April 28, 1996
I started at Auburn in the summer of 1965. I majored in mathematics because I wanted a good basic education more than for any other reason, and I felt this curriculum offered that: it had good strong courses in languages, history, philosophy, literature, and the social sciences, as well as a lot of mathematics and science courses. I liked math by then, and I did well in it and tested well in it, but it didn't particularly "turn me on." In the middle of my sophomore year (winter quarter, 1967), I took my first post-calculus course. At that time I was actually considering picking another major--I had made all A's in my calculus courses, but I could basically spend a few hours a week a week doing the homework to keep up, and I just didn't find it all that interesting. The foreign languages and literature courses I had taken seemed much more exciting.
I had been told by various students at that time that I was going to "hate" the upper level courses, and that they were taught "funny" here at Auburn. I had no idea what "funny" meant, but I sure intended to find out. Within one week of beginning that first upper level course (introductory algebra taught by Bill Transue), I knew that this was what I wanted to do. "Funny" meant that instead of lecturing and assigning homework, the professor started day one with a list of definitions, theorems, exercises, and questions. We were told to go home and start working through this list. We were not to use books, old notes, nor consult with other students. When we returned to class, individual students would be called on to go to the board and present those proofs, answers, solutions and he/she had been able to provide in the intervening time. This is interesting, I though. I went right home and got to work.
I went right home and got to work. That statement in itself is extraordinary: in other courses I had always, if I could possibly get away with it, done everything at the last minute. I was a pro at all night cram sessions and could get my A's with no problem that way--with the exception of Mrs. Faulk's classical lit class. I continued to go right home and get to work throughout the quarter. I loved going to class, but I couldn't wait until it was over so that I could go back and work on my "theorems" some more. (Somehow the concept of proof has never been difficult for me--I just knew what that meant and if I was ever "taught" it, it was when I took geometry in high school.) Suddenly mathematics went from being something mildly interesting, but rather dry and dull, to being alive. I was involved with the material and challenged by it. I was "in love" and I still am now, 30 years later. I was pathetically shy and withdrawn at that time in my life, and one would think the requirement that I go to the board and present my results to the class would have been a problem for me, but it wasn't. I could work everything out when I was alone and could think deeply, write it all down carefully, and then go to the board, write it all out, and explain and defend it. I was proud of what I could do. I felt like a duckling who had been raised with the chickens and had somehow finally stumbled onto a pond. I just took to it.
After that, I never voluntarily took a math course given in any way but the "funny" way. I later learned that this was called the Moore method, or the Texas method. Spring quarter of that year I took the second quarter introductory algebra course from Jo Heath. The next year I took introductory analysis from Ralph Bennett. (Here again I had been told, "Well, ok, so you did all right in the algebra courses. The analysis sequence is much harder though. You'll definitely hate it." The moral of this story: don't listen to what people tell you. I liked analysis better than algebra.) When courses were only offered in the more traditional lecture style, I had no choice but to take them. I didn't enjoy any of them, and don't remember now anything I learned in them, although my grades were fine.
I never got around to applying to graduate school anywhere but Auburn. (It had only a one page application form, and even I, the ultimate procrastinator, could handle that.) I had no idea that the way mathematics was taught at Auburn was truly unique. In hindsight, even though I know now that a person isn't really supposed to go to graduate school at the same institution as the undergraduate, I believe Auburn was a good choice for me. I started with real analysis (Ralph Ford), topology (Phil Zenor), and algebra (Dick Ball--not Moore method). I liked topology even better than analysis, and I eventually wrote my thesis in topology under the direction of Ben Fitzpatrick, Jr. I still consider myself a topologist, even though now I have strong interests in dynamical systems, too. (The topology of dynamical systems is what I am now doing. Please note: the topology of dynamical systems is not topological dynamics.) Through the years, I took many topology courses (from Phil Zenor, Ben Fitzpatrick, an dJo Heath), two courses in complex analysis (from Ralph Ford and Bill Transue), for or so quarters of real analysis (Ralph Ford), and two courses in ring theory (Jo Heath). After the algebra sequence from Dick Ball, I never took a regular lecture course again.
After taking courses by the Moore method, regular lecture courses seemed awful to me. I could hardly stay interested enough to keep up with the material. I doubt that I ever would have gotten my Ph.D. had I not been taught the way I was. Lecture for me turns something that is alive, creative, and incredible into something dry and boring. I am there in the class to be poured information into something dry and boring. I am there in the class to be poured information into, not there to produce anything myself. I like the hands on approach much better. I learned very early that anyone the ed majors (most of those folks giving me all the lovely advice about math courses) thought was a good professor I should avoid like the plague. They preferred someone who watered material down, put it through a blender, and turned it into baby food. They said such a professor "explained the material clearly." I'm talking about the kind of professor who would probably have won then and would still win now a teaching award in the math department, were one been offered. And the kind of professor who would have been very bad for me.
Something else happened to me at Auburn that I suspect is fairly unique to my own situation. I have this rather fierce, nontrivial mother who was and is, to put it bluntly, emotionally abusive. This was particularly true during my very awkward adolescence. I think I have finally made my peace with all that. My mother has a lot to do with both what is good about me and what is not so good. She certainly wasn't ordinary and she didn't produce ordinary children. However, my personality at the time I finally left home for college (ten whole days after graduating from high school--and I have not been back for any longer period than was absolutely necessary) was in tatters. The way I was treated at Auburn helped me start putting myself together. I'm sure none of my professors had any idea that anything like this was happening, nor did I myself.
Being taught by the Moore method means being treated with respect. The professor has, after all, made the students largely responsible for their own learning. He serves only as a guide. They must get actively involved and they must produce something. It is implicit in the whole approach that the professor believes the students have enough sense to be able to do this. After many years of being treated this way, in class after class, and feeling that I was valued as a human being for the first time in my life, that people actually thought I had something valuable to contribute, I began crawling out of my shell.
Another nice feature of the Auburn math department was the way that the department and graduate students got together on a regular basis for socializing. (This took the form of "War Eagles" at a local pub, picnics at Miss Emilie's and many other parties at the homes of various professors and students.) From the time I started as a graduate student, I was invited to participate. It took three years, many questions about why I didn't attend, many excuses on my part, before I finally gave up and went to one of those dreaded picnics. To my absolute amazement, after drinking a fair quantity of beer to anesthetize myself, I looked around and I found I was having fun. This had never happened before. Anytime I had to be around people on a social basis, I just wanted to get it over with as quickly as possible. This was different. I saw that everyone there was a little "different" from the usual average student I had always failed to be, and nobody seemed to mind. Being a little weird was ok. In fact, nobody seemed weird, they just seemed interesting. Another epiphany for me! There does exist in this world a group of people I feel comfortable with--they are called mathematicians.
I got my Ph.D. in the summer of 1975. A few days later I got married, knowing then I would be going to Columbia for several years with my husband, an assistant professor in the fisheries department. I had wanted to be a researcher since I was twelve years old (although I didn't pick a field to do research in until that first post-calculus course at Auburn). I had also wanted to have a family. For me, these two desires turned to be somewhat in conflict, unfortunately. I never managed the family part, and the marriage didn't work out. I'm not sorry my marriage happened, nor am I sorry South America happened. It was all a part of my life and a part of my education, and I wouldn't trade it. It did slow me down professionally though. It also probably has a lot to do with why I have been as successful as I have been. I was mostly miserable while I was down there, and I thought a lot about my life, what was important to me, and what constructive action I could take to make my future not miserable. I decided that doing mathematics was important to me, and that I would work on mathematics. I decided I was either going to do research or die trying. It is amazing how much it is possible to do when this much feeling and stubbornness is involved. I didn't die--I did write a couple of papers while I was there--the first results since my dissertation work. when I got back, I was lucky enough to become an instructor at Auburn. The rest is outlined in my vita. It was so hard to get up the nerve to really try--it was so hard for me to believe that I could do it, and that I wasn't just being ridiculously silly. When I finally did get a paper written, it was even hard to get up the nerve to submit it. I mean, who did I think I was anyway? But I did.
In retrospect, how effective do I feel my education was? On the whole, I feel that it has served me well. It has much to do with my being able to do something about my situation when I was in Colombia, and not just being helpless. Given the person I was, I don't think any learning approach would have been better. It gave me a deep, basic confidence in myself about what I was capable of doing that I could build on. It is true that when I graduated, I didn't know so many "facts," but I have never found this to be a terrible problem. It seems to me that part of the deal with doing research is that a person has to keep learning in order to keep up with a changing world. When I don't know something and I need to know it, I find some way to make myself learn (such as--teach a class, referee a paper, give a seminar, start a new problem about which I know nothing and have to read papers to understand what I am doing). I have had to learn more than most young Ph..D's have, but some of them don't seem to have realized that it is not possible to be "finished" with one's education, that one has to prove oneself even if one does have a degree from Berkeley or Princeton, and at some point, whether one has performed adequately after that degree is what matters. There always was a part of me that was totally independent and stubborn. There was always a lot going on in my mind, but I'm sure no one would have believed that until I was well into graduate school. (One girl in my freshman dorm described me as "the one with no personality.") It took Auburn to bring all that out. In some ways I am almost fearless (in that when I am sitting alone thinking about mathematics, I am quite willing to tackle just about any problem that interests me) and I believe my education is the source of this.
When the Unabomber was arrested, and it turned out he had been a mathematician, one of my first thoughts was, "there but for the grace of God (and that Auburn math department) go I." I am not kidding, although I don't think I ever would have been violent. But what if I had never found a way to start healing?
What would my life have been like? I don't even want to imagine that. Maybe the Unabomber would have been better off at Auburn than he was at Harvard and Michigan. In the education world, much attention is paid to those students who have problems learning mathematics. Not much is paid at all to the bright students--it is just felt that they will do ok no matter what. I don't think that is true. My mathematics education at Auburn was clearly aimed at the good, hard-working, creative, nonpassive students, and it clearly valued those students, and I am thankful for that.
I have not had many opportunities for using the Moore method myself. It is "out of fashion" presently, and I usually have to worry about covering the syllabus. I would use it more often if I felt I could. I have used it to teach our introduction-to-rigor course here at Delaware, with varying degrees of success. That is an ideal course for it: not only is it designed to bridge the gap between the first elementary, largely computation courses to those more abstract, rigorous math courses, but it also is the only course we offer where how much material is covered is not so important. It works quite well with the bright students, not so well with those not so capable. However, these kids need to have some idea at this point whether they have any real talent for mathematics, and I don't feel so bad about those who don't perform so well. Our students come into the course having no idea what a proof is though--the high school geometry course has apparently been modified so that those "proofs" that "nobody can understand" are gone (I wonder what brilliant educator came up with this one), and the little rigor that used to be done in calculus has been removed ("too hard for them"). Thus, our students come into this course with absolutely no clue about what mathematics really is.
This past summer I taught an REU (research experience for undergraduates) course at Carleton College in Minnesota. The program was one month long, and the attendees were sophomore level women interested in pursuing advanced degrees in mathematics. Eighteen students selected from 120 applicants came from all over the country. I used the Moore method here, and I thought it was quite successful. Again, I was in a situation where the students were exceptionally bright and motivated, and what or how much material I covered was not nearly so important as helping these young women learn about the process involved. My materials from that course, including the evaluations the students gave at the end are included. That experience was by far the most satisfying teaching experience I have ever had.