In “Skipping Lecture” (below), I referred to a column by David Bressoud called “The Worst Way to Teach.” He posted his follow-up column, “The Best Way to Learn,” recently. While it may not be as concrete about how to “shut up and teach” as some may have hoped, it is as clear an articulation and justification of inquiry-based learning (IBL) as I’ve ever seen, and I highly recommend it. It seems appropriate that instead of giving me a detailed algorithm for how to change my calculus course, the column inspires me to work it out for myself by thinking hard about what I want my students to learn, and what “student-centered activities” would be most effective.

Bressoud mentions the Academy of Inquiry-Based Learning. I’ve explored the site, but have given up on looking at the videos there, since I’m on vacation at the moment and have a slow internet connection. I did, however, follow the link to the Journal of Inquiry-Based Learning in Mathematics, which is a repository of course notes for topics ranging from Foundations to Analysis and Topology.

I’ve also poked around at the site of the Center for Inquiry Based Learning (no hyphen this time) at the University of Michigan Mathematics Department. Check out some of the course listings, which are explicit about the IBL structure (I particularly like the term “mini-lecture.”) This is important. I’ve found that most of my students are so used to being talked at in math class that I need to explain early and often that their learning will, I am convinced, benefit from a different approach.

What about secondary-school mathematics? The AIBL sent me to Phillips Exeter, where one can actually download course materials. Now this is intriguing — a problem-based, exploratory integrated program. Sorry if I’m going overboard with the education lingo; “integrated” means that algebra and geometry aren’t separate courses as they were for me (and for my sons). There’s a lot to like here, but what stands out for me is the obvious care that the faculty have put into developing the materials.

This is not unique to private schools — I see the same care in the program developed at Mount Abraham Union High School in Bristol, Vermont (which is also an integrated program — see the “Course Selection Guide”), where my students and I sat in on classes last fall. In both cases, it’s clear that teachers have invested a lot of time on the details as well as the big picture. While the cost is obvious to those of us who have tried to write good problems, one of the benefits must be that the teachers guide the courses, rather than being guided by textbooks. (At Mt. Abe, the textbooks are in the cabinets, to be used for reference occasionally.) Yes, there are good textbooks available, and no, most high-school teachers don’t have the time or freedom to develop courses from scratch. (I did it in Linear Algebra after years of using texts and in a semester when my other duties were relatively light.) Still, I’m taken with the idea of a team working together to construct a program that they themselves then execute and adapt.

There are student testimonials to the effectiveness of the Exeter math program on the web site — this one, for instance. Since I usually work with slightly older students, though, I’m not sure how one helps a ninth-grader move from resistance to enthusiasm, or at least acceptance. Ideas?