Thursday, June 02, 2005

Freshman Advising (and Peak Calculus)

In some ways, advising is like a version of that game telephone. The math department needs to say things to the advisors that they will hear, believe, and repeat accurately. Today I went to advisor training with the person giving the math spiel; I'll be taking over her tasks as of August 1, so I'm sort of tagging along with her as she does things this summer. I also talked a little bit about some of our courses. Next time I will need to prepare more specific talking points. Somehow I need to bring up the idea that there isn't an absolute measure of "easiness" in terms of math classes: one student might find math 112 harder than math 116, but another student might find math 116 easier.

I've also found myself wondering about the origins and history of the term "freshman calculus." Until a few years ago, this term had a sort of biconditional connotation for me: In one direction (and this still holds, to some extent), that this was a calculus class suitable for freshmen -- mainly computational (possibly including "hard" problems) and with relatively few proofs. And, conversely, there was a sort of hidden assumption that this was the standard math class for freshmen to take.

This second direction is obviously not true in general: only a small fraction of freshmen here are even allowed to take calculus. But I wasn't always aware of this situation. When I was at Dartmouth, the lowest level general-admission math class was calculus. (There was also a by-invitation-only version, slow calculus.) Even at UCSD, most of the freshmen took calculus. The number of sections of pre-calc was extremely small compared to the number of sections of calculus. And when my parents were in college in the late 1960s (SUNYA and the University of Rochester), I'm pretty sure that the standard freshman math class was calculus.

Obviously this couldn't have always been the case (see, for example, the early history of the Dartmouth College math department). And now even schools like Dartmouth (I'm told) are adding courses below calculus to their math curriculum. So I'm wondering: to what extent has my assumption been true? During what time periods and at what types of institutions was it assumed that freshmen could (and would) take calculus? And how has this changed? (A lame pun about calculus and "change" is left as an exercise to the reader.) A search of MathSciNet for MSC codes 01 (history/biography) and 97 (math education) has turned up nothing. What is the history of freshman calculus?