Well, here we are-seniors, parents, faculty, members of the board and administration-dressed in our academic regalia ready to begin our celebration of graduation 2003 at Hobart and William Smith Colleges-clearly a joyful, momentous occasion for us all.
A month or so ago when I was invited by Mark Gearan and Lesley Adams to speak today I began to worry about what I would say-I knew I wanted to say something special, something that would be meaningful. After all, this is the Baccalaureate Ceremony, we're in historic Trinity Church-my address would have to be important, serious, profound. After several weeks of not finding the perfect theme, the message that was just right, I did what I tell my students not to do when they are stuck-I put the little I had written aside and ignored it.
But even as my notes became buried in the growing volume of papers and books on my desk, I could not stop thinking about all of the things I might say today and the theme of transitions kept popping up. This weekend we are celebrating an important step in the lives of graduating seniors. They face the transition from many years of school into "the real world"-whatever that is. This weekend also marks a rather significant transition for me, my retirement from the HWS faculty. I have worn many hats at the Colleges-first as a student in the early 70s, then as a member of the faculty and a parent of three HWS students. So my departure is especially significant for me. As I look back on more than three decades of memories, I know the Colleges will always have a special place in my heart.
Our departure gives us the opportunity to reflect back on our days at HWS and think about how we have changed and grown because of our experiences here. We can think about how the Colleges have prepared us for whatever lies ahead in our lives. This self-reflection is good because many times we are not aware that we have changed or grown. The day-to-day chores of being a student or faculty member leave us little time for self-reflection. I am always amazed at the workload of my students. They are not only busy doing the things students are supposed to do-writing papers, studying, going to class, keeping up with a tight schedule (which seems to become almost impossible by the end of each term). In addition, most are involved in activities outside of the classroom-with sports, community service, tutoring, working at a part-time job.
Sometimes it takes several years after graduation before students step back and realize that their liberal arts educations have given them skills that they find valuable in their lives and their careers. Over the years I have kept letters from former students and a number of new letters have come my way because of my retirement this year. In these our graduates have spoken about the value of the education they received at Hobart or William Smith. I would like to let their voices and the voices of other HWS graduates convey the message I want to share with you today-that all of us leave the Colleges well prepared for whatever lies ahead in our lives.
Before I begin, I want you to know that, because I am a professor in the sciences, the graduates I cite today were generally science majors or ones who took courses from me, so their comments are mostly directed at our department and my teaching. However, I know that each department and each member of the HWS faculty could present similar reports from their former students.
Without doubt students at any institution tend to undervalue their undergraduate experiences-until they leave the Colleges for graduate school or a job. Professor Carol Parish, of the chemistry department, received a copy of an e-mail written by a Hobart graduate who is currently a doctoral student in chemistry at the University of Buffalo. The purpose of his message was to give advice to a current chemistry major thinking about graduate schools. He wrote:
Of course, there are things that I complain about here (at UB), but that is always the case wherever you go. For what it's worth, I didn't think HWS was a great place to go to school until after I graduated and realized what a solid education I had received.
In addition, some of our students see no reason for some of the requirements in their majors or even the general curriculum. We call this the "When am I ever going to use this?" syndrome. Professor John Vaughn, a colleague in the math and computer science department, received an e-mail from a former CS major who had begun his first job as a computer programmer-a job he hoped would lead to the position of software engineer. While at Hobart, he had complained bitterly to anyone who would listen about the mathematics requirements which are a part of our computer science major.
Soon after he began his job, our student found himself at work one day sitting with a group of colleagues trying to solve a distributed computer network problem. In this group were people with impressive backgrounds, from much larger schools than HWS, who were much higher in the ranks of the company than he. As the conversation developed our student, seeing a connection between the problem at hand and material he had studied as an undergraduate, suggested: "This is just a matter of finding a spanning tree." And he was right. Of course, he had learned about spanning trees (a part of graph theory) in one of the math courses he had been required to take as a part of his major. He wrote to tell John that maybe the math requirements for CS students were a good idea after all.
Knowing facts and procedures about one's field of study is generally accepted as a basic result of a good education. Math majors should know about vector spaces and analysis, English majors about literature and writing, economic majors about macro- and microeconomics. However, as they leave college, many students aren't quite sure what they might do with the facts and procedures they learned as undergraduates. Therefore, when they become involved in a job or graduate school, they are pleased and excited to find a connection between their newly learned knowledge and "the real world."
For example, during the time my daughter, Kathleen, was working as an actuary for a large company in Manhattan, she found herself discussing business with another actuary from a company in Boston. It just happened that the woman in Boston had taken econometrics with Kathy when they were students at William Smith. Both were delighted with the fact that, several years after graduation, they found themselves discussing topics related to a course they had taken together as undergraduates.
I also believe that most students enter college to "learn things" -hopefully useful things. Although the example of our CS student suggests that it may take a while for graduates to distinguish between what will and what will not be useful. But in their letters and e-mails few, if any, former students selected content knowledge as the most important thing they brought away from their college experience. Instead they described the importance of being able to think for themselves, to think outside of the box-skills that they acquired as undergraduates at the Colleges.
A number of students enter college not knowing that they should and are able to think for themselves rather than simply memorize facts as they are presented in class. And for many, the transition from memorization to conceptual understanding is difficult. I have saved only one paper in my 25 years of teaching-one written by Rich, a first-year Hobart student who was in my Discovering in Mathematics class. I had given graph paper and scissors to my students and told them to cut out an 8 by 8 grid. They then cut the square into four pieces, and rearrange these pieces into a rectangle. The puzzle was that the rectangle had an area of 65 square units while the area of the original square was 64. The assignment was to write a paper about this "paradox."
What follows are portions of Rich's paper:
Where It Came From
I took a class with you this summer and you emphasized how the answer to a question is not as important as how you got it. You told us that math should be more thinking and less memorizing. You wanted us to explore and understand math concepts, not just memorize and forget. I had never met a teacher like you who had this style and you put me through Hell all summer. I would leave your class having to use my mind, because you never came right out and gave answers. I would still be thinking math well after the class was over. I had some terrible headaches that summer. Now I find the same thing happening all over again, sort of like deja-vous, what are you doing to me?
We took an 8x8 perfect square which had an area of 64 and bisected it twice. When we cut along the lines the square broke into four pieces. We then arranged the pieces into a perfect rectangle, which seemed harmless enough, but to my dismay the rectangle had an area of 65.
To me this was not logical at all because the pieces were still the same size. How can pieces from a 64 area be arranged to make a 65 area? The extra area could not have appeared out of nowhere.
Rich went on to solve the problem correctly and ended his paper with:
Once again I have to take my hat off to you. I found myself thinking about this dumb thing all the time, even at parties this weekend. You have a way of getting my mind going. I hated you at first for it, because I thought I was going to get another "D" and there was nothing I could do about it. I am not sure if my answer is the right one, but it satisfies me enough so that I can sleep at night and my headache is gone.
What made this wonderful paper even more exciting for me was the fact that Rich came into college doubting his ability to succeed. And yet, he wrote the most elegant, memorable paper I have seen in my career.
Thirteen years after graduation, Patti, one of my advisees from the class of 1990, wrote an exceptionally good description of her transition from memorizing to understanding. She also reflected on the value of this change not just for her job, but also the joy she felt when she took ownership of material.
Experiencing Math is the best phrase I have in explaining a math lesson by Professor Oaks. She taught through understanding, not memorization, and I was able to experience the concepts thoroughly. It has been many years, but I will always remember my jubilation when finally one day-it hit me. The concepts weren't for memorizing but actually made sense. Suddenly, I could figure out my own solutions, not because I had memorized formulas, but because I understood. It was fun. I still use (my problem-solving skills and) the simplest concepts that I learned to solve complex equations for analysis in my daily work.
The HWS experience forces, encourages, cajoles students like Rich and Patti into using their own minds-into making sense of the world, into not only understanding the ideas of others, but also into developing their own. The result is that our graduates are not only capable of solving unfamiliar problems, they have an added bonus of enjoying the process. My daughters, Kim and Kathy, and, Jamie, a member of your class of 2003, have a saying that they use when they think they have been clever about solving a difficult problem: It is: "See what a William Smith education will do for you." How right they are.
I want to end my talk today with another theme that has also been in my mind since I agreed to give this address today. Moments of joy-the times when we experience that wonderful glow of emotion of being truly happy. I am sure that this weekend our graduating seniors, their parents, teachers, deans and all of the other people who have supported them through the last four years will experience moments of joy.
My grandchildren give me many such moments-one of which occurred when my six-year old grandson, Peter, and I were out for lunch at the local pizza parlor. Pizza is Peter's favorite food and he was having a wonderful time as we carried on one of those conversations that can take place only between grandmothers and grandsons. Suddenly, he looked at me, face and shirt covered with tomato sauce, and said, "Grandma Ann, you're the greatest!" My heart sang.
But we can also experience moments of joy in our careers and in the everyday things we do. Andrew Wiles, a professor of mathematics at Princeton, comes to mind when I think of these joyous moments. Professor Wiles is the mathematician who finally proved Fermat's Last Theorem, a problem that had gone unsolved for more than 350 years. When he was interviewed for the NOVA program on his achievement, he cried with emotion as he described the process through which he solved the problem-a problem he started thinking about when he was 10 years old. This was an exceptional moment of joy for Dr. Wiles.
Because the HWS curriculum was designed to help you develop the motivation and skills needed to solve difficult problems, you can expect to experience your own moments of joy resulting from your own accomplishments. I have spent my career designing classroom experiences that will help my students grow conceptually. In fact, this has been the primary goal I have held as a teacher over these many years. I want to thank all of my students this year-from my Math 100 and Math 135 classes in the fall to the students in Multivariable Calculus and my problem-solving seminar this spring. You have provided me with many moments of joy as I watched you grow and succeed as mathematicians. You are wonderful students.
While we may not expect to achieve at the level of Andrew Wiles, we can all experience these wonderful moments during the course of our everyday lives, through our jobs, through relationships with people for whom we care, or through giving back to our community, whether in the village where we live or in the world community as a whole. Working to help others to improve their lives can also bring joy to you.
In closing, I wish you joy in everything you do. Stay curious and enthusiastic about your world; have a healthy and productive life; and write once in a while - we will miss you.
"Transitions and Moments of Joy," Ann B. Oaks, professor of mathematics
Baccalaureate Address, May 11, 2003