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 …
MOOCtalk 
I am very happy to take this course, is a great opportunity.Tanks! The material is interesting, the form is impeccable. I sorry to be inscribed late, but I enjoing to leerning.
It has been said that physicists, lacking proper tools to treat their sphere of concentration, will invent the requisite mathematics. Some engineers, speaking of myself, have similar aims: to develop the mathematical procedures and tools to describe and document as yet uncharted territories of the world with which we interact. Those of us “in the trenches,” persistently come face-to-face with tool-less problem areas that we are motivated to “fix.” It is very beneficial to have courses such as your “Introduction to Mathematical Thinking” that can assist us to develop the mindset necessary to make worthwhile contributions to our respective fields.
I would venture to extend your description of mathematical thinking to many other areas of science. The combination of precision when required, and finding the courage to venture beyond and explore unknown paths is for me the core of scientific research. Your course is so interesting for me exactly for this reason – mathematical thinking is not just the realm of math, it is present in many other scientific endeavors and much more universal. Thank you for putting this MOOC together; I am thinking of asking all my grad students (not in math) to stop by your blog and maybe take the course.
It will be interesting to see the see reseach papers generated after this course. Virtual learning and the benefit of studying/attending class at ones own convenience thru to Self forming study groups. The addition of an end of week problem set is good , helps focus the mind those who might procrastinate
I am enjoying the class. I’m not the typical high-school to Uni student who’s looking for a bridging course. I’m in mid-career (early 40s) and I’m looking to transition from Software Engineering to Actuarial Science. That’s my main reason for taking the course. I loved high school mathematics and was good at it, so I was a little worried when you said it would be more difficult for those of us who excelled at high school mathematics, but so far it has been very interesting and challenging. Very well organised, I must say. And I love the fact that you delay assignment results until the deadline has passed. Keep up the good work!
Frankly I would love to see most of the k-12 catch up to the 21st century. With a small exception, most are teaching math in an antiquated manner. Hell I passed most of my applied math class just using the software after I got a strong foundation (wasn’t even math really, it was accounting). Now learning modern mathematics is another thing. Takes almost over a decade to be up to date. And this class is a great way to start getting used to the language and work style of a mathematics. Baby steps.
I think you over-simplify the problem. Your Coursera mail regarding your course says ” There is no big secret. Discounting a small number of individuals who do seem truly gifted, the vast majority of mathematicians are just regular folks who have learned to think a certain way”.
This is tautological. It;s like saying “There is no big secret. Discounting a small number of individuals who do seem truly gifted, the vast majority of Olympic champions in “insert sport here” are just regular folks who have learned to conditions their bodies in a certain way”. Obviously true. There is no silver bullet. But the real question is: Why so few humans ever manage to be good mathematicians or good sportsman ? Why so few can learn the way to raise to a good performance in any domain ? At what age should you expect “performance level X,” ? A good answer to this question would be truly benefiting education. Ignoring those kind of issues will only lead to a new wave of failures in general education IMO. Coursera is not a very good sample to take conclusions regarding education in general. Your audience there is self-selected. You cant infer too much regarding what the public school system should do based on this lot. Just my 2 cents.
Dan, I agree that there is a tautological element to my statement. The reason I made it is that several studies have shown that (at least in the US) K-12 students have a strong belief that being good at math is something you have to be born with. (Some studies have shown that this belief is actually more common in the US than in other parts of the world.)
Your other questions are all good ones. I’m definitely not suggesting results from a MOOC should form the basis for educational change, rather I mention them in my blog about the MOOC because they highlight observations that have been made elsewhere. Thanks for responding.
It is I who must thank you. I have a lot of respect for humans who put free math — and hard sciences — related learning materials on internet.
Dear Professor and course team, reading about your experience on the MOOC is almost as fun as being a part of it. Thanks for sharing this with all of us. I felt the same way about the students who complained on the forums. I was shocked to see some of the responses. I thought, I am sitting in South America, probably 5000 miles from California and I am watching a world-recognized professor in Stanford teach me mathematical thinking. In my age and economic position, I would have never been able to even imagine what a math class in Stanford is like. I recall back when I first entered college(1996) looking for copies of terrible quality copy-of-copies Don Knuth texts and videos to soak up as much as I could. I am still thrilled by the experience, every time I turn Coursera on I feel the thrill of being a part of this. Congratulations for your intiative, this shows the world how education and knowledge leads to a better civilization. While some places in the world are only interested in war and destruction, there is within the world a civilization that is spreading knowledge, sharing, innovating and creating a world community that functions independently of violence, prejudice or much worse, or the sum of all those, war. I open my computer and learn programming from Lausanne, and watch a Stanford class in California. Sir Arthur Clarke was right, this is indistinguishable from magic.
If there were ever complaints on that forum, well here’s another humble up-vote contrary to those.
I hope you do keep this course going and improving, it has been a very thrilling experience and though I’ve done some math before, it’s already helping me with my thinking. Here in Brazil we are taught to mechanically solve things. Richard Feynman even mentioned something to that extent in his famous book Surely You Must be Joking[1] that in Brazil knowledge is mechanically taught.
Cheers!
PS. Today I picked up an old yellow cover Springer book on Set Theory, lo and behold, I jumped back when I opened it and saw that it’s written by prof. Devlin in 1992 or 1993! Cool coincidence, I can tell everyone now I have been a virtual “student” of his!
[1] http://v.cx/2010/04/feynman-brazil-education
To be fair to Professor Devlin, I think there is a way in which his statement is not merely a tautology, and that is by his emphasis on the contrast between the relatively small number of individuals who might not have to work as hard to succeed in math (or sports) due to their genetic and other advantages versus the much greater number who may be not so endowed yet committed to arduous effort. We can conceive of the opposite, a situation where almost everybody in the math field, or competing in the Olympics, just found it very easy to do and only a few outliers managed to belong by the sweat of their brow.
I find myself wondering whether the former even really exist in a pure state. I remember taking an organic chemistry class in college where one kid was the acknowledged whiz of the class. I like many others was struggling to assimilate what seemed obvious to him, and I assumed that he must be extra brilliant. We happened to work in the same lab and one evening I noticed his orgo textbook sitting out on a chair. I was shocked to see that the book had every appearance of having been run over by a Mac truck: dog-eared, crumpled pages rife with markings and a shabby-looking cover. I pictured my own nearly pristine book back at the dorm and had to admit that the guy was working a lot harder than I was for his reputation.
Even those have may have been identified as gifted at some point in their lives are made vulnerable by the misconception that talent matters more than hard work, or that having to work hard at something might be some indication that a person is not “actually” gifted. The blessings of high intelligence then take on too great an importance in the person’s mind, and can become something that can be lost or disproved and thus even a source of anxiety or shame. Such persons would benefit from far greater emphasis on the important of engagement and struggle.
Sorry, that’s “Mack”! 😀
Please don’t discount those of us who are “simply” watching the videos. To me the videos are the most important part of the course. As you say, many of us are older and have a lot of experience with real problems — so we don’t necessarily need you and your staff to create quizzes and assignments for us — we can examine REAL problems we’ve come across. If you’re going to challenge traditional education, why arbitrarily retain parts like “The professor must give assignments and those who don’t do them aren’t real students” (they’re simply watching videos)? Were Socrates’ students not real students because they were simply listening to him talk? (he didn’t give homework assignments as far as I know). I offer these thoughts as feedback in good cheer! : ) I greatly enjoy your lectures — I listen to them driving to and from work each day and I feel like you’re right next to me in the passenger seat.
Margret, even genetic freaks in athletics have to work **extremely** hard to accomplish anything at high level. Performance doesn’t come easy. This is not the point.
Are you sure that the ability to “work hard” is something anybody can do, and this behavioral pattern has no genetic component, as you seem to hint? IMO, no, discipline and commitment to tasks are behaviors modulated by a lot of factors genetic ones included.
The sad and banal truth is that the ability to do “hard work”,is a pretty rare talent. Its probably linked to the development of the frontal cortex and the dopaminergic systems of the brain, and as sure as hell not everybody can work hard, keep the motivation to work hard, keep the concentration … and so on.
The irony is, this is the start of all lies we tell our kids. We tell them that everybody is born equal (ofc we are not born equal, neither biologically, neither socially), that everybody can be whatever they dream (of course we cant ). We need to stop selling them vaporware and dreams.
The truth is, when you see a top dog, you don’t only see one talent displayed, you see a lot of talents on display. Including the ability to do intense and focused work. No matter we talk about a supermodel,a high level sportsman, or a highly academically accomplished individual.
IMO, your hard work vs talent issue is a false dichotomy,
Good Professor,
You deserve the everyday virtual apple.
All my life I was looking for the knowledge and the point of view that you are trying to share with us.
I began 20 years ago ( in a third world country, no English speaking, no Internet by that time) looking in the library of my university and the only thing that I found was the book of Tobias Dantzing in order to appreciate mathematics in another way. I mean, trying to find what thinking is behind it. In the spectrum I also tried to read the book of Richard Hamming: The Art of Doing Science.. . In this quest, some day during last year I found your book: Mathematics: The Science of Patterns, and I began to read your others books and articles and I said Eureka.
Now, I have the honor to participate in this MOOC with you.
PS: Thanks for sharing the J.B. song. It helps at 2:30 AM when I feel frustrating trying to solve the Assignments.
Well Dan, I hope you will humor me a little if I indulge in positing scenarios that seem wrong or nonsensical to you. After all, we’ve had many moments in this MOOC already of playing with statements that may be true or false, just to see how they interact. I think the scenario we’re considering, of natural born math whizzes or athletic stars who don’t have to work hard for their success, is worth discussing perhaps primarily because we can see that it is false. And so too the related belief that you can’t make it without special talent. And yet, many people still believe that math takes a special talent, that it is the consequent if you will to the antecedent of success.
I love your other points about success depending upon many variables, and about the biology of hard work and motivation—as a parent raising a young child and as someone who has a loved one with ADD, I think about those things frequently. I don’t know how you may propose to measure how hard is hard when it comes to “hard work,” or what “rare” means to you in terms of this quality. If I understand you correctly, you believe that as a special “talent” the ability to maintain one’s motivation is limited to only a few, and that once the brain has finished developing (and when do you think that is?) one’s “hard work talent” is largely defined for life, true?
And yes, the old canards “Everybody is born equal” and “You can make it if you try,” otherwise known as the opening to the body of the Declaration of Independence and the American Dream. Actually I think the original phrasing on the first was “All (Anglo-Saxon) men are created equal (under the law)” but we have since revised that view to include women, along with people of minority and mixed races here in the U.S. who are rapidly becoming the majority. Perhaps with the benefit of Professor Devlin’s wise counsel these concepts could now use some further revision:
WE hold these truths to be self-evident, that all persons are created with potential, that they are endowed by their humanity with certain unalienable talents, that among these are math, beauty and the pursuit of athletic prowess; that to secure the natural fruits of these talents dopaminergic pathways must be encouraged to develop in the brain….” 😀 😀 Best regards,
Actually, I should not have excluded you when I said “Professor Devlin’s wise counsel” as this is certainly a collaborative effort, no? 😀
Because just back from one week trip, I missed some lectures and assignments, I will make up whatever. It is a great course. like you said:” provide a real bridge between K-12 education and life in the world that follows”, in my high school and college, I just think mathematics as formula and symbol, it was boring even i got high scores from examination. That coure help think how to use it in real life problems, it is hard but intreseting. Thank you for all your effort.
Dr. Devlin,
I am also auditing your class cousera.edu. I am a single, middle age mom and have to work a lot to support my famiy so the time I can spend on my own is very limited. Even though I cannot follow your progress each week, I truly appreciate you and your TAs have put in so much work and time to the course. I can tell you really want us learn and gain some beniftis out of it. Keep it up; I may give it another shot again. I am not that easy to give up. 🙂
I am struggling with something: learning a subject is a massive investment in time – at minimum a few weeks on concentrated effort. So what would be better, a MOOC, or a textbook?
I know a MOOC is free and a textbook will cost money, but in terms on what I want to learn the time invested makes the materials cost negligible. From the point of the view of the learner a MOOC seems a step backwards? Its just selected parts of the textbook being read out by the professor (very slowly I might add and no way to jump around the content according to my need).
I just don’t get the point of these online videos, and having tried 2 coursera courses now, I would rather buy a good textbook. On the other hand I did a javapassion course a while ago and it was great (but it wasn’t a MOOC, just an online course). Really confused by the difference!
Marco: The video segments of me working at my desk are not intended to be “here is how you do it” instructions (of the Khan Academy type). And they are definitely not me reading my textbook!
The videos provide an example of one professional mathematician (me) engaged in mathematical thinking. I verbalize my thinking as I work on a problem. I make mistakes, and correct. Sometimes I do not express myself as well as I’d like. They are recorded in real time. The only editing is that I ramp up the speed of some of the handwriting (though not in the Tutorial Sessions, as those are recorded just hours before I post them on the Coursera site), and occasionally cut out a cough or an unusually long pause while I am thinking of what to do next.
The textbook, in contrast, was worked on over many weeks, and was professionally edited by an experienced mathematics textbook editor. It covers the same material, so of course it stays close to what I do in the lectures — especially as I have given the course many times in real universities.
But I (and others) think there is real value in allowing a student to “sit alongside” an expert and observe them as they work. It’s how most of us professional mathematicians learned our craft when we were Ph.D. students.
It is a mistake to view the video segments as just a variant of the textbook. The textbook focuses on the content. The videos are all about the *process*. If you watch the videos looking for content, you will miss the value that (I hope) they have.
The learning is all up to the student. Seeing an expert working up close is just one of many resources that students can draw upon as they themselves learn how to think mathematically.
I hope this helps.
As someone who counts as gifted at maths, I can’t emphasise how much work is needed.
I spend a *lot* of time when I was 9 or so thinking about fractions, and ratios and what makes one fraction bigger than another.
When I got books on calculus and trig out of the library when I was 10 and 11, I spend a very long time trying to follow what was going on. That took a lot of effort.
You learn by really thinking about these things hard, and trying to create your own proofs. Seeing where your proofs lack something is what teaches you.
Thanks KD for the course, which came just in time to save me from giving up. Unfortunately, I couldn’t finished it, but I’ll keep at it while it stays on line and then I catch you on the nex…..
What a great thing MOOC turned out to be.
Raul