This year my department (and Physics) are putting on the fourth offering of a two-semester course called Integrated Physical Science. This effort arose from a complaint by the Physics Department that we were teaching the calculus a year after the physics majors needed it. We had a matching complaint – that the physicists were teaching advanced topics in calculus early and wrong. Without going into the details, both claims clearly had merit. The real problem was that the province of Ontario had idiotically removed Grade 13 – the college prep year. This meant we went down from a year of more of calculus to half of one semester. You may have seen that Occupy Math is not a fan of teaching calculus too early or making it the sole goal of mathematics education, but physics is a discipline that really needs calculus.
The solution that Occupy Math came up with was the integrated course which teaches more calculus earlier and uses physics as an example to anchor the calculus. The course is worth twice the credit of a normal course and it was co-developed by Occupy Math, a physics professor Joanne O’Meara, and other professors and graduate students. The course covers about 150% of the calculus that our standard course does, offers more “assessments” (tests, homeworks, quizzes) than the normal course, and defers the theory of calculus to the later part of the course.
One of the ideas driving development of this course was that we were teaching calculus so slowly that good students got bored and stopped coming to class.
The results, after three full offerings of the course, are as follows:
- Out of 110-120 students we have less than five students drop and zero to two flunk. This compares with a 20-40% drop/flunk rate in typical first year calculus classes.
- While I’m not allowed to use attendance as part of the grade, I have better than 90% attendance. This is also an usually high figure for a large-lecture, first-year class.
- The course has tests that examine both physics and calculus – meaning that the students have fewer total tests and at least those two topics are unable to have schedule conflicts.
- The course is unusually popular with the students. I’m contrasting it against, for example, business math which the students hate (50% attendance if I’m lucky).
The course previews multi-variable calculus, linear algebra, and differential equations which means it establishes connections to other disciplines in math.
This preview of a large variety of other mathematical topics is needed for physics. These connections, together with the integration with physics, mean that the question “what use is this?” pretty much answers itself. The course has been taught by other people with similar results, suggesting that while Occupy Math is a pretty good teacher, his teaching is not the key factor. This leads to a hypothesis about university education in general.
Teaching knowledge in disconnected silos is not an effective technique.
This is not a particularly original thought, and the problem arises from the basic structure of universities. We are organized into departments and colleges that compete for resources, have little or no social contact, and mostly study only within our own discipline. Occupy Math works on biological data, as both a mathematician and a computer scientist. While there are biologists that I enjoy working with, the average biologist treats me as a technician. They don’t contact me until they have already gathered their data, in some cases they are remarkably disrespectful, e.g. “if you’re in computer science then you’re just a service provider” – a direct quote from a biology prof.
Given how well it works in the one instance that Occupy Math co-developed, why don’t we have more integrated courses? There are some, but they are pretty rare. There are several reasons. The integrated math/physics course was developed as part of an initiative at the University of Guelph to develop cross-disciplinary first-year courses. There were three departments in the biological sciences that tried to integrate their introductory courses and instead ended up developing a fourth course that explained the connections – they compressed three courses into four. Not what the people funding the integrated course development really wanted. The ability to accept that other points of view and disciplines have worth is far too rare.
The biggest problem is that most professors neither know nor care what can be done outside of their discipline with the results they study and create.
Sadly, this contempt for other disciplines is built into the reward structure at universities, which is called the promotion and tenure process. Occupy Math is an interdisciplinary researcher; because of that I can state that interdisciplinary work is often undervalued and sometimes punished. When other researchers review interdisciplinary work they often comment only on the part that is in their discipline. This makes the accomplishments of the work somewhere between obscure and invisible. This is changing, but slowly. Guelph is a leader in not punishing interdisciplinary work, a good part of the reason Occupy Math hangs out there.
An even larger problem is that teachers work, for the most part, in isolation.
I’ve been teaching the integrated math/physics course with Martin Williams. He is a teaching focused physics professor, a pleasure to work with, and he and I co-design tests and details of the course content. Both university and high-school teachers usually don’t do this. As anyone with a good friend knows, just having someone to talk to helps with a lot of problems. Integrated courses have a lot of potential to permit mutually supporting teams to offer a course. Together.
I’ll end with a bit of a confession. The most popular post Occupy Math has had so far is one about the connections between math and art. The reason Occupy Math was able to write that post was because of an early attempt to develop an integrated course. The image below is a simple example of mathematical art – click it for more examples.
I worked with five students to develop a first-year math course for fine arts majors.
We found a large number of connections between math and art and had a pretty good course designed. We did this the year the cascade of course cuts started – so the math/art course was never even reviewed. Do you have experience with teaching from inside a silo or lack of support as a teacher? Do you teach an interdisciplinary or multi-disciplinary course? Comment on this blog to let us know or tweet about it.
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics