MAA Focus — August/September 2013
Math, Medics, and Metaphor
For a meeting about mathematics, the Legacy of R. L. Moore Conference included a lot of talk about language.
And it wasn’t just Ruthmae Sears (University of South Florida) stressing the need to “orchestrate the discourse” in high school math classes to provide opportunities to engage with proof or Ryan Gantner (St. John Fisher College) mentioning the importance of good writing as he described a course in which students analyze games like Nim.
No. In the first plenary of the conference, G. Edgar Parker (Guilford College) advocated including in math classes exercises traditionally part of the language arts curriculum. He has his students examine “sentences that they find in the wild.” They dissect and diagram these artifacts of English, disentangling grammar from semantics.
More so than traditional approaches, inquiry-based learning (IBL) requires students to communicate mathematics, to explain at the board or in writing how they arrived at a solution and how they know that it is correct. In an IBL classroom, a student’s inability to verbalize mathematics casts doubt on his or her conceptual understanding of it; command of natural language is key.
That said, Parker cautioned against importing into math classes one literary device familiar from high school English: metaphor. A linguistic shorthand, metaphor in the mouth of a student runs the risk of masking underlying misunderstandings.
“Metaphors are great for having ideas,” Parker said. “Mathematics is great for validating ideas.”
Brian Katz (Augustana College), however, regards metaphors as useful for characterizing the role of the IBL teacher.
“I used to think that my students and I were . . . in the trenches together,” Katz recalled during his five-minute talk. “They sort of wanted to think of me as their commander, but I was really more of the medic.”
But even casting himself as support staff didn’t sell Katz on the battlefield comparison. Although he liked what it implied about the intensity of the classroom experience, he didn’t want to think of his students as fighting mathematics.
He rejected another metaphor—in which students are wild horses and the instructor a corral— because a teacher should guide rather than restrict.
Eventually Katz began pondering what would happen if he were a landscape architect and his students pebbles.
“I design the layout and they would roll because it would seem the natural thing to do,” he said.
Though the landscape architect metaphor communicates the idea that an IBL instructor sets up for students—largely unbeknownst to them—an environment in which the desired behavior—internalizing mathematics—comes naturally, it too has its problematic aspects. Pebble students aren’t consciously doing hard work, for example.
So the quest for the perfect metaphor continues, and Katz must appeal to different metaphors to illuminate different angles of the IBL dynamic.
He credits his colleague Katy Hanson with co-opting for educational purposes a “me and my shadow” metaphor from Peter Pan. Talking about what his shadow is doing allows Katz to provide his students insight into the how and why of his nonstandard teaching methods.
Given this glimpse of his pedagogy, Katz’s students have come to appreciate the centrality of communication to his philosophy of teaching and learning. They don’t conceive of Katz as merely a mathematician. Recognizing that their professor is master of more than numbers and geometric figures, they think that “word ninja” more accurately captures what he does as a seasoned practitioner of IBL.
As Katz put it: “I can hone language into an extremely powerful and focused tool.”
Got an Idea??
The MAA Committee on Short Courses is looking for the next great idea for a short course to be offered at MAA MathFest or the Joint Mathematics Meetings. And, once you’ve got that great idea, we urge you to turn it into a proposal! Guidelines and deadlines can be found at maa.org/node/119904.
-We are especially interested in proposals for an MAA Short Course for MAA MathFest 2014 and beyond, which will be reviewed by the committee in January 2014.
-Questions? Contact the committee chair, Jennifer Galovich, at email@example.com.