The standard American math curriculum is anything but inspiring. Based on
memorization and timed tests, it encourages boredom and anxiety. A lucky few
students get the inspiration and motivation required to enjoy and excel in math
from a parent or teacher. The rest muddle through, often quitting at the first
opportunity. How can we disrupt this depressing state of affairs?
Look at Math Instruction Through a Different Lens
By exploring math instruction through the lens of other subjects, we can start to see why the way it’s usually taught fails to excite most students. What if we taught music the way we teach math? Students would learn to read and write music on blank sheets of staff paper. They’d learn all about music theory, but they’d never play an instrument or listen to music. They’d miss the joy of making sound or keeping a beat, the emotion of expressing oneself or getting wrapped up in a melody.
What if we taught art the way we teach math? Instead of allowing students to paint, they would learn color theory, the ins and outs of different paint brushes and types of paint, and the names and accomplishments of a few great but dead artists. They would learn how to paint by numbers in high school, but they would never be encouraged to express themselves through painting on a blank canvas—or even scribbling with crayons on printer paper—until graduate school. Most students don’t make it that far.
“Sadly, our present system of mathematics education is precisely this kind of nightmare,” writes Paul Lockhart in his essay “A Mathematician’s Lament.” “In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”
Fortunately, Lockhart and other math teachers have some ideas about how to change things.
Don’t Try to Reform Math Education—Scrap It
A common refrain is that kids don’t get interested in math because they don’t see the point in learning it. The solution, then, must be to show them how math will help them in their careers and adult lives. Lockhart disagrees. He thinks it is the wrong approach, because kids don’t care about calculating compound interest.
How do we learn?
“We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math.” — Paul Lockhart, “A Mathematician’s Lament”
So what might make math interesting? One idea is to treat it as an art form. The American Mathematical Society’s webpage on mathematical imagery is a good source of inspiration that showcases the beauty of infinite loops, the geometry of nature, even the whimsey of fractal pancakes. Math comics and graphic novels are two other ways to combine math with art to make the subject more fun and less intimidating.
Tie Math to Current Events
Ask students about the topics they’d like to explore, then design math lessons around their interests. For instance, teachers can show pupils how to apply math to social justice problems.
An advanced placement high school statistics course can explore wealth inequality and immigration. Algebra 2 and precalculus lessons can be applied to the impact of fundraising on a candidate’s vote tally. Teachers can consult the best-selling book High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice, the website SkewtheScript.org, and the Math and Social Justice wiki for ideas.
Emphasize Problem Solving Over Memorization
An after-school K-12 math program called the Russian School of Mathematics teaches students to solve math problems by thinking through the logic, not by memorizing and regurgitating formulas and proofs. Students develop narratives to describe how to solve equations. Given a few numbers, they create their own stories and explanations. The approach is designed to instill an excitement about math that keeps students engaged and helps them learn the material, as reported in the Atlantic.
Math is fundamentally about wondering, imagining, and playing, Lockhart writes. It’s about “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations.” Depending on whom you ask, it might also be about memorizing multiplication tables, but math education shouldn’t rely so heavily on rote tasks.
Play Games and Incorporate Media
Instead, allow mathematics to be about play. “Play is part of what makes inquiry-based learning and other forms of active learning so effective,” said mathematician Francis Su, in his 2017 farewell speech as outgoing president of the Mathematical Association of America (MAA), “There’s overwhelming evidence that students learn better with active learning.” Su believes that by allowing mathematics education to be playful, it can build hopefulness, perseverance, community, and rigorous thinking.
Lockhart suggests doing puzzles and teaching students to play games that require deductive reasoning skills, such as chess, go, hex, backgammon, sprouts, and nim.
For other ideas check out the National Math Festival’s collection of suggested puzzles, games, books, and videos for ages 2 through 18+. Participate in the National Math Festival’s online events. Explore the interactive experiences at the National Museum of Mathematics in New York City when the pandemic is under control and it’s able to open again. Right now it offers many programs online, including virtual field trips for K-12 classes and YouTube videos.
The “math as play” teaching technique even works at the college level: Check out the inquiry-based learning math books, downloadable as free PDFs, from Discovering the Art of Mathematics, a math approach geared toward liberal arts students.
Foster Inclusive Classrooms
What does an inclusive math classroom look like? In many ways it’s similar to an inclusive classroom in any other subject, where the instructor makes sure to use students’ preferred names and pronouns regardless of what’s listed on the course roster. It’s one that roots out microaggressions and implicit bias from both the instructor and the students. And it’s one where students with different physical abilities are able to access all the course materials.
An inclusive classroom is also one where students learn about contributors to the field from all backgrounds, so they can see themselves as the type of person who could be good at math. In the math classroom, fostering inclusion might mean teaching students about standout mathematicians who are not white men.
For example, former NFL player John Urschell, a doctoral candidate at the Massachusetts Institute of Technology, is proof that two groups stereotyped as not being good at math—athletes and Black men—can excel in the field, as reported by the Associated Press. (He’s even written a book about his experiences, Mind and Matter: A Life in Math and Football.) Such instruction can help offset what is known as “stereotype threat.”
Understand Stereotype Threat
Stereotype threat—in which a reputation for underperformance by members of a certain group actually causes them to underperform—seems to affect women’s and minorities’ outcomes in math. Stereotyped groups may have untapped potential their teachers can draw out if they learn how to fight back against the threat. Teaching students that math ability is not innate but acquired through effort is another way to reduce the threat.
Also important is not giving an inferior math education to groups that researchers have identified as underperforming. When teachers constantly hear that Black, Latinx, and Indigenous students perform worse than Asian and White students in math, they may lower their expectations and simplify their lessons for those students, which can prevent these students from ever reaching their potential, as reported in the Atlantic.
Don’t Ignore Math Anxiety
Two-thirds of math teachers in a representative 2020 survey told EdWeek Research Center that their students experience math anxiety, a challenge that can cause students to avoid math and underperform. They can pick it up from elementary school teachers or parents who themselves suffer from math anxiety.
A pilot program called StoryStrong in Maryland’s Howard County asks eighth-grade students to explore their emotions surrounding math, from the experiences that have shaped their relationship with the subject to their insights on how they can succeed. It’s meant to give students the psychological support they need to develop a positive “math identity.” As it’s so new, we don’t know how well it works, but it seems to hold promise.
Advocate for Struggling Students
Frustrated teachers sometimes write off students who are struggling and tell them they aren’t cut out for math. Instead, teachers should advocate for them, MAA’s Su urges. Likewise, be aware that we all hold biases about the gender, race, and socioeconomic status of those we expect to be good or bad at math.
What does a mathematician look like?
“The demographics of the mathematical community does not look like the demographics of America. We have left whole segments out of the benefits of the flourishing available in our profession.” — Francis Su, “Mathematics for Human Flourishing”
Push back when a student says they aren’t a math person. Let them know that even if they struggle with one aspect of math, they might enjoy another type. Emphasize that, as stated above, math ability is not innate and must be acquired. Students who appear to be gifted may just be better educated. Perhaps they got a head start from math-fluent parents. They shouldn’t be the metric against which other students judge themselves.
Help Students Pursue Extracurricular Math
Struggling or not, students can benefit from math classes and programs outside of school that take a different approach than the typical curriculum and engage pupils in activities that make math fun. Math camps, math circles, and math competitions can provide the spark a child or teenager needs to increase their math self-esteem and develop an interest in the subject. Financial aid may be available for families who can’t afford the fees.
In the battle against stereotype threat, math anxiety, and mind-numbing curricula, teachers have many weapons to fight back. With a little creativity—and, admittedly, enough flexibility to do anything other than teach students how to pass their next standardized test—instructors can employ art, play, current events, and psychology to inspire a love of math in more students.