In case you have not come across the acronym MOOC – it stands for Massive Open On-Line Course. Last year I wrote a review of Santa Fe’s first MOOC – Introduction to Complexity in relation to the future of education. Having taken on board and implemented a large amount of feedback from the first students, Santa Fe Institute have now launched a second course, an introduction to dynamical systems and chaos, and this year will also be running a number of other courses relating to complexity and complex systems (see their full list of courses here).
The Introduction to Dynamical Systems and Chaos is run by David Feldman, Professor of Physics and Mathematics at College of the Atlantic, who served as the school’s co-director between 2006 and 2009, and who is the author of Chaos and Fractals: An Elementary Introduction. This course follows the same format as the previous course, being divided into modules which are placed on-line at weekly intervals, and which contain a mixture of lectures plus quizzes and homework (see below) which are designed to test the student’s continuing understanding of what is being taught. At the end of each module is a test, the score of which counts towards the final mark of the students. Those receiving a final mark of 70% or higher receive a certification of completion.
At this moment of writing only the first two modules have been uploaded, but these two are foundational modules which explore iterated functions and differential equations. Students on this course need to have a working knowledge not so much of the actual mathematics, but of what the functions represent, what is the meaning behind the functions and equations, and for me this was a huge opportunity to revisit long forgotten A level maths (in the UK, A levels are the exams taken at the age of 17-18 before leaving school and entering university).
For some years now it has frustrated me that I used to be able to solve all sorts of equations, including second order differential equations, and even though I say so myself, I was pretty good, getting an A in maths, but I never needed these skills again, not even at university where the maths involved in Psychology was all statical). Feldman not only provides a comprehensive introduction to these functions, but as he says in one of the first classes, he does so in a manner which also differs from the way in which we were taught at school, a manner which is absolutely focussed on ensuring that students understand the meaning of what is being represented. Although slightly hazy, I am sure at school I could absolutely solve equations but I did not have a deeper appreciation of the meaning be hid the equations, and how they could relate to complex systems.
A great example was this question, seen above, in one of the quizzes. You really have to focus not on the equations, but what the graph is representing, and then focus on the relationship between the graph and the function in the question. I initially tripped up, as I think a few of my fellow students did, but this is the point of the quizzes. They really help the student solidify their knowledge, as opposed to just being passive recipients of information.
The course website also features slides which can be downloaded, and an active forum where participants can ask questions to their fellow students, with other students with advanced maths and computer skills uploading simulations and solutions for the other students to play with. The course is therefore of relevance to a quite wide public, with Feldman also playing an active role answering questions in the forum as well.
Now that MOOCs are becoming more widely available, the educational value of them is now being more widely debated. While I do not feel that all subjects are suitable for the MOOC format, with students who are highly self-motivated and disciplined to find the 3 hours or so a week necessary for this type of course, I continue to feel that they can play a much needed role in taking new teachings and practices from schools, colleges and universities out to a wider audience. And for those of you who are interested in complexity and complex systems, I can certainly recommend Santa Fe’s courses. At this moment the second version of Introduction to Complexity is currently coming to a close, but it will be run again on the 30th September of this year.
Santa Fe Institute – Complexity Explorer MOOC homepage