I’ve always felt that the focus in university mathematics education should be on student-led learning, not teacher determined instruction. The key ability the student needs to develop is being able to take a novel problem and figure out a solution. That is, after all, what professional mathematicians do! As far as I can tell, I share this model of university mathematics education with the vast majority of my colleagues in the professoriate.
That’s not to say we – at least some of us – don’t reflect on what we do in the classroom, nor that we don’t attend courses, workshops, webinars, and presentations on educational technique. But my sense is that those of us that do this end up spending far less time providing “well crafted instruction”, and putting more of our effort into creating an environment in which our students can learn for themselves, and stimulating and encouraging them to do so.
In adopting this approach we capitalize on a hugely important factor you find at university but typically not at school: we are professionals who love our subject with a passion and have devoted our lives to its pursuit. When we stand in front of a class and write on a blackboard (mathematicians still prefer a blackboard to a whiteboard), we are not giving instruction so much as providing an example of how a pro thinks.
For, at heart, contact with the pros is what university education is about. For the vast majority of students, university is the first time in their lives they come shoulder-to-shoulder with the disciplinary experts. Those disciplinary pros do not have the pedagogic content knowledge required of a good K-12 teacher – at least nothing like to the same degree – but that is compensated by something that I think is far more important at that more advanced stage of a student’s development: learning by up-close observation of, and interaction with, a domain expert.
For sure, you will find university professors who have a different overall philosophy than the one I just sketched, but as I noted already, I think most of my colleagues have a similar view to mine.
Certainly, the celebrated physicist Richard Feynman, in the Preface to his 1963 book Six Easy Pieces, wrote:
The best teaching can be done only when there is a direct individual relationship between a student and a good teacher – a situation in which the student discusses the ideas, thinks about the things, and talks about the things. It’s impossible to learn very much by sitting in a lecture, or even by simply doing problems that are assigned.A key element of operating in the fashion I am advocating (as is Feynman) is, then, the person-to-person interaction that takes place between a student and a professor (admittedly, often limited to the few short weeks of a university term). When a professor tries to port a course to a MOOC, however, that personal interaction goes out the window.
The primary issue is not the second O in MOOC – “online”, with the professor and students in different physical locations. That may be a significant factor, but just how significant is not yet known. (With the availability of rich social media, I think only empirical research will tell us the answer. Intuition is no longer a reliable guide to the importance of physical co-presence, if indeed it ever was.)
Rather, the key factor is that initial M – “massively”. In an online class with twenty-five students, the professor may be able to interact regularly with each student. But when there are 65,000 students, scattered around the Information Superhighway, there can be no meaningful interaction. The flow is asynchronous and entirely one way, from the professor to all those students.
That means the student becomes totally responsible for his or her learning. There can be one-on-one interaction, but it has to be student-to-student, perhaps within small study groups.
The task of the professor is then to design a course that can succeed as a result of student-student and small-student-group interactions.
As I was planning, and even more so when I was giving, my first MOOC, I felt very much like the conductor of a 65,000-player orchestra. I got to choose the pieces the orchestra will perform, I controlled when to start each piece and when to stop, and to some extent I dictated the tempo. I observed and occasionally commented on the overall group’s performance. I sometimes gave hints and advice. But each one of those 65,000 members of the orchestra did the actual playing. In principle, by pulling together, they should have been able to complete the current piece tolerably well, if I had suddenly been taken ill and had to put down the baton.
In fact, for the first time in my career, I was able to conduct a class the way I’d always wanted to: as an experienced guide who helps the committed learner in a minimal way, only when absolutely necessary.
That approach to university “teaching” can be done in a traditional class setting, but it takes an unusual individual and an even more unusual environment in which to do it. R L Moore is the most famous example of a mathematician who “taught” that way. (It’s so unusual, I need to put quotes around the key verb.) (See my MAA columns from May 1999 and June 1999.)
I tried the Moore Method, as it is called, a few times in my career, but it never worked well. I have enormous respect for my colleagues who have made it work – and some have. But, faced with teaching a MOOC (better make that “teaching”), I had to rely on one (but by no means all) major element of the Moore Method: the students would have to figure things out for themselves.
Moreover, I was of necessity relieved of the factor that has always led to my abandonment (or severe weakening) of the Moore method whenever I tried it: students who can’t handle the approach drop out.
In a physical class of maybe twenty-five students, I always felt a responsibility to do the best I could for each one. Particularly problematic were the ones who had gotten to university by virtue of “good teaching,” who could jump through all the templated hoops that were placed before them, but were floored when presented with a totally novel problem. After all, it was not their fault they were disadvantaged by “good teaching.” I felt it was my job to rescue them as best I could.)
With a volunteer student body of tens of thousands, on the other hand, you can’t avoid losing a few thousand, and you can afford to do so. There will still be many thousands of students who remain. Indeed, the “end of course evaluation” is bound to be overall positive, because the ones who don’t like, or cannot cope with, your approach simply drop out along the way.
In short, a MOOC is very much a survival-of-the-fittest affair.
At this early stage, MOOCs are being developed and offered very much in an experimental mode. But if, and when, they become an accepted part of the global educational landscape, then it’s not just higher education that will change, but society, as the international playing field gets truly leveled, with the most talented and ambitious people from everywhere in the world competing on merit alone.
Facing that possible future, maybe we need to ask ourselves if we do the best for our own students here in the US by being “too helpful.” And if the answer is “no” at university level, maybe it should be “no” in the high school as well.
For further discussion of my MOOC, see my blog MOOCtalk.org.
