We are all math people. No, really. We just don’t all know it.
There’s a false divide between artsy types and the mathematically inclined, and creative teachers are trying to unite us all with a more holistic understanding. ”What professional mathematicians think of as mathematics is entirely different from what the general population thinks of as mathematics,” writes Carthage College math professor Sara Jensen in the Smithsonian magazine.
Jensen believes that most people who claim to hate math feel this way because they don’t know how to think about it.
How artistic and math endeavors inform one another
Physicists illustrate equations with doodles while artists use math to draw. In fact, physicist, astronomer, and graphic novelist Clifford V. Johnson says that comic books are works of “sequential art” that double as physics projects themselves. Everything from cooking to crafting to gardening to sports involves some critical thinking and problem-solving skills, which can be assisted with an understanding of the philosophy of math.
To convince students of this, Jensen decided to teach a math class at Carthage that involves no textbooks or calculators. It’s called “The Mathematics of Knitting.” Her students learn math through discussion, blogging, gestures, and crafting. They deal with equations hands-on, literally, and learn calculations painlessly—which leads to a deeper understanding of math than slogging through the old-school way.
For example, in Jensen’s class they knit hats to understand “rubber sheet geometry,” the concept that most shapes become a circle if made with a flexible material. On the needles, their knitting looks triangular, but once off, the students have classic, round hats. By contrast, students also knit infinity scarves and can see with their own two eyes a thing they made with their own two hands that can’t form a perfect circle despite the flexible material.
These are sophisticated mathematical concepts made easy. “[A]bstract algebra and topology are typically reserved for math majors in their junior and senior years of college. Yet the philosophies of these subjects are very accessible, given the right mediums,” Jensen says. “In my view, there’s no reason these different flavors of math should be hidden from the public or emphasized less than conventional mathematics.”
She is not alone in this approach. At Cornell University, students enrolled in “The Art of Math: Mathematical Traditions of Symmetry and Harmony” use music, games, journal writing, discussion, history, and cross-cultural study to grasp mathematical abstractions. “Math is about exploration and strategy and creatively finding solutions,” explains Courtney Roby, an associate professor of classics who teaches the course with a music and medieval studies specialist. “We turn concepts into games to encourage students to think about how to prove them. The activities distill proofs into other ways of thinking.”
The role of hands in understanding things
Increasingly, imaginative teachers are making math more accessible and practical to break down the mental barrier students of all ages have about this topic. And they’re using their hands to do it.
A 2014 University of Chicago study published in Psychological Science found that hand gestures increase young kids’ understanding of math. “Children who use their hands to gesture during a math lesson gain a deep understanding of the problems they are taught,” the researchers conclude. More than kids who interacted physically with numbers on a magnetized board, third-grade students who grouped numbers using hand gestures were able to both solve specific problems and generalize about the underlying principles later.
The gesturing kids didn’t just know how to do math. They also understood the principles underlying the problems. The kids who were taught gestures had a deeper and more flexible comprehension of instruction they could apply after the lesson.
That’s important because it’s better to understand something than to know it. Although the concepts are related, knowing and understanding are distinct. Knowing is static and refers to discrete facts, while understanding is active. It’s the ability to analyze and place knowledge in context to form a big picture. Without knowledge, understanding is impossible. But having knowledge doesn’t necessarily lead to understanding of a greater narrative, which is the real point of learning.
Math is an important part of that grand narrative. But for many students, and adults, it becomes something to avoid rather than understand. As Jenny Anderson explains in Quartz, parents and teachers with anxiety about algebra and equations transmit those feelings to younger generations, who then share the fear, shirk math, and perform poorly on exams.
“The idea that some of us are ‘math people’ and some are not is a myth that pervades Western society,” Jo Boaler, a math education professor at Stanford University, writes in a study in Education Sciences. “This damaging idea has been challenged in recent years by neuroscience showing that mathematics is a subject, like all others, that is learned through hard work and practice.”
Work and practice don’t have to be painful, however. As math teachers are showing their students, it can be practical, hands-on, and even result in charming accessories.