## The Good Old Days

[From AMS, courtesy of Alan Tucker]

I received my copy of the latest American Mathematical Monthly today. The Monthly is a publication of the Mathematical Association of America, which describes itself as “the largest professional society that focuses on mathematics accessible at the undergraduate level.” (They complement the American Mathematical Society, whose mission is to “further the interests of mathematical research and scholarship.”)

An article in the new Monthly caught my eye, Alan Tucker’s “The History of the Undergraduate Program in Mathematics in the United States.” This is not likely to interest you as much as me, so you may not be too disappointed to learn that for non-members it sits behind a pay wall, available at JSTOR for $12. Thus you’re likely to miss out on the following paragraph:

In the early 1950s faculty at many leading research departments still saw teaching as their primary mission. Even senior administrators often taught two courses per semester. When my father, A. W. Tucker, was chair of the Princeton mathematics department in the 1950s, not only did he have the same teaching load as other senior faculty, but every other semester he was also in charge of the freshman calculus course taken by almost all students. When I questioned him years later why he took on this huge extra obligation, he responded, “The most important thing that the Princeton Mathematics Department did was teach freshman calculus and so it was obvious that as chair, I should lead that effort.”

Just as well. I wouldn’t want you to get any crazy ideas.

(It may be useful to explain that at many large research universities, including mine, the math department chair has no teaching obligations.)

## Saucepan Reasoning

Two weeks ago, I wrote again post about the edible idiom feature at Clotilde Dusoulier’s blog Chocolate & Zucchini, in which she discusses a French idiom related in some way to food or cooking. Once more I can’t resist writing about her latest, which this week is “Raisonner comme une casserole.” Clotilde offers the translation “reasoning like a saucepan” and the explanation that “it means demonstrating poor logic, formulating arguments that are evidently flawed. It is a colloquial expression that should only be used in informal conversation.” She goes on to reveal the underlying pun, which becomes merely a near-pun in English:

It’s not hard to imagine that debating philosophical matters with a saucepan would lead you nowhere, but there is actually a little more to this idiom than that: it is in fact a pun that plays upon two homophonous verbs,

raisonner, which means to reason, andrésonner, which means to resound. So when you say, “il raisonne comme une casserole,” it is really a double entendre, meaning that the person has as much sense as a saucepan, but also implying that if you banged him on the head, it would likely echo.

I should explain that I may have been particularly charmed by this expression because I graded the last homework assignment and the final exams for my spring quarter course in the two days before Clotilde’s post appeared. The course is named *Introduction to Mathematical Reasoning*. It is intended to prepare students who have taken our standard lower-level math courses (calculus, linear algebra, differential equations) for the more rigorous courses that lie ahead. I had something to do with the department’s decision to introduce this course a decade ago, but by the time we started offering it, I had begun my multi-year teaching hiatus. Now that I’m back in the classroom, teaching it seemed like a good idea.

I would prefer to adhere to my general policy of not discussing my teaching experiences here at ronsview. I’ll restrict myself to two points. First, I’ve been humbled by the discovery (or, really, re-discovery) of how hard it is to teach reasoning. Second, I’ve had the opportunity to hear a lot of saucepan reasoning. My ears are still resounding.

## Preparation vs. Winging It

In an earlier post, I described my worst recurring dream: I am standing in front of a classroom of students without having prepared for class. I know in general terms what topic I’m supposed to cover, but haven’t thought about it and have no idea what to say. What brought this nightmare to my consciousness was the experience of watching Katie Couric interview Sarah Palin.

One thing I learned as a student was that it wasn’t always a bad thing to have an instructor who was not fully prepared. How the instructor deals with the situation can be enlightening. The student gets to see how an expert on the subject works through the issues spontaneously, thereby (on occasion anyway) learning a lot more than might be learned from a perfect exposition with all the real thinking hidden from view. And the student gets to see how an older adult handles real-life stress.

I had an eye-opening experience along these lines in December 1969, the first semester of my freshman year at Harvard. I will describe it below, but first let me give some background on the nutty course I was taking, Math 55. To provide the proper context, I need to say a few words about calculus. Read more…

## Bad Dreams

Each of us must be plagued by certain families of recurring dreams, dreams we are happily free of until the next time we awaken from one of them. For me, there are the elevator dreams, the low-flying-airplane dreams, and perhaps worst, the not-prepared-to-teach dreams.

Mind you, thanks to a variety of administrative jobs, I haven’t taught a regular class in years (though that will change soon). But I remain shaken by dreams in which I find myself in front of a class of math students with no idea what I’m supposed to cover that day. There is no better feeling than waking up to realize that I don’t actually have to teach, that I can escape the humiliating experience of standing in front of a group of people with no idea what I’m doing.

Maybe Sarah Palin is hoping she will awaken with similar relief. “No, John McCain didn’t really ask me to be his vice-presidential running mate.” Or, “No, I didn’t really say yes when I was asked.” I do wonder how she feels.

One thing about mathematics: you can’t fake it. The subject is unforgiving. If you have a statement you wish to prove, either you have a proof or you don’t. And if you don’t, saying everything you can think of that is germane is no substitute for a proof. Sometimes silence really is golden. (I don’t mean to suggest that it’s a bad thing to state everything you can think of as part of the process of searching for a proof. But searching for a proof is not the same as having a proof, and it is important to know the difference.)