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A report from Keith Devlin's and Coursera’s introduction to mathematical thinking MOOC

I’m six or so weeks into Keith Devlin’s  10 week  Introduction to Mathematical Thinking, along with some tens of thousands of others.

Here is a longish thumbnail sketch of the design of the course, followed by two appendices. Appendix 1 concerns peer review. Appendix 2 is what the course web site has to say about grading and certificates of completion.

Comments, questions and corrections would be most welcome.

1. The course is advertised as needing about 10 study hours per week. This is about right: though in my case I had to skimp a lot while I was on holiday, other than wrestling unsuccessfully with a proof that had been set as course work, the non-fruit of which is shown above.

2. There are one or two 15-30 minute video lectures per week. All have so far has consisted of a mixture of Devlin talking confidently and intently to camera in sort of “newscaster” mode, and Devlin explaining things with pen and paper, very much in the vein of the 2011 Norvig and Thrun AI course. Devlin has retained his East Yorkshire/Hull accent, which has the effect of making him sound local. To me at least.

3. The videos have some nice technical features. For example, you can play them at up to 1.75 x normal speed whilst just about retaining Devlin’s vocal register correctly; handwriting is cleverly sped up to keep pace with Devlin’s voice.

4. At several points during each video there are embedded correct/incorrect answer quizzes. These range from quite challenging to almost silly checks on whether you’ve been listening. Each quiz allows you three attempts before you are taken to an explanation of the “correct” response.

5. The embedded quizzes also exist separately from the videos, which is useful for practice or revision purposes.

6. There is an accompanying self-published 80-page book by Devlin also called Introduction to Mathematical Thinking, which I bought online for £6.29. I have made use of the book particularly whilst travelling, but I could have managed without it. My guess is that most students have not bought it.

7. Each week there are one or two assignments. These are 1-4 page PDFs – with poor typograph, especially if printed from within Chrome or Firefox – with perhaps half a dozen questions relating to the material that has already been covered. They seem to be based mainly on the questions that appear in the book. (This is no bad thing.)

8. Assignments are not submitted for marking (but a helpful feedback video is made available in the next week in which Devlin explains how to answer a selection of the questions). In the first few weeks of the course Devlin puts a very prominent amount of emphasis on the need for all students to discuss the course with others in an informally established study group. In my case I chanced on and joined a Google Group called “Mathematical Thinking UK Discussion Group”. This initially had about 40 members. About seven were helpfully active in the first three weeks, but the study group has seemingly since ceased to function. So I am on my own: it feels a bit late in the day to try to find another study group, nor to attempt to breath life into this one.

9. Each week there is a multiple-choice machine-marked problem-set, for which there is a tight deadline, and which we are required to complete alone, though this is not enforceable.

10. The final exam (yet to take) will be marked by peer-grading; and during week six (the current week) we received our first bit of training in the peer-review process, with one of today's machine-marked problem-set being to grade a short mathematical proof, guided by a rubric provided by Devlin. This felt rewarding to do in its own right. And of course the method itself can be used at very large scale. [For more on this see Appendix 1 below; there is also a discussion about peer-based marking in the Ufi Trust's May 2012 Scaling Up report, in which I had a hand.]

11. About every two or three days, at least during the first few weeks of the course, all students get a “do not reply” email from Devlin. This might tell us that new material has been published, or it might draw our attention to a discussion in the Coursera-provided course forum that Devlin considers relevant. For example, a discussion had cropped up about the decision to pen and paper rather than Udacity or Khan Academy style digitized writing using a tablet. Devlin had contributed to the discussion and we were encouraged to read the thread. Devlin also seems to have decided that there are benefits for learners in exposing to learners the thinking that has gone into course design, and we’ve occasionally been encouraged to review a set of short (~one to ~six minute) videos – so far there are about 30 of these. Some of these focus on design decisions about the course. Others are fragments of Devlin in action teaching at Stanford. 

How am I finding it?.... 

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