Scott Adamson, of Chandler-Gilbert Community College, kicked off his talk by asking the audience this: “How can we create a more joyful mathematical learning experience where the beauty of mathematics can be shared and be engaged in by our students?”
I’m reminded of the need to answer this question every time I introduce myself as a graduate student in math and am met with the classic response—“I was so bad at math in school.” But it can be difficult to try out new methods of teaching when instructors are pressed for time and resources. Adamson articulated the specific way our education system is failing students—by asking them to memorize formulas without any understanding of the underlying mathematics—through examples he’s seen in his work. Students, for instance, learn how to calculate the average of a set of numbers, but often they don’t understand what it means conceptually. Teachers, he explained, frequently try to make math “fun” by introducing gimmicks—following mathematical steps to reach the end of a maze or attacking zombies with a line of best fit—but in the process, send the message that math is too painful to endure without turning it into a game. At the college level, there is rarely an attempt to make math fun at all.
The result is students who implement formulas mechanically and cannot solve problems that differ from what they’ve seen in class. Adamson suggested an inexpensive way to getting students engaged in problem-solving: vertical non-permanent surfaces, or VNPSs (that is, whiteboards, or chalkboards, or some approximation). Research by Peter Liljedahl has shown that students who work on permanent surfaces—those where you can’t erase your work—participate less, persist less in their problem-solving, and take significantly longer to start writing—two minutes as opposed to 20 seconds. Any non-permanent surface is good, but vertical surfaces are slightly better than horizontal surfaces. They let students work together more easily, and also look around the classroom at one another’s work for ideas.
Although students may struggle at first with a teaching method that requires them to solve new kinds of problems, Adamson suggested students are empowered when they are able to “discover” math for themselves.