Mathematics professor Dan Kalman wants to change the status quo of high school math teacher training. “There’s a tradition in this country that you should take somebody who’s going to be a high school math teacher and push them as far into math curriculum of the college or university as possible,” he says. “But in some ways, that’s a wrong-headed approach.”
His book, Uncommon Mathematical Excursions: Polynomia and Related Realms, covers topics that would not typically be addressed in the standard math curriculum from sophomore year of high school up through the second year of college but are very closely related to that curriculum. Kalman got the idea for the book when he and a colleague were discussing secondary education and the preparation of the next generation of math teachers. Their conversations, and later the book, centered around the question, “What would it mean for somebody to have very deep content knowledge of mathematics, but focused on the mathematics you actually see in secondary school?”
Kalman describes the book using the metaphor of a travel guide. On a first or second visit to France, you would go to the major sites like the Eiffel Tower. But on your sixth or seventh trip, you might want to see some of the lesser-known, yet still important, attractions that contribute to your overall appreciation of France, but that the first- and second-time visitors wouldn’t see. “The whole book is set up as if you were a long-time visitor, let’s say to the study of polynomials in high school mathematics. You’ve made the trip along this highway ten times,” says Kalman. “Now let’s take some exits off the highway and see some other things that are nearby that are pretty interesting.”
Current high school math teacher training dictates going as far as possible in college mathematics, then only teaching high school-level math. During those first few years, “you’re focusing on a much smaller part of the curriculum repeatedly,” says Kalman. “After the first few years, you know that information backwards and forwards. Meanwhile, this information you learned in your advanced math courses is fading into nothingness.”
This kind of training can backfire when it comes to answering questions in the classroom. “A person that only knows one way of doing things, that only has the most direct route from A to B, has much less to draw on when trying to teach students who find that that one explanation is not illuminating or motivating,” Kalman explains.
While Kalman acknowledges that there’s not enough time to cover every topic in high school math classes, he considers the topics in his book a kind of refresher for current or future high school math teachers. “They are topics that a person who’s preparing to teach high school could profitably look at, find intrinsically interesting, and make connections back to topics they’re actually going to be teaching,” he says.
He spent his sabbatical working on the book, though his original plan was to work with a colleague at Montana State University to create curricular materials for professional development. But that doesn’t mean he’s changed his mind about wanting to alter how math teachers are trained. “The model I’m envisioning for secondary education professional development is that you want to entice people to come back into the classroom, go online, or to read on their own about mathematical topics that extend what they know,” says Kalman. “It wouldn’t just focus directly on the curriculum.”
His publisher, the Mathematical Association of America (MAA), awards the Beckenbach Book Prize to authors of a distinguished, innovative book that they’ve published. The award is not given out annually, but only when the MAA decides that a book is deserving of the prize. Kalman counts many Beckenbach winners among his favorites.
On January 5, Kalman was given the 2011 Beckenbach Book Prize for Uncommon Mathematical Excursions. He’s clearly humbled by the honor. “When I look at the other books that have received this award and I contemplate the fact that they’re now giving it to me, I can’t believe it,” he says. “I can’t imagine something that could be more validating or give me a greater sense of accomplishment than to have my work recognized in this way.”