many approaches as MOOC instructors.

The Stanford-MOOC-pioneering computer science professors Thrun, Koller, and Ng set their initial sights on large numbers of students around the world being able to take CS courses, 100,000 or more (maybe a lot more) at a time.

Recognizing that (introductory-level) computer science is almost certainly a special case – because it is suited to instruction-based learning and a lot of what is being taught is, by its very nature, machine gradable – instructors in other disciplines set different expectations for their courses.

In my case, I had two clear teaching goals in mind, one very much focused on “the world”, the other “egalitarian elitist”.

As a mathematician who has devoted a lot of my career to community outreach, through public talks, newspapers, general-audience books, magazines, radio, television, movies (occasionally), blogs, and podcasts, I saw MOOCs as yet another medium to “spread the gospel of mathematics”, moreover a medium that offered the possibility of taking my audience a lot further down the mathematical path than any of those other media.

Broadly speaking, the first six weeks of my Mathematical Thinking MOOC attempt to cater to that general audience. I very definitely want to capture and sustain the interest of as many individuals as possible. Massive (the M of MOOC) is the goal. My focus is not so much on getting my students to learn mathematics – there is precious little of it in those first six weeks – but to raise their awareness of the nature and power of mathematics, and to help them come to realize that they actually do have a (creative) mathematical mind, it just needs to be unlocked from the panic-inducing prison that traditional K-12 math education so often drives it into.

[Time for another Ken Robinson video. This one is a doozy. It's the one that made him world famous - unlike MOOCs, TED talks can make you famous. For the evidence that what Sir Ken says applies to mathematics, see my own book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip.]

In the final weeks of my MOOC, I slowly shift attention to my second audience. That audience is a lot smaller. I am looking for people who, in certain key ways, are very much like I was as a teenager.

Hull

Alexander Dock in the 1950s, about half a mile from my childhood home

Growing up in a working class family in post-Second-World-War England, in the grimy, Northern industrial city and port of Hull, with no ready access to quality education (let alone higher education), and no role models for learning in my family or my neighborhood, my innate talent for mathematics would likely have gone forever un-realized.

(Through to my early teens, my school teachers advised me to focus on writing, since they felt I had no mathematical abilities, as evidenced by the fact that I was always the last person to master each technique, and kept asking pesky “What?” and “Why?” questions when “everyone knew” that doing math was all about “How”. “Our’s not to reason why, just invert and multiply.”)

Fortunately, at high school I encountered a math teacher who recognized something else in me, and pulled me out of his regular math class to teach myself, with his occasional guidance, from his own college textbooks.

I also started to pore through every available “popular mathematics book.” (There weren’t many back then, but most were available as cheap paperbacks.)

That got me started on a rewarding and fulfilling mathematical journey I have been following ever since.

I am certainly not unique in having stumbled my way into mathematics through chance. For most of my professional career I have been surrounded by people who are a lot better mathematicians than me, and a lot more accomplished, and many of them can tell similar “humble origins” stories. But they come from all around the world. Not many of them, if any, come from where I grew up. Similar places, but not the same place. (It’s a density issue.)

In fact, I was surprised to discover a few years ago that the official listing of “Famous People of Hull” includes just two mathematicians, John Venn (of Venn diagram fame) and yours truly.

That may or may not be a comprehensive listing (I never knew John Venn was from Hull until I saw that entry), but it does suggest that you may have to extend access to quality mathematical learning to populations in the hundreds of thousands (Hull’s population was about 300,000 when I was growing up there, it’s considerably less today), in order to connect with just one or two who have talent.

I want to do just that. Citizen Devlin wants to provide mathematical outreach to millions around the world. Keith Devlin the grown-up kid from Hull, wants to reach those few individuals who have talent for mathematics but neither learning role models nor access to good education, and provide an educational opportunity analogous to the one that changed my life.

If the “Famous People of Hull” data is even remotely correct, I need to reach many hundreds of thousands, and perhaps millions, around the world, to stand any chance of connecting to those talented few who currently do not have a seat at the educational table.

(It’s probably not an issue of raw talent density. I am sure there are many people will significant mathematical ability in every part of the world. Rather the challenge is the density of talented individuals you are able to connect with, and as a result recognize and bring out their talent.)

Large dropout rates in MOOCs? Though I work hard to try to keep everyone in my course for the first half, and put considerable effort into keeping as many as possible through to the end of the Basic Course (see earlier posts), as far as my second motivator is concerned, those dropout rates are not a problem at all. They are part of the filtering process.

I’m looking for “me” – that talented young person with no access, and probably no hope – to give them a similar opportunity to the one that chance brought my way all those years ago.

MOOCs have given me that dream.

In each of the three iterations of my MOOC I have given, I have seen a small number of students who I think may be such individuals. They are the ones for whom I have made an exception to my (obviously essential) rule of not communicating individually to MOOC students. That’s reason enough to continue.

In other words, my involvement in MOOCs is in large part driven by my own educational Selfish Gene. Not to replicate me, but to replicate what happened to me. Now you know.

Liftoff: MOOC planning – Part 7

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.

Let’s teach the world

This coming October, I’ll be offering my first MOOC — massive(ly) open online course — one of a growing number of such offerings that have started to emerge from some leading US universities over the past few months. In this blog, I’ll chronicle my experience as it happens, and hopefully get useful feedback from others. This introductory post is a shortened version of my May 1 blogpost on Devlin’s Angle for the MAA.

Higher education as we know it just ended. Exactly what will take its place is not at all clear. All that can be said with certainty is that within a few short years the higher education landscape will look very different.

That is not to say that existing colleges and universities will suddenly go away, or indeed change what they do – though I think both will occur to varying degrees in due course. What is changing now is what classifies as higher education, who provides it, how they provide it, who will have access to it, how they will obtain it, and how it will be funded. Distance education, for many years the largely-ignored stepchild of the higher education system, is about to come of age.

This is not just my opinion. My own university, Stanford, recognizes what is going on, and is taking significant steps to lead and stay on top of the change, and a number of Silicon Valley’s famed venture capital firms, who make their fortunes by betting right on the future, have sunk significant funding into what they think may be key players in the new, higher ed world.

Last fall, Stanford computer science professor Sebastian Thrun used the Internet to open his on campus course in artificial intelligence to anyone in the world with Net access, and 160,000 students from 190 countries signed up. Some 22,000 of those students finished the course, receiving “certificates of completion” signed by Thrun (and co-teacher Peter Norvig of Google), but no Stanford credit. (For that, a student has to be on campus and officially registered; annual tuition is $40,050 and entry is fiercely competitive.)

Demonstrating the entrepreneurial spirit that Stanford faculty are famous for, Thrun promptly left Stanford to found a for-profit online university, Udacity. With Udacity receiving financial backing from a large Venture Capital firm, the MOOC – massive open online course – suddenly came of age. A short while later, two more Stanford computer science faculty, Andrew Ng and Daphne Koller, secured $16M of venture capital funding to launch a second Stanford spin-off company, Coursera, a Web platform to distribute a broad array of interactive courses in the humanities, social sciences, physical sciences, and engineering.

Initial courses offered on Coursera include, in addition to several from Stanford, offerings from faculty at the University of Michigan, the University of Pennsylvania, and Princeton. Stanford president John Hennessy appointed a blue-ribbon panel of Stanford faculty to develop a strategy for developing, and delivering, online courses. For free. To the world.

Not wanting to be left behind, just this week, MIT and Harvard announced the launch of edX, a joint effort to mount their own MOOC distribution platform, with each institution committing $30M to the project.

Yes, you read that correctly. The faculty, the universities, and the new platforms are making the courses available for free. All the funding is coming – for now – from for-profit investors and the private universities themselves. Why are they doing that? If you have to ask the question, you don’t really understand the Internet and how it changes everything. Think Napster and the music industry or Skype and the telephone industry. Like the settling of the American territories in the nineteenth century, the initial focus is on establishing a presence in the new land; monetization can come later – almost certainly in ways very different from today’s.

Computer-assisted, distance learning is not new, of course. Stanford was one of the universities that pioneered it the 1960s; many universities have for several decades offered adult professional education courses for a fee, largely to raise funds; and there are the for-profit online schools like the University of Phoenix. More recently, led by MIT, a number of universities started making recordings of their regular courses, together with course materials, available online for free. So what has changed now?

The answer is the platform and the target audience’s experience and expectations have changed. What has been missing so far is the active participation of the distant student in a learning community. Building on technology developed at Stanford to support flipped classroom experiences for its regular students, Udacity and Coursera have secured the major investments required to build scalable, robust platforms that can take the small learning seminar and create a similar experience across the Internet.

A generation that has grown up on the Web has taken to the new online learning medium like fish to water. For instance, during the term when Thrun made his AI course available online, most of the Stanford students enrolled in his class stopped attending his lectures and took their information delivery online, at times convenient to them. But the convenience of Stanford students is not what the MOOC initiative is about. What excites me and my colleagues is the possibility to reach millions who currently have no access to any university at all.

Welcome to the age of the MOOC.



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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