When Jacqui Young studied pre-calculus as a high school junior, she found the experience unexpectedly fulfilling. She didn’t consider herself a “math person,” but pre-calc came more easily to her than it did to most of her peers, and she spent a lot of time helping fellow students grasp the concepts. “It felt good to be able to understand something and then be able to walk someone else through it,” she said. “It was so gratifying, and made me want to stay on top of the subject.”
Satisfaction and engagement may not be the most common feelings among students studying introductory calculus. According to Jo Boaler, a professor of math education at Stanford, roughly 50 percent of the population feels anxious about math. That emotional discomfort often begins in elementary school, lingering over students’ later encounters with algebra and geometry, and tainting the subject with apprehension—or outright loathing.
Professor Mary Helen Immordino-Yang, associate professor of education, psychology, and neuroscience at the University of Southern California has explored how emotions are tied to learning. “Emotions are a piece of thinking,” she told me; “we think of anything because our emotions push us that way.” Even subjects widely considered to be outside the realm of emotion, like math, evoke powerful feelings among those studying it, which can then propel or thwart further learning.
Is there a way to separate negative emotions from the subject, so that more students experience math with a sense of satisfaction and pleasure? Immordino-Yang believes so. “It’s not about making math ‘fun’,” she added; games and prizes tend to be quick fixes. Instead, it’s about encouraging the sense of accomplishment that comes from deep understanding of difficult concepts. “It’s about making it satisfying, interesting, and fulfilling.”
Adam Leaman, who teaches variations of algebra, trigonometry and calculus to high schoolers in Summit, N.J., said that a sense of awe about mathematics drew him to the subject beginning with algebra 2. “There’s something satisfying about knowing there’s an answer and knowing I have the ability to get it,” he said. Today, he sees the same pattern with his students: they are most engaged when they’re figuring out hard problems.
There are several ways teachers can replace student fretfulness over math with a sense of appreciation.
Be clear about why understanding math concepts matters. Kids who believe that they must simply endure algebra and calculus until they’re through with school—and that the actual learning is pointless because they’ll never use it again—should be reminded why understanding mathematical concepts is valuable. Most importantly, being able to comprehend a “symbolic, representative system,” Immordino-Yang says, teaches the brain how to think theoretically and logically. “Learning how to think abstractly is a useful ability in all aspects of life,” Immordino-Yang said. In fact, people who have studied complex math in high school tend to have better life outcomes, she said. Teachers who share this information may persuade reluctant math-learners to stay engaged.
Assign projects that help kids see math’s usefulness. Students are more apt to participate if they see a practical application to their studies. “This goes beyond learning how to balance a checkbook,” Immordino-Yang adds. By studying how fast and far vegetable oil spreads on tissue paper, for example, students can learn not only about the math concept of direct variation, but also about how oil spills are measured. Sharing stories from the news where math understanding is featured in the narrative—in a story about price fixing, say, or one on climbing interest rates—also can help students see its usefulness in the real world. Learner.org, a free educational resource from the Annenberg Center, provides such practical lesson plans for math at all levels, including the oil spill example.
Discuss mathematical role models, and share how their ideas have changed the world. Because math is the foundation of so many other fields—physics, engineering, finance, astronomy, among others—history teems with mathematical virtuosos whose creativity and curiosity shaped the modern world. In addition to the usual suspects of math icons, including Pythagoras, Rene Descartes, and Ptolemy, more contemporary role models might spark student appreciation for the subject. There are many: Alan Turing, who’s code-breaking during World War II helped defeat the Axis powers; Ada Lovelace, who created the Analytical Engine, which presaged modern programming; even Nate Silver, a popular mathematician who uses statistical forecasting to predict outcomes in Major League Baseball and political elections. The humbler discoveries made by annual recipients of the Presidential Early Career Awards for Science and Engineering might also inspire.
Strive to minimize the sources of fear. Math anxiety stifles clear thinking. At those moments when students most need to marshal their intellectual resources—during a test, say, or when called up before class to work a problem—those who fear the subject are apt to panic and shut down. Sian Beilock, a professor of psychology at the University of Chicago, and author of Choke: What the Secrets of the Brain Reveal About Getting it Right When You Have To, describes the anxious over-reaction to high pressure situations as a “malfunction of the prefrontal cortex.” For nervous students who feel pressure to perform well on a test, that worry causes them to execute beneath their skill level. “Anxiety is robbing you of working memory,” Immordino-Yang explained. “You’re wasting your thought powers,” she added. Math phobic kids need help from teachers to lessen their fear.
Keeping the classroom “kid-centric,” Immordino-Yang said, can help. Teachers who act as facilitators, or resident experts, rather than omniscient instructors, invite students to explore without fear of messing up in front of an authority. Freeing up fellow students to explain problems also allows for more personalized instruction. During Jacqui Young’s happy year studying pre-calc, she worked with peers who struggled to keep up with the teacher’s pace. “I think it was better because I’d be working one-on-one or two-on-one with my classmates,” she said. Another way to tamp down dread is to set up class in a roundtable and encourage student-led give-and-take. Known formally as the Harkness Method of teaching, this collaborative approach to learning may be especially useful in math subjects.
Returning to older math processes and ideas when introducing new material also works to lessen anxiety about the new learning. While teaching synthetic division to his Algebra 2 class, for example, Adam Leaman reminds students that this “new” concept is a cousin of the factoring they did in Algebra 1. “They have something from the past to draw reference from when tackling this new subject,” he said. Bringing up old material this way also helps students who might have struggled when they learned it the first time. Leaman said that some kids groan when he brings up factoring, but that they often end up understanding it better when going through it a second time, and in relation to a different concept. “Even if they have the perception that they’re not good at it, when we come back to it I have students say, ‘I get it now’.”