It's a little risky charging in and reporting on a conversation that had been going on for years before one joined it--bear that in mind as you read (you might get a less slanted version from Ken Plochinski, who has been in it from the first.) But it was far too interesting for me to leave unreported just because I may make some bloopers. Basically, what was going on was a sharing of the ups and downs of a whole bunch of efforts at a whole bunch of places to pull calculus out of the mire and into the present--one of the most cohesive bunches, I gather, of the many spawned by the "lean and lively calculus" movement. Cohesive, but not monolithic--that was one of my first discoveries. Most, but by no means all, are using Deborah Hughes-Hallett's Harvard Calculus text. Many, but certainly not all, have a heavy computer component. Collaborative learning plays some part in most, but what part varies quite a lot. The one universal attribute is that use of graphing calculators is taken as a given. On the other hand, even that doesn't mean that graphing calculators were held to be central, or that the use of them was anything like uniform.
Before the discussion of everybody's current state even got under way I found out about a past development that I immediately cashed in on: in the course of the four years, the group has put out two books (of the loose-leaf-to-go-in-a-notebook variety.) One is called The Washington Center Sourcebook for Revitalized Calculus, and is a tremendous compilation of teaching resources that have been tested out by the people who describe them. There are worksheets for in-class group work, and extended problems, projects and writing assignments for differential, integral and multivariate calculus, all neatly organized and laid out and ready to nab. Less of a tome, but likewise fascinating, is the more recent "Assessment in Reform Calculus", which describes a batch of non-standard formats different people have used in the attempt to gain some insight into what their students really do know. With suitable encouragement, I will put both of these volumes in some accessible spot and even tell you where they are.
I will not attempt a chronological summary of the discussions (heaven forfend!) Some, in fact, dealt with issues which I could say, with a sigh of relief, we don't have to face (notably a necessary heavy reliance on part-timers.) Others were questions which strike me hard every time, even though I know full well they are simply previous questions slightly re-phrased: how do we deal with the desire to add depth without losing "coverage"? How can we simultaneously serve well, in the same classroom, students who will never see another math course beyond this quarter and future math or science PhD's? For that matter, how can we serve well, in the same classroom, potential math PhD's and potential science PhD's? One of the participants remarked feelingly that he was attracted into mathematics by the sheer beauty of calculus, and it bothers him that that beauty is being buried in the heavy applications orientations. That discussion ended with a highly articulate plea that as a foundation to the decisions we all have to make, we as departments, and even more as an entire community, need to put some thought into just what mathematics is. What is it that we are trying to teach--globally, not locally?
And once we have taken care of that--well, all right, that was a bit high flown (I got carried away.) But I think there were some serious issues there, before my clarion call soared up out of human hearing range.
I came out with a lot of ideas jostling about in my head, and a great appreciation and admiration for the people who have been working at this for the past four years (also, I might add, for the Rainbow Lodge, which is a stupendous place for a retreat!) One notion is now most firmly rooted in my consciousness: when, in the cyclic nature of things, the moment arrives for us to assume lotus position and begin contemplating our calculus offerings, there's a batch of expertise right around us which it would be absolutely silly not to tap into.