Reflections on Teaching
by Kenneth W. Wachter
Distinguished Teaching Award Ceremony, Division of Social Sciences, UC Berkeley
12 October 2002
It has been suggested that if my poodle puppy Ambrose had submitted a teaching evaluation, I would not be getting this award.
What I do especially is help students toward a sense of comfort with mathematics, using it on humans, learning to quantify the demographic prospects of their own lives, graduation, marriage, childbirth, survival, and to quantify the changing state of the very peopled world we live in.
I've been helped by my wife Bernadette and by so many of my students, colleagues, and outstanding graduate student instructors here with me today.
What often lasts, we know, is not the subject or the skills we teach, but what slips in during the asides -- symbols, traditions, values -- and the classroom rhythms of discouragement and discovery, return, reviewing, revisiting, revising. Some hard-to-pin-down part of teaching is liturgical.
Notes on Teaching, 1993
The courses that I teach most often, demographic methods and statistical analysis, are nobody's idea of inherently fascinating subjects. My students take them because they need the skills or the units or jobs down the line. In a demography course, at least the math is about humans. But it isn't what you choose for pleasure.
We were working once, I remember, through some grueling calculations with lifetables -- tables that show probabilities of dying or surviving from age to age. I was trying to be cheery and enthusiastic. Later one of my students, Robert, said,
``Do you know what you remind me of ?''
``From Latin class. Aeneas telling his tired hungry sailors, `Don't mind. Some day even this will be fun to look back on.' ''
I remember. I had to memorize that line too in Latin class. Memorizing Virgil. Now it's even fun to look back on.
A moment later, I'm thinking to myself, Robert's just done for me what I am always hoping to do as a teacher : Suddenly, out of the blue, making connections.
Not all connections that come in the process of teaching and learning come suddenly out of the blue, of course. Mathematical formulas, for instance, when you look at them, often connect up slowly and logically with something very familiar in some other part of life. One of the things my teaching is about is helping people who are rusty or anxious about mathematics use mathematics. This is now a priority for schools and universities, and there are good new ideas about how to do it, which I try to use. Many of these ideas come down, in the end, to making connections or to listening for connections.
I feel the best idea for overcoming math anxiety and any ``gender gap'' in math anxiety is in fostering teamwork. My statistical research is mostly teamwork. I want to recreate that real research setting in courses. I coteach one course with Gene Hammel in Demography in which we divide into teams. Each team creates a census of an artificial population using the computer, building in secret relationships between education, race, income, kinship, marriage, and fertility for the other team to uncover with our statistical techniques. Working together as teammates, we don't get stopped by stuff that seems to stop us on our own.
Some of the students from my courses, a few years later, are making their own way deeper into the mathematics of human population dynamics, population cycles and population randomness. At that point, what being a teacher requires from me is mostly listening, and the joy of it with my Berkeley students is hearing five ideas spring out of the one idea of a minute before.
The main useful fact I know about classroom teaching I heard from my statistician friend Fred Mosteller. Some people learn best with their eyes by seeing words and equations appear on the blackboard. Others learn best with their ears, hearing me repeat. Others learn by the motion of copying things down; others with their voices, by saying it back. Each person is different. Make every point I make in all four ways!
Another idea is the importance of cycling back. On the first day of my methods class I talk about a crude model for a kind of rapid population growth called ``exponential growth''. Periodically in the course I try to come back to exponential growth, each time with a more sophisticated, realistic model. Quite apart from the subject matter, we need this rhythm of return, reviewing, revisiting, revising. Some hard-to-pin-down part of teaching is liturgical.
Each person is different. There is an accepted idea that teachers instinctively care about each and every student. I don't find it that way. I come to care about my students over time, as I get to know who they are, who I can joke with over a wrong answer, who needs space and a stretch of silence before she speaks up and says that this equation is about overlapping generations like her own family. Caring isn't automatic. It grows in a process of personalization.
I have been very lucky in my courses to have as my assistants students who care a lot about the people in the courses and give a lot of themselves. This makes a big difference.
I work out the first lifetable example in my methods course with the mortality histories of some characters in Shakespeare's plays. Students have told me that they like it. It also takes me back to when my high school English teacher George Moffat had us act out scenes from Shakespeare, picking the speeches for each of us from what he knew or tuned into of our own hang-ups and hopes. That was good teaching. That's what I want to do.
At the end of my methods course we come back to lifetables. Lifetables may seem remote and technical, but they measure things that are very personal. How many of those born with us in our birth years haven't made it to college ages? How many of our parents are living now past 80 or past 90, beyond their dreams? How many of us will live beyond 100? My students, and me with them, as we live from each year to the next, are living a lifetable. It's funny to think about. But there it is. What's out there on the blackboard is in here in our lives.
That came home to me all of a sudden one year when my students gave me a present. It was a paperback picture-book of children's rhymes, The Favershams:
One day in eighteen fifty-one
These parents posed beside their son.
The son (that's him inside the pram)
Was Charles Augustus Faversham,
And now this book relates the life
Of Charles Augustus and his wife ...
The book takes Charles and Gwen from birth through school and work and courtship and marriage and war and childbearing and childrearing and retirement out to the end of life in two-dozen pictures. My students had marked each picture in this kids' version of Everyman with a formula from our class and had pasted on a subtitle, ``A Book on Lifetables.'' Yes!
Why was it fun, after all, for Aeneas' sailors to look back on being sea-worn and hungry together? Surely, because it was together. Berkeley is the same way. For me, the fun of teaching and learning is the joy of being in it together. Making connections with ideas is a special form of making connections between people.
Ken Wachter and his award
Ken Wachter, family and friends