Project NExT is an MAA professional development program for undergraduate professors who have recently acquired a Ph.D. You can recognize a Project NExT fellow at any MAA national meeting by the colored dot on his or her nametag. When I learned in spring of last year that I had been accepted as a NExT fellow, I speculated that the award might be little more than a feather in my cap (and an orange dot on my nametag). It is no exaggeration, however, to state that my experiences as an orange dot fundamentally changed my approach to teaching. I am grateful for the chance to tell the stories of two professors who spoke to us and inspired me to change.
Thomas Banchoff of Brown University demonstrated the online system he uses to collect and respond to homework. Programmed by his undergraduate students, this system informs Dr. Banchoff when a student has posted the answer to a homework problem, allows him to reply to the student’s work, notifies the student, and so on. Once a certain deadline has passed, the system releases these discussions for public view. Like many professors, I have on occasion allowed students to rewrite their homeworks, hoping that the dialogue thus created will benefit the students in a way that the simple “here is your paper with my comments” model cannot. Dr. Banchoff’s approach, however, takes the dialogue approach even further by moving it into the public forum.
Since hearing his presentation a year ago, I have experimented with Dr. Banchoff’s idea in two classes. In a special topics class on the constants ø, π, e and i, my students posted their homework answers in a shared folder, accessible to all. Because I did not have software that would unlock the answers at a given time, the students were able to view answers that were posted before the deadline. Thus, I asked them to give each other credit every time credit was due — e.g., “I was stuck, but saw how Shawna factored the polynomial to get started, so I used that idea to finish the problem myself.” If a student made a mistake, I replied in the shared folder, and expected a response. At the end of the year, the students’ evaluations of the course included only positive reactions to this approach.
This past semester, I team-taught a course in advanced logic that met once a week. My colleague from philosophy and I chose an article each week (e.g., “Computing Machinery and Intelligence” by Alan Turing) and asked the students to read it at least once during the next two days. While reading, they were to formulate a list of questions that were raised by the material, then choose one and post it to a shared folder. Later, after having read the article more carefully and discussing it in class, they each were to choose another student’s question and respond to it with an essay. All of this discourse was public to the rest of the class; a general shared folder collected whatever discussion spilled over — further questions, links to websites, and so on.
The second professor, sarah-marie belcastro of Xavier University, surprised the orange dot crowd with her approach to teaching, an approach I like so much that I plan to teach over half of my classes next year in her style. During her presentation she said, “If all we want is to convey information to our students, we might as well just read a text to them, and in that case, they might as well just read the text themselves.” I think that statement is perfectly well put, and I could not agree more.
A month after hearing her speak, I taught a real analysis class with her approach. We read Elements of Real Analysis by David Sprecher page by page; at the start of each class, I asked who had written questions into their reading journal, and what the questions were. Usually, other students answered these questions, and occasionally I suggested my own answers. Every now and then, none of us knew what to say, and we spent the class puzzling out the answer on the whiteboard. There is still one proof in chapter 8 that none of us can explain! Once again, the student evaluations were all positive, and one bright physics student points to that experience as the reason why he is applying to graduate school next year not in physics, but in mathematics.
These are by no means the only pedagogical impacts that Project NExT had on me. My attitudes toward both undergraduate research and my own research, for example, have also changed greatly. Consider this my thank you to an undertaking that has affected me profoundly, and an encouragement to you to let your new colleagues know about Project NExT. You can find out more at http://archives.math.utk.edu/projnext/.
Dave Perkins is an assistant professor of mathematics at Houghton College in western New York. He is particularly interested in discrete mathematics. His email address is david.perkins@houghton.edu.