The Calculus Diaries - Jennifer Ouellette [100]
Consider Deborah, whose fourth-grade teacher held multiplication table competitions in class. Deborah was highly competitive, so she worked very hard on memorizing her multiplication tables and practicing at home. As a result, she excelled in these competitions and became known as being “good at math.” This had a significant impact on her later on: Whenever she struggled with an especially tough problem, she pushed through, thinking, “I should be able to do this because I’m good at math.” Yet her belief in her innate ability, and her success at math, were actually the product of a lot of hard work and repeated positive reinforcement in the classroom.
Tavris also believes that American culture has an unhealthy attitude toward failure. It is considered a shameful thing rather than a natural stage of the learning process. Calla initially failed high school algebra. It shattered her confidence and instilled the telltale dislike of math that such failure so often brings. “I hated math for making me feel stupid, and because there was nothing enjoyable about it,” Calla said. “It was just there, like a big black wall I would run into every once in a while, not letting me know why it was there or why I should I care.” In reality, failure is how we learn. Take away the freedom to fail, and it is no wonder our students aren’t learning. Science, too, relies on failed experiments and null results just as much as its justly touted successes in order to advance human knowledge.
The good news is that, regardless of the combination of factors that conspire to discourage any given individual from pursuing math and science, one good teacher can make up for all of it. I had Alan and Sean. Calla had a dedicated high school math teacher who literally changed her life. Everything changed when she took a class taught by a young woman who emphasized hands-on demonstration and applications for the math. It took some time for Calla to work through her mental blocks, but that teacher patiently guided her every step of the way with all kinds of creative approaches. They hammered away at the big black wall together until Calla finally broke through and realized she was “good” at math. She went on to major in physics in college.
There are many excellent high school math teachers, laboring in the trenches for very little pay and even less appreciation. But they are fighting an uphill battle. The way calculus is so often taught is clearly not reaching a substantial fraction of students; more often than not, like my high school self, they end up solving problems by rote, with little comprehension of why they must perform these tasks—or get so frustrated at their inability to solve problems that they reject mathematics for the rest of their lives.
Every teacher I know is heartened whenever they see that light bulb of genuine comprehension turn on in a student’s brain: “Oh! This is that!” In the same way that our favorite works of art, literature, music, or theater tend to be those with elements we recognize and can respond to emotionally, we tend to respond more to books, lectures, or classroom curricula that enable us to make similar connections between the abstract concepts of math and physics and our real-world experiences. If our emotions are engaged, even better: That excitement and enthusiasm serve to fuel students’ desire to persevere past the inevitable frustrating roadblocks in the quest for knowledge.
Actor