Perhaps it is useful if I sketch some of the background to this project of mine. The first concrete idea came in early fall of 2010 when I sat down to write a contribution to a Swedish anthology about Liberal Arts education. The idea behind that was to discuss various aspects of the liberal arts tradition and how it could inspire Swedish higher education. All the authors had some personal experience from the American tradition, many from having spent a term at a college under the STINT Excellence in Teaching scholarship. I volunteered to write about mathematics. Not because I knew very much about it, but rather because I did not know very much and I was very interested in mathematics teaching and learning.
When I started to write, I realized I knew next to nothing about mathematics teaching at Liberal Arts colleges. When I was at Skidmore College in NY in 2004 my focus was elsewhere. During the writing process I learned about the corresponding Swedish discussion on mathematics and ”bildung” from the last decade that I had missed. It became a learning experience.
So why was I at all interested in going in this direction? It goes back to a long time interest in the history and philosophy of mathematics. Also there is my interest in didactics of physics and mathematics. I worked for six years at a gymnasium (corresponding to school years 10-12). I then came into contact with learning theories based on meta-cognition, constructivism and Ference Marton’s research on deep and surface learning strategies.
About ten years ago, a year or so after I started to work at the University of Borås, I planned and carried through a pedagogical experiment in mathematics together with two colleagues. The background to that project was discussions among mathematics teachers at the institute about the weak background knowledge in mathematics among the incoming students. I wanted to do something about it.
The experiment did not go very well. Some of the ideas were good (I’ll write about them elsewhere), but our implementation was shaky and I now realize that we missed many important ideas that I just recently have become aware of. After that, I got the opportunity to study computer science for some years, and my teaching also turned to programming courses as well as basic courses in natural science (for students lacking that from high school). But the last couple of years I’ve moved back to mathematics teaching. And I see that not very much has changed, at least not to the better. Incoming students are still very weak in mathematics.
There is one special circumstance that is of importance. In Sweden we have educational programs in engineering that are 3 years long. There are just two mathematics courses in general (linear algebra and calculus), sometimes a third course and/or a course in mathematical statistics. The standard length of a Swedish university course is seven weeks. That means that 3-year engineering students have one half semester of mathematics (they take two courses in parallel), which is not that much. So the resource in terms of available time is scarce. It is of course almost impossible to go very deep or far in calculus in such a short time. Most engineering students have had some calculus in the gymnasium, at least a brief encounter with derivatives, but some haven’t seen integrals. So the problem would seem to be unsolvable.
Why then try a humanistic approach to engineering mathematics?
The students that enter engineering programs have 10 – 12 year of mathematics from school. That is indeed a lot, and they do have a lot of knowledge, but it’s a kind of implicit knowledge. It’s not really workable knowledge, very many have problems with simple numerical calculations and algebra. Functions are dim concepts. It’s like all the acquired knowledge from 12 years of school need to scattered on a large table, like jig-saw puzzle pieces, and then put together into a coherent whole, with new pieces added and context provided. That sounds like a humanistic endeavor.
Even though mathematics is a supporting topic, subordinated to technology, that does not mean it must be taught and learned that way. The question is: How can the scarce resource in terms of time be used in an effective way? The students must be engaged so that they are prepared to invest extra study time for home work.