Prof Keith Devlin of Stanford University is running a Massively Open Online Course (MOOC) on Coursera, titled “Introduction to Mathematical Thinking“, with a stated goal to “help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.”

MOOCs are big news, lately, with a popular AI course offered for free online by Sebastian Thrun from Stanford last year. Of course, distance learning and the ability to put course materials online are not new. “So”, asks Devlin in his May 2012 MAA column, “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.

This is interesting, coming from Devlin, because as recently as March he wrote about the difference between teaching and instruction:

As a child, I never experienced what I would now call mathematics teaching. … What I was presented with at school was instruction. … The teacher would explain some new concept or demonstrate to the class a method to solve a particular kind of problem, and then we would all work through several problems of the same type. … As far as I can tell, most people in the US (and the UK) who last took a math class at high school have never experienced good mathematics teaching. Nor have many students who went on to take math classes at college level, but were not able to sit down one-on-one or in a small-group setting with the professor, as I did. All they have ever had is instruction.

Distance learning via online video is perhaps the very definition of instruction. And Devlin is aware of this. Which is perhaps what makes his MOOC a very interesting prospect. On his ‘MOOC Talk’ blog, he explains:

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 … I need to assemble a small army of volunteers. … I am inviting any instructor who will be giving [a transition 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.

Gathering together experts as well as students, Devlin hopes to develop a supportive user community to take the online course beyond simply instruction.

Introduction to Mathematical Thinking is the kind of course in American universities which provides a bridge between school mathematics – which “typically focuses on learning procedures to solve highly stereotyped problems” – and the mathematics found at university. The course description explains:

The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

The course is therefore primarily pitched at “first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind”. Additionally, “because mathematical thinking is a valuable life skill”, the course description recommends that “anyone over the age of 17 could benefit from taking the course”.

Will it work? Devlin is very clear this “a big, big experiment“. But it’s an interesting idea and, I would say, in safe hands.

The course begins in September and you can sign up for it now.

**Source:** Keith Devlin on Twitter

**More information:** Introduction to Mathematical Thinking on Coursera.