Posts Tagged 'transition math'

Final Lecture: MOOC Planning – Part 9

Published October 20, 2012 Free online courses 8 Comments
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A real-time chronicle of a seasoned professor embarking on his first massively open online course.

I gave my last lecture of the course yesterday (discounting the tutorial session that will go out next week), and we are now starting a two week exam period.

“Giving” a lecture means the video becomes available for streaming. For logistic reasons (high among them, my survival and continued sanity — assuming anyone who organizes and gives a MOOC, for no payment, is sane), I recorded all the lectures weeks ago, well before the course started.  The weekly tutorial sessions come the closest to being live. I record them one or two days before posting, so I can use them to respond to issues raised in the online course discussion forum.

The initial course enrollment of 63,649 has dropped to 11,848 individuals that the platform says are still active on the site. At around 20%, that’s pretty high by current MOOC standards, though I don’t know whether that is something to be pleased about, since  it’s not at all clear what the right definition of “success” is for a MOOC.

Some might argue that 20% completion indicates that the standards are too low. I don’t think that’s true for my course. Completion does, after all, simply mean that a student is still engaged. The degree to which they have mastered the material is unclear. So having 80% drop out could mean the standard is too high.

In my case, I did not set out to achieve any particular completion rate; rather I adopted a WYSIWOSG approach — “What You See Is What Our Students Get.” I offered a MOOC that is essentially the first half of a ten week course I’ve given at many universities over the years, including Stanford. That meant my students would experience a Stanford-level course. But they would not be subject to passing a Stanford-level exam.

In fact, I could not offer anything close to a Stanford-exam experience. There is a Final Exam, and it has some challenging questions, but it is not taken under controlled, supervised conditions. Moreover,  since it involves constructing proofs, it cannot be machine graded, and thus has to be graded by other students, using a crowd sourcing method (Calibrated Peer Review). That put a significant limitation on the kinds of exam questions I could ask. On top of that, the grading is done by as many different people as there are students, and I assume most of them are not expert mathematicians. As a result, it’s at most a “better-than-nothing” solution. Would any of us want to be treated by a doctor whose final exam had been peer graded (only) by fellow students, even if the exam and the grading had been carried out under strictly controlled conditions?

On the other hand, looking at and attempting to evaluate the work of fellow students is a powerful learning experience, so if you view MOOCs as vehicles for learning, rather than a route to a qualification, then peer evaluation has a lot to be said for it. Traditional universities offer both learning and qualifications. MOOCs currently provide the former. Whether they eventually offer the latter as well remains to be seen. There are certainly ways it can be done, and that may be one way that MOOCs will make money. (Udacity already does offer a credentialing option, for a fee.)

In designing my course, I tried to optimize for learning in small groups, perhaps five to fifteen at a time. The goal was to build learning communities, within which students could help one another. Since there is no possibility of regular, direct interaction with the instructor (me) and my one TA (Paul), students have to seek help from fellow students. There is no other way. But, on its own, group work is not enough. Learning how to think mathematically (the focus of my course) requires feedback from others, but it needs to include feedback from people already expert in mathematical thinking. This means that, in order to truly succeed, not only do students need to work in groups (at least part of the time), and subject their attempts to the scrutiny of others, some of those interactions have to be with experts.

One original idea I had turned out not to work, though whether through the idea itself being flawed or the naive way we implemented it is not clear to me. That was to ask students at the start of the course to register if they had sufficient knowledge and experience with the course material to act as “Community TAs”, and be so designated in the discussion forums. Though over 600 signed up to play that role, many soon found they did not have sufficient knowledge to perform the task. Fortunately,a relatively small number of sign-ups did have the necessary background, as well as the interpersonal skills to give advice in a supporting, non-threatening way, and they more or less  ensured that the forum discussions met the needs of many students (or so it seems).

Another idea was to assign students to study groups, and use an initial survey to try to identify those with some background knowledge and seed them into the groups. Unfortunately, Coursera does not (yet) have functionality to support the creation and running of groups, apart from the creation of forum threads. So instead, in my first lecture, I suggested to the students that they form their own study groups in whatever way they could.

The first place to do that was, of course, the discussion forums on the course website, which very soon listed several pages of groups. Some used the discussion forum itself to work together, while others migrated offsite to some other location, physical or virtual, with Skype seeming a common medium. Shortly after the course launched, several students discovered GetStudyRoom, a virtual meeting place dedicated to MOOCs, built by a small startup company.

In any event, students quickly found their own solutions. But with students forming groups in so many different ways on different media, there was no way to track how many remained active or how successful they have been.

The study groups listed on the course website show a wide variety of criteria used to bring the groups together. Nationality and location were popular, with groups such as Brazil Study Group, Grupo de Estudo Português, All Students From Asia, and Study Group for Students Located in Karachi, Pakistan. Then there were groups with a more specific focus, such as Musicians, Parents of Homeschooled Children, Older/Retired English Speakers Discussion for Assignment 1, and, two of my favorites, After 8pm (UK time) English speakers with a day job and the delightfully named Just Hanging on Study Group.

The forum has seen a lot of activity: 15,088 posts and 13,622 comments, spread across 2712 different threads, viewed 430,769 times. Though I have been monitoring the forums on an almost daily basis, to maintain an overall sense of how the course is going, it’s clearly not possible to view everything. For the most part I restricted my attention to the posts that garnered a number of up-votes. Students vote posts up and down, and once a post shows 5 or more up-votes, I take that as an indication that the issue may be worth looking at.

The thread with the highest number of up-votes (165) was titled Deadlines way too short. Clearly, the question of deadlines was a hot topic. How, if at all, to respond to such feedback is no easy matter. In a course with tens of thousands of students, even a post with hundreds of up-votes represents just a tiny fraction of the class. Moreover, threads typically include opinions on both sides of an issue.

For instance, in threads about the pace of the course, some students complained that they did not have enough time to complete assignments, and pleaded for more relaxed deadlines, whereas others said they thrived on the pace, which stimulated them to keep on top of the material. For many, an ivy-league MOOC offers the first opportunity to experience an elite university course, and I think some are surprised at the level and pace. (I fact, I did keep the pace down for the first three weeks, but I also do that when I give a transition course in a regular setting, since I know how difficult it is to make that transition from high school math to university level mathematics.)

A common suggestion/request was to simply post the course materials online and let students access them according to their own schedules, much like Khan Academy. This raises a lot of issues about the nature of learning and the role MOOCs can (might? should?) play. But this blog post has already gone on long enough, so I’ll take up that issue next time.

To be continued …

The Crucible: MOOC Planning – Part 8

Published October 6, 2012 Free online courses 23 Comments
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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 …

Why MOOCs Look Unprofessional: MOOC planning – Part 4

Published August 17, 2012 Free online courses 18 Comments
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A real-time chronicle of a seasoned professor embarking on his first massively open online course.

From an educational perspective, my goal in offering a MOOC on mathematical thinking is very modest. I have not approached the task as one of developing a whole new pedagogic model. That is a future goal — for me or for others. Rather I set out to see how much we can take current university teaching (of transition mathematics material) and make it available to a wide audience. Indeed, almost all the Stanford MOOCs currently being offered are free, online versions of regular Stanford courses, in many cases running concurrently with a physical class on campus. (As I noted in an earlier post, the technology that supports these MOOCs was actually developed at Stanford in order to facilitate flipped-classroom learning in on-campus classes.)

The underlying assumption of university education — at least at major research universities (as Stanford is) — is that the principle value for the student comes from studying with a world expert in a particular domain. Though many professors at research universities do in fact put enormous effort into their teaching, what is really being offered (sold) to students is the expertise (and reputations) of the faculty. (Other parts of the value proposition, such as the prestige of the university, stem from the faculty, both past and present.) It’s a method that works well for very bright, well-prepared, and highly motivated students, but it is not ideal for everyone.

In fact, even at less prestigious universities, where there are fewer leading research faculty, and at liberal arts colleges, where the primary focus is on undergraduate education, field-content knowledge hugely outweighs pedagogical content knowledge — how to teach the subject and how students learn it. (A Ph.D. is usually required for a faculty position.) That makes universities and colleges very different from high schools.

One of the implicit purposes of  a math transition course, such as mine (as well as many other first-year courses in different disciplines), is to help incoming students adjust to the different approach to teaching. More precisely, it is to help them adjust to not being “taught”, but having someone help them learn. This is particularly significant in mathematics — at least in the US — because of the hugely formulaic, procedures-focused nature of K-12 mathematics education in this country.

My challenge then, like that facing most of my colleagues offering their first MOOC, is to figure out how to take an existing educational model, hitherto used to teach (or help to learn) twenty-five or so students in a classroom, and make it available to thousands, spread around the world.

Since my topic is mathematical thinking, the biggest, and most obvious challenge is how to compensate for the complete absence of regular interaction between the students and me, the instructor. Sure, I give lectures when I teach a physical transition class, but the lectures are one of the least significant components. They really just set the agenda for learning. In order to help the students develop the ability for mathematical thinking, I need to see them in action at the board, to read their work, and to discuss their attempts face-to-face. Learning to think mathematically is more like learning to drive or to play tennis than soaking up knowledge. You have to do it alongside an expert or coach.

It’s a challenge I think cannot be completely overcome in a MOOC. The question is, is it possible to get part-way there? I suspect it is, but we’ll only find out for sure by making the attempt. So here we are.

One thing a MOOC does offer that is not possible in a physical class — and hence is a plus — is that all the instruction and professorial-learning-assistance can be on a one-to-one basis. Sure, it’s all one way, but if you set it up right (and if your voice/personality/whatever work over an ethernet cable), then the student can get that sense of working alongside the instructor — the expert.

Though by no means the first to discover that, Salman Khan, by virtue of his huge following at Khan Academy, demonstrated just how powerful is that sense of “working together, side-by-side”. Though I share the dismay of many of my colleagues at his less-than-expert content knowledge and his almost non-existent pedagogical content knowledge (neither of which he could be expected to have, given his background), where I seem to part company with many of them is the huge significance I attach  to the way he pulls off that human-connect. For online learning, I suspect it trumps almost all other factors.

(BTW, in developing my MOOC, I soon lost track of the number of times I made a decision based on a “suspicion” — or a “guess” or  ”hunch”. MOOCs are generating enough research questions to sustain several generations of doctoral dissertations in education research.)

Based on that suspicion (admittedly a suspicion comfortingly buttressed by a Khan Academy user base that numbers in the millions), Khan’s format was my starting point, as I observed in my last post. Not just the physical aspect of “sitting alongside in a one-on-one tutorial” but the associated human connect (and with it reassurance and encouragement) that Khan delivers.

In Khan’s case, his now widely familiar format originated with him informally helping his school-age relatives (who lived a long way away) with their math homework. What the viewer gets on their computer screen is, well, just “Uncle Sal”, doing what he would have done if he were really sitting alongside one of his relatives. For my MOOC, I wanted to achieve a similar outcome. Not a slick show, not a polished, rehearsed performance. Just me doing math.

Of course, the logistics of putting together a complete course that has to run automatically, and be scalable to many thousands of students around the world, many of them not native English speakers, meant that there had to be a lot of detailed advanced planning. Everything had to be scripted. But when it comes to the bits where I explain some mathematics, I put the script to one side and just start to work through the material as if I am sitting next to a student.

You might not like it. It might not work for you. You will surely despair at my handwriting. You might hate my accent. (I did cut down drastically on my jokes and puns, in deference to a multilingual audience.) But as far as I can make it, absent being physically in the same room, it’s what you would get if you were taking the course with me here at Stanford.  [Some time spent in a campus video-editing studio made my into-camera segments look a lot smoother than they were when we recorded them! If it's digital, it's plastic. But the goal there was to reduce the length of those segments.]

Which brings me back to my starting point: seeing the extent to which we can take existing university education and make it available to the world.

Once we can do that — and it will surely take several iterations to iron out all the kinks and make an altogether better job of it — we can look at how to change the underlying model. In addition to MOOCs making accessible to the world some aspects of university education, I think that the act of designing them, mounting them, and analyzing the results, will lead to changes in the way we organize learning within our universities.

It is because the current goal is to see how well we can deliver (current) real university education to the world for free that most of the MOOCs being offered have an unpolished, unrehearsed look. By deliberate choice, to the greatest degree we can achieve, what you see is what our (on-campus) students get. (I think this WYSIWOSG philosophy — I just made up that term —  is also one of the reasons for the success of Salman Khan — including the fact that in his case, unlike university MOOCs, he does not even lesson-plan his instruction sessions.)

So much for the most visible part of the MOOC: the instruction. But instruction is still just instruction. As I’ve said before, the learning takes place elsewhere, through other mechanisms, none of which we understand very well. So where is that educational  meat?

Now we are about to really enter speculative territory.

To be continued …

COMMENTS: As always, comments are welcome, provided they remain on topic.

I'm Dr. Keith Devlin, a mathematician at Stanford University. In fall 2012, I gave my first free, open, online math course and this spring I am giving my second. This blog chronicles my experiences as they happen.

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