Socratic mathematic

American students may lag behind in math and science, but Professor Dan Hurwitz is part of the solution. A pub- lished scholar in math (specializing in geometric group theory) and also math education, Hurwitz won Skidmore’s Ciancio Teaching Award this year for making math classes fun, productive, relevant, and philosophically engaging. There’s been a longstanding misper- ception, he argues, about math and sci- ence learning. “More than facts and num- bers, math is really all about reasoning and problem-solving. The answer isn’t as crucial as how you arrived at it. It’s about understanding the question and learning to value that process.” As a consultant and workshop facilitator on mathemati- cal inquiry for the Center for Initiatives in Pre-College Education, area school dis- tricts, and other groups, he has coached hundreds of teachers (and education- studies majors at Skidmore) to incor - porate laboratory-style, inquiry-based pedagogies in math classes. In a 200-level course recently, he en- gaged students in a variety of exercises and proofs. The arithmetic was simple; it was the patterns and logic that he was ex- ploring, leading stu- dents to discover some surprises and new ap- plications of concepts.

He handed out grid-based puzzles, offer- ing, “If you don’t like this one, here’s a different one to play with.” For an aside, he drew on Gulliver’s Travels: “If Gulliver is, say, 6 feet tall and weighs 180 pounds, then a 1-foot-tall Lilliputian must weigh 30 pounds, right? Of course not! Because weight is a function of what? Volume, not height, that’s right. We’d need to know the volume of a Lilliputian.” Using the principle of mathematical induction for proving a formula in binary code—

MATH, LIKE PUZZLE-SOLVING, IS MORE ABOUT PROCESS THAN PRODUCT FOR TEACHING- AWARD WINNER DAN HURWITZ.

WHEN A STUDENT ASKS A QUESTION, HE EXPLAINS

“NOT JUST THE ANSWER BUT WHY THE QUESTION WAS INTERESTING.”

zeros and ones—he chalked equations bristling with superscripts and parenthe- ses, paused to ask students if his nota- tions were right, and restated with a grin the elementary but syllogistically pivotal truth that “subtracting minus-one is the same as adding one.” “Professor Hurwitz is always excited about opportunities to pursue some new wrinkle,” says Carol Brown ’13. “In math there are often little ‘what if’ questions

without a straightforward answer. When a student asks a question he can’t answer right away, his first response is usually ‘Oh! That’s interesting!’ Then he comes to the next class with a whole explana- tion not just of the answer but of why the question was interesting. I feel more involved as a student when I know that my questions are appreciated.” Sandy Stonebraker ’13 says Hurwitz “is willing to completely abandon a planned lesson in order to go over a homework assign-

ment that students didn’t understand.” Brown recalls an office meeting about one question on a take-home exam: “We ended up having a long conversation about the nature of the question. He drew me pictures and gave me examples that made me understand it. I felt like we were working on the question together.” As Hurwitz himself has described his role, “The facilitator of an inquiry is not communicating information but helping direct the inquirers toward developing and then testing hypotheses.” That’s what he’s done in class and out since joining the Skidmore faculty in 1976. It’s what he did for the Skidmore Prob- lem Group, helping students submit so - lutions to major math journals. It’s what he’s done for years in devising and lead- ing activities for the Ticonderoga, N.Y., middle-school math club. It’s what he does as a mentor to his students present- ing their work at Academic Festival each spring. As Stonebraker says, “He genuine- ly loves to teach. He makes you excited about math.” —SR

6 SCOPE WINTER 2013

GARY GOLD

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