Can we make constructive use of machine-graded, multiple-choice questions in university mathematics education?

A good metaphor for the current state of MOOC education is provided by this historical video. But when you look at those images, please remember what those events led to. Unless you are able to keep that history in mind, you should not at this stage get into the MOOC business. For there be only dragons.

With the second edition of my Stanford MOOC Introduction to Mathematical Thinking starting this weekend on Coursera, I have once again been wrestling with the question of the degree to which good, effective mathematics learning can be achieved at scale, over the Internet.

Once I had made the decision to try to take (elements of) my 35-year-old mathematics transition course into the then emerging MOOC format—less than a year ago!—I was immediately brought face-to-face with the necessity of making use of two educational devices I had loathed (and never used) throughout my entire career in higher education:

1. machine-graded pop quizzes
2. machine-graded multiple-choice questions

For MAA readers, I don’t think I need to explain my dislike for either of these über-simplistic devices, which can surely be justified in a regular classroom only in terms of making life easier for the instructor.

Simply putting a class online does not require the use of either device, of course. Technologies such as video conferencing and screen sharing can make learning at a distance almost as good as traditional classroom learning, and in some circumstances can make it better in some respects. But making a class available to tens of thousands of students online changes everything. With such large numbers, the “class” dynamics change dramatically. But it’s not all for the worse.

The first thing to realize is that a MOOC is in many ways like radio or TV. Though both of those familiar features of modern life are referred to as “mass media,” they are in fact highly individual. The newsreader on radio or TV is not addressing a large audience; she or he is talking to millions of single individuals. The secret to being good on the radio or TV is to forget the millions and think of just one (generic) person. After all, the listener or viewer is not in a room with millions of other people; in fact, if the broadcast is successful, that listener or viewer is cognitively in a room with just the presenter. The really successful radio and TV newsreaders and presenters are the ones who can do that really well. They create that sense that they are talking just to You.

In my own case, I already knew that from many years of occasional media work, but I think all MOOC instructors come to that realization very quickly. When your voice, with or without your face, is in someone’s living room, there is a direct human connection that in important ways is far more intimate than is possible in a lecture hall filled with anything more than a handful of students.

Once you realize this feature of the MOOC medium, the underlying pedagogic model is obvious. It’s one-on-one teaching/learning—something that in the traditional academy is (of necessity) reserved only for doctoral students.

At which point, the appropriate use of both pop quizzes and multiple-choice questions starts to look feasible. (They ought to; doctoral advisers use both extensively, and to great positive effect, though they do not refer to them as such, and there is no machine-grading!)

Of course, in a MOOC it remains the case that the student cannot communicate directly with the professor, nor can the professor see and comment on an individual student’s work. That means two further techniques have to be used as well:

3. peer tutoring
4. peer evaluation 

In the first version of my MOOC, last September, I built the course around the doctoral-student education model, deliberately setting out to create the experience of a student sitting alongside me at my desk. (There is a low resolution example here.)

But as a result of a career-long dislike of the first two and a deep suspicion of the fourth, I used all but the third of those auxiliary devices reluctantly and as little as possible. (The one I did embrace, peer tutoring, did not work well the way I set it up. See below for details of Attempt Two.)

Because of my caution, I think I avoided a fate reminiscent of NASA’s first attempts to launch a rocket into space. But that was a first, exploratory experience, and I wanted to live to try again. This time around, based on what I learned, I am going to use all four much more aggressively, but in ways I think might work.

I’ll be describing how I’ll be using them in a series of posts to my blog MOOCtalk.org. For a brief—and decidedly limited—foretaste, check out this video excerpt of a conversation my MOOC TA Paul Franz and I had recently with radio and TV personality Angie Coiro, host of the syndicated radio and television interview show In Deep.

The goal of Version 2 of the course is not to reach the Moon. Chances are high that we’ll crash and burn. The goal is to at least get off the ground before we do, and, if we are lucky, maybe even reach the upper atmosphere. For sure, there will still be a long way to go.

If you want to live dangerously and be part of this huge experiment, and if you have a Ph.D. (or pending Ph.D.) in mathematics and several years of college teaching behind you, I am still looking for well qualified volunteers to act as “Community TAs” for the course, to answer students' questions on the course discussion forums. So far I have 14 volunteers, comprising 5 college professors, 3 Ph.D. students, 3 individuals currently working in the software industry, a K-12 education consultant, a research laboratory scientist, and a stock analyst. If you want to volunteer, and have the requisite experience, please drop me an email at devlin@stanford.edu. (There is no payment for doing this—that includes me!) But being part of a large and truly global community, who come together for several weeks for the sole purpose of learning how to think mathematically (the course carries no college credit), is truly a wonderful experience.

The future of textbook publishing is us

In my May column, I announced my intention to give a free online course (a MOOC) this coming fall, and asked for assistance from the mathematical community.

That course, a school-to-university transition course, titled Introduction to Mathematical Thinking, is going ahead, with the first lecture on September 17. There is a brief description of the course, together with a short promotional video, on the Coursera website.

I have started a blog, MOOCtalk.org, to chronicle my experiences working with this new format and to provide a platform for feedback and discussion once the course gets going.

I also wrote a short textbook to accompany the course, Introduction to Mathematical Thinking. Though the textbook is not required for the course, some of my Stanford colleagues who gave the first generation of “Ivy League MOOCs” – just a few months ago, so fast has this new movement taken off – told me that many students want an old-fashioned physical book. On the other hand, all the transition textbooks I am familiar with are fairly pricey, which would put them well beyond many of the students who are likely to enroll. Moreover, none of them are designed to accompany a MOOC. So I decided to write one.

My two main criteria were: it had to be short (no more than 100 pages) and cheap (less than $10 in the US). The only option was to self-publish in print-on-demand format with Amazon’s CreateSpace service. I did not quite hit my page-limit; when I include the front material, the tally comes out at 102 pages, but that’s close enough. But I figured I’d cover my costs if I set the retail price at $9.99, just below my target.

The procedure is so ridiculously straightforward, I can see no reason why anyone should ever publish another textbook a different way, given the huge expense of textbooks. We authors have been typesetting our own manuscripts ever since Don Knuth first released TeX in 1978, and all that is required to produce a book with CreateSpace is to generate a PDF file that fits the page-size you select.

CreateSpace does not provide TeX support (by way of a style file), but they do provide sample pages for authors submitting manuscripts in Word, and I just played around with the page parameters in LaTeX until the output matched their samples for both odd and even numbered pages, which I checked by printing out copies of both, putting my output on top of theirs, and holding the two up to the light. (Low tech, but effective.)

In my case, I decided to produce my book in the standard 6 in x 9 in format, and the key LaTeX parameters I came up with are (for the record)
\oddsidemargin 1 in \evensidemargin .55 in
\marginparwidth .75in \marginparsep 7pt
\topmargin -.5in \headheight 12pt
\headsep .25in \footheight 12pt \footskip .35in
\textheight 7.5in \textwidth 4.95 in

When I submitted my final PDF file, CreateSpace’s automated checking system flagged the manuscript as possibly not being correctly formatted, but I pressed forward, since the next stage is that one of their employees examines the manuscript, and indeed that individual accepted it, confirming my suspicion that I was probably off by a millimeter or two, something that could upset an automated checking system but is close enough to pass a human eyeball test.

The point is, the whole process is so well designed, there is no reason why anyone who can use LaTeX should do anything other than self-publish from now on. With a very small number of exceptions, no one who writes a university-level textbook does so to make money. Our goal is to get material in front of students as quickly and cheaply as possible. If there were a way to do so that can save the students money, I am sure we would all want to do so, the more so given the way textbook costs have skyrocketed in recent years. With modern print-on-demand technology, we now can do just that.

You don’t need to know anything about publishing to do this. CreateSpace does for book publishing what TurboTax did for filing your tax return, and it does it in much the same way, by taking you through the entire process in a simple, step-by-step fashion, including cover design, securing an ISBN code, and selecting marketing channels.

For sure, the finished product is not quite as good as would be achieved with the professional expertise of a good publishing house. But to my mind, for a textbook, it’s close enough, especially when the resulting book can be sold for as little as a tenth the price a publisher would charge.

The one thing I paid someone else to do was copy-editing. I have written enough books to value highly the services of an experienced copy editor. (You might also want to pay an indexer. I did my own, but I have done so for several of my previous books.)

Of course, even with good copy editing, occasional errors creep through. Not long after my book was on the market, I was looking through one of my author’s copies (you have to buy them, but at an even lower price than the retail mark), and spotted a couple of small typos. A few minutes editing the LaTeX file, followed by a quick upload of the replacement PDF, and the correction was made, ready for the next person to buy a copy.

Returning to the MOOC now, let me re-iterate the request I made in my May column. I am giving my MOOC in the early fall to coincide with the many transition courses offered at colleges and universities across the US, in the hope that instructors of such courses will incorporate my MOOC in their courses in some way. My reason for this is that I think the only way to make a transition course MOOC work is to have enough participants who either are already familiar with the material (such as instructors) or else have direct access to such expertise (e.g., their students in a transition course). I see no other way for students struggling to understand the material to get the help, advice, and feedback they will need to progress. Social media provides various platforms for students to interact, to ask questions of one another and to comment on others’ work. But there has to be a mechanism for mathematical truth to find its way into the discussions!

So the key to making something like this work is, I think, to build up a Wikipedia- like community of instructors who, for five weeks each year, will make available their expertise to the thousands of students around the world who are taking advantage of a MOOC to obtain an education they would otherwise not have access to.

The benefit to the students in the transition classes given by MOOC-participating instructors is that their learning will assuredly be enhanced by acting as tutors for the students who are not so privileged. Both because teaching others is a powerful way to learn – as most of us discover when we become TAs at graduate school – and because those students will surely feel much more incentivized to understand by playing such a feel-good role.

Stay tuned to my MOOCtalk blog for updates on the project. And if you are an instructor giving a transition course this fall, please consider getting involved.

“Can’t we all get along?”

Unless you follow several mathematics education blogs or subscribe to certain Twitter feeds, you may well have missed the recent revival of the US Math Wars. The protagonists in the latest salvo are not the traditional foes, Mathematically Correct versus NCTM and MAA, but two groups who are making use of new technology in education, with Khan Academy squaring up against a number of web-savvy, younger mathematics and science educators who believe the US can and should do a lot better (and differently) in math ed than we do.

I summarized some of my own views on KA in an article in The Huffington Post on March 20 of this year, but this article focuses on another issue than the one I discussed there. Namely, the large numbers of fanatical supporters Khan has gathered, who respond to even the mildest and well meaning criticisms of anything Khan with venom, hatred, and personal attacks.

The first round of this new skirmish I was aware of (likely not the first to occur, since I check in only occasionally on developments in K-12 mathematics education, though now the excellent EdSurge provides me more useful news than I can possibly keep up with) was in February of this year when Mathalicious founder Karim Kai Ani posted a critique of KA pedagogy on his company blog. (Disclosure: I knew that posting was coming up, since Karim emailed me beforehand with questions about gamification and individually prescribed instruction, both of which he wanted to discuss in his article. I also voluntarily endorse his educational materials.)

The KA–Mathalicious deluge began within a few hours of the blog being published, with a lot of the venom unleashed on Y-Combinator’s Hacker News. From the nature of many of the comments, which were personal, and often visceral attacks on Ani rather than reasoned responses to what was a very well thought out and cogently presented argument, it’s a reasonable assumption that they were contributed by schoolkids. Which to my mind makes this phenomenon worth thinking about. For schoolchildren are what K-12 education is about. When a substantial number of our main customers speak, we should listen, even if the method by which the message is delivered leaves a lot to be desired.

Actually, I don’t know what percentage of the K-12 population is represented in those Hacker News (and other) blog posts, but what we do know is that Khan Academy has a large and devoted following. In some ways, I too am a fan of sorts, though less so than when I participated in a TV discussion with Sal back in 2010. For sure, I am dismayed by the huge number of mathematical errors and pedagogic shortcomings in his videos. (We’ve learned a lot about mathematics education in the past fifty years.) In the early days it was easy to overlook them – any new enterprise is buggy, particularly a one-person show like the early KA. But once the Silicon Valley millions started to roll in, and with those funds a staff, it would have been an easy Web exercise to crowdsource curriculum improvement/development to the many mathematics teachers and university mathematics education specialists who would surely have been eager to help.

My enthusiasm came not from the KA site’s contents, but from something else I saw: Sal Khan himself. Up close – and I have met him a few times – he comes across as a really nice, approachable guy with a great sense of humor. Well, so do a lot of people. But there is something else. Sal has the ability to project that identity and that personality over the Web, using just his voice and the trace of a digital pen on a tablet. In the Age of Social Media, that, it seemed to me, was powerful. And, at least to date, extremely rare.

Effective teaching is a human-to-human activity. Good teachers strive to achieve a connection with our students in the classroom. (I say “our students,” since I like to think I am a good teacher, albeit not at the K-12 level.) I’m told my voice conveys my enthusiasm for mathematics when I go on NPR as the Math Guy. If true, and some people seem to think so, then I can’t really take credit for it. I just speak into a microphone. No training, no rehearsing. Just me.

Sal Khan has that natural ability in spades. As he tells us (all Silicon Valley enterprises have a creation story, and in his case it’s true), Khan Academy began as his attempt to help his younger cousins with their math homework, by posting video tutorials on YouTube. He did not set out to build an education empire. People outside his family simply came across his videos on the Web and found them useful.

From a pedagogic perspective, his videos do not provide student learning, they deliver instruction – a distinction I discussed in my March Devlin’s Angle. It would be easy for me to critique them, and many have. (Read on.) But to me at least, providing learning is not where their real value lies.

Learning mathematics is hard. Very hard. It is easy to get discouraged and give up. Some of us, when we are learning math the first time, are lucky enough to have a parent, grandparent, uncle or aunt, older sibling, or family friend who can sit down alongside us and help us. I suspect that a great many of today’s professional mathematicians owe their eventual success in the subject to someone who mentored them in the early days.

But not everyone has such a person in their lives. At least, they did not until Sal Khan came along: friendly, non-threatening, patient, and a good explainer (actually not brilliant, but that might be all to the good, since a brilliant instructor could easily discourage a less-brilliant student). Above all, human. A regular guy. Just think about that for a moment. It’s a valuable weapon in the educational landscape.

Much of the attraction of KA came from its very amateurish nature. It really was just Sal Khan in his converted closet. Sure he did not really understand (as a mathematician does) a lot of the math he explains (though he knows an awful lot more than most people), nor was he trained in mathematics pedagogy. (Ditto for me, BTW – on both counts! – though I think I know more about both than Sal, which makes it possible for me to critique many of his lessons.) But that was a huge part of what made KA so popular. Millions of people around the world, young and old, whose experiences of math class was or had been awful, saw him as on their side. He was everyone’s friendly, helpful Uncle Sal. (I hope this does not come across as a hagiography. I have a lot of issues with KA. But I am trying to understand what leads to KA having such a passionately supportive fan base. I think there is something for us all to learn here.)

For millions of users of KA, what they find on the site is far better than anything they have had or are getting. For them, it’s not just a homework helper, it’s a lifeline. Their only lifeline.

Sure, they probably don’t really learn any mathematics. (I have yet to be convinced you can really learn mathematics over the Web, though that does not stop me wanting to try, as indicated by my other blog MOOCtalk.) The fact is, many people actually don’t want to learn mathematics, they want to pass a math exam. And if Sal Khan helps them do that – and millions say that he has done exactly that – then is it surprising they become KA fans? (And educational establishment enemies!)

Then Bill Gates comes along, and KA goes global. Expectations change. Now things have gotten more tricky. When a resource like KA becomes the primary vehicle by which millions of people acquire many or all of their mathematical skills, the stakes become dramatically higher than when it was a one-man homework-help service. Like it or not, ask for it or not, KA now has (in my view) an obligation to get things right. Doing so without destroying a major part of its appeal, is clearly going to be tricky.

Which brings me to the more recent skirmishes.

On June 18, two math professors, John Golden and David Coffey, posted to YouTube a parody of Mystery Science Theater 3000, which they called MTT2K, in which they watched and critiqued a KA video (an old one, as it happens) about multiplying and dividing negative numbers. To my mind, the target of their theatrical sarcasm was not KA, rather the reverence that many seem to have for KA, but many Khan fans (perhaps the reverent ones) seem to have reacted differently.

In any event, KA immediately took down the video, replacing it with two new videos, one on Multiplying Positive and Negative Numbers, the other on Dividing Positive and Negative Numbers. The two new videos appear to have been made in direct response to the MTT2K critique. A short while later, Khan released another new video, Why a Negative Times a Negative is a Positive, providing further elaboration.

Unfortunately, as John Jay High School (New York) physics teacher Frank Noschese noted, that third video was awfully similar to one produced some years earler by James Tanton. Things were escalating (or spiraling down, depending on your favored metaphor).

The pity was that critiques by knowledgeable teachers and pedagogy experts resulting in modifications to KA instructional materials is surely the way to take something that has value and make it even more valuable. But that tended to get lost in the MTT2K-parody sarcasm and the barrage of name calling that followed.

Incidentally, Noschese is a 2011

Presidential Award for Excellence in Math and Science Teaching awardee, and the author of an excellent science education blog Action-Reaction. He has commented and tweeted extensively (and to my mind constructively) on KA. I hope KA follows his blog and takes note of what he says.

Another experienced STEM teacher with excellent suggestions (for KA and for teaching in general)  is Dan Meyer, a former Google Education Fellow and now a PhD student in education at Stanford. He joined in the MTT2K exchange in his usually witty fashion in two blogposts, Bill Gates Just Put Out a Hit on John Golden and David Coffey, on June 20 and Sal Khan Comments On MTT2K In Chronicle of Higher Education, on June 28.

The latter was about an article in the Chronicle of Higher Education that day, summarizing the MTT2K affair. The Chronicle article was inspired in part by the article by Justin Reich in Education Week on June 22 about the “MTT2K Prize”, a cash prize to be awarded for the best video commentary on a Khan Academy video. (Actually it’s a great idea, if it can be done collaboratively with KA, absent any negativity.)

The final episode in this skirmish (at least so far, based on what I have seen) was an entry video to the MTT2K Prize competition on June 29, by Wired blogger Rhett Allain, an Associate Professor of Physics at Southeastern Louisiana University.

To my mind, Allain’s blog description is better than his videoed critique. Allain just does not come across on video as well as Khan does. Many teachers, and most academics, spend a lot of their time critiquing one another. We get used to it. It’s how we learn and improve. But when you put it on YouTube, it is viewed by millions of people totally unfamiliar with the process, and they can – and, in the cases I am citing, did – react negatively.

Which brings me back to my starting point. Education is hard, mathematics education particularly so. It takes a lot of different kinds of knowledge and expertise to get it right. The focal point is – and I think has to be – a single person, a teacher. Either in the flesh or over the Web. That teacher has to be able to connect to the students. Being a great classroom teacher does not make someone good at doing it on YouTube. In fact, most teachers come across pretty badly on video. But that does not matter if the people who are able to use the medium will listen to what they say.

Sal Khan’s strength is that he comes across extremely well on video (with or without his face on screen!). I just wish he would work (with real experts) on the content more.

But the real problem is not the stuff on the KA site. Flawed as it is, it is, as I noted earlier, a lot better than many people have, or ever had, access to. The fact that many of Khan’s fans describe him as “the best teacher ever” speaks volumes about the poor quality of the mathematics education that many receive. I’ve visited many math classrooms both in this country and around the world, and I’ve seen great math teaching. You won’t find it on KA. Instead, you will find something else, something unique and of value.

Sure, KA has lots of weaknesses and could be improved. That goes for any product. The real problem is that the US (and other nations) identify mathematics learning with instruction and passing procedural tests. In that world, KA meets a clear market need for instruction to help people pass procedural math tests.

In contrast, Ani, Noschese, Golden, Coffey, Meyer, Allain, and all the other KA critics in the educational world are interested in facilitating something quite different: real learning among their students.

Sal Khan says he is trying to move into the real, conceptual learning space as well, but so far I have not seen much that would qualify, and as I noted earlier, my own interest in trying out the MOOC format notwithstanding, I have yet to be convinced that it is possible over the Web.

Khan has something of real value to offer, most uniquely his ability to do well both locally and at a distance what many teachers find hard or impossible even in the classroom, namely connect with and inspire students. But he seems not to have deep conceptual understanding of mathematics or knowledge of the highly complex field of mathematics learning, and given his background it would be strange if he did. (For a good, reasoned series of articles pointing out the problems with KA, see the 2011 articles by Sylvia Martinez of Generation YES.)

On the other side, there are many teachers and education researchers who do have knowledge of mathematics and mathematical pedagogy, but are not able to connect well, at least on video, where they come across as cold or impersonal or condescending – video is a harsh medium.

If each party recognized that the others had something of value to offer, and if  we could get beyond the squabbles and the name-calling, we could produce something that benefits the people we all care about: the students.

Los Angeles police brutality victim Rodney King died recently. The words he famously uttered during the riots that followed his beating in 1992 seem equally pertinent to the current state of affairs regarding KA: “Can't we all get along?”

Math MOOC – Coming this fall. Let’s Teach the World.

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.

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 medium like fish to water. 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.

Is this the beginning of the end of physical universities? I doubt it. Though online courses are excellent for in-career professional learning, the absence of being a member of a physical community makes them a poor substitute – arguably no substitute – for a traditional college or university when it comes to providing first-pass education. But what about the millions (make that billions) in the world who do not have access to a university education? “Let’s teach the world” is a buzz phrase you hear increasingly among the Stanford faculty these days. And Stanford is putting resources into making this attractive dream a reality.

What makes it fascinating to a faculty member, is figuring out how to take a learning experience that works in a small-group setting on a campus, and re-creating a similar – or equivalent – experience online. Having decided last December that I would offer a math MOOC this fall, I found myself at once faced with a number of challenges.

By far the greatest problem is how to provide the personal, expert feedback that is essential to good mathematics learning. Web delivery is fine for providing instruction, but that is just a part of learning, and a minor part at that, as I discussed in the March Devlin’s Angle. At first, it seemed an impossible task. But with Stanford and the now independent Coursera building innovative new platforms, I began to see the glimmer of opportunities. Over the coming months, I’ll use this forum to write about my progress. And hopefully get your assistance.

My focus for this first foray into this new educational landscape is the high school to university transition. As every university mathematics instructor knows, many students encounter difficulty going from high school math to college-level mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a transition course. I myself developed one of the first transition courses in the late 1970s, when I was teaching at the University of Lancaster in England.

Such courses typically comprise a mix of some elementary mathematical logic, proof techniques, some set theory through to an analysis of relations and functions, with a bit of elementary number theory and introductory real analysis thrown in to provide examples.

Given the problems students typically have when they meet this material for the first time, doing this at a distance is a challenge. Even if they did well at math in school, most beginning university students are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the “mathematical thinking'' characteristic of much university mathematics. Clearly, offering such a course as a MOOC is a huge experiment.

This is where you come in. (I hope.) One of the things we’ve learned at Stanford from offering MOOCs, is that a key component is the creation of a strong online community. Learning is all about human interaction. The technology just provides the medium for that interaction. In offering my math transition MOOC at the start of the fall term, when many colleges and universities offer their own transition course, I am inviting any instructor who will be giving such a course, together with their students, to join me and my MOOC students online, making interaction with other students around the world a part of a much larger learning community.

The result could be a total failure. I won’t know until I try. On the other hand, anyone who joins me might just find themselves at the start of something major, new, and exciting. The online learning revolution is going to happen, and existing educational institutions are going to have to adjust to it, just as the music industry did to the iTunes revolution. Why not jump on the train as it is leaving the station?

I’m going to make my course just five weeks long, starting in early October. By incorporating participation in my Stanford course part of your students’ learning experience, everyone could benefit. For one thing, your students are likely to be inspired by being part of an educational revolution that for millions of less privileged people around the globe can quite literally be life changing.

Because they will be supported by being part of a physical learning community, with the personal support of you, their instructor, your students will be highly empowered, privileged members of that online community. They can take advantage of your support so that they can help others. And as we all know, there is no more powerful way to learn than to try to teach others.

For that student half way round the world, trying to improve his or her life through education – by learning to think mathematically – the potential benefit is, of course, far greater. Helping that unknown young (or not so young) person make that step might just help inspire your own students to put in that bit of extra effort to master that tricky new transition material. Everyone wins.

If my Stanford MOOC draws a student body in the tens of thousands, which it might, based on the experience of my colleagues here, there is no way I and a couple of graduate TAs can provide individual feedback to every student. But if instructors and their students across the US join me, then maybe we can collectively achieve something remarkable.

I am making my MOOC deliberately short, five weeks, so participation will leave most of the semester open for participating instructors to concentrate on giving their own course, perhaps using their students’ initial experience in the MOOC community as a springboard for the rest of the course.

By the time I post next month’s column, I hope to have more details available. In the meantime, I ask anyone giving a transition course this fall to consider joining me in this experiment. The only cost is our time. There is no need to make any advance commitment to me or to Stanford. At this stage, all I ask is that you consider joining me. I believe we will all benefit. Let’s teach the world.