Implications for Teacher Preparation from MathScape

I would like to start with an anecdote about a significant experience in my own background as an undergraduate math major headed for a career in teaching. The anecdote illustrates one of the key elements necessary for the preparation of mathematics teachers who will be implementing new curricula. Headed for a career in teaching, I took a Number Theory course from David Burton at the University of New Hampshire. Beginning the second day of class, we were asked to write homework solutions on the board for the class to discuss. During the first week, few volunteers were forthcoming so Dr. Burton drafted “volunteers.” Reluctantly, we would slink up to the board, write out our answer and sit back down hoping there was little to criticize in our work. To my surprise and delight, Dr. Burton did not focus on criticism, but instead asked us to explain what we had done and then asked the rest of the class what they thought about the response. Invariably, a discussion of mathematics would ensue. Our responses were viewed as work in progress, and over the first few weeks, Dr. Burton built an atmosphere in the classroom in which it was acceptable and safe to work with incomplete ideas, to be confused (and even wrong) because that was part of learning to think about number theory. I finally had something to contribute to the creation of the mathematics we were doing. We became a small community of mathematicians, doing number theory, and it was rich, exciting and fun. By the end of the course, my classmates and I were no longer slinking up to the board. Instead, we were enthusiastically volunteering to write up problems with which we had struggled because class had become a place to think about and explore mathematics.