Teaching Math as an Act of Resistance

During the September Presidential debate, Kamala Harris pulled a surprising judo move. She invited the audience to attend one of her opponent’s rallies. In addition to the people leaving early, clearly a sore spot for her opponent, what I saw at those rallies was a large group of people unquestioningly believing what someone on the stage was telling them. They were followers of an authoritarian leader.

The global trend toward authoritarianism (strict obedience to authority), a much bigger trend than just the most recent US election, carries with it important lessons for us in the mathematical sciences community. In particular, I believe this trend…

imperils democracy,
is at least partly the fault of those of us in the mathematical sciences community, and
points to how we can all teach in ways that protect our democracy.

Teaching math, if done well, can be an act of resistance against the authoritarian tide sweeping the globe. Let me explain.

When we teach mathematics – to grade school kids, to high school students, to college students – we are the leaders in the room. We are the authority. Our students aren’t just learning how to add decimals, take derivatives, or multiply matrices, they are also slowly building a sense of what it means for something to be true, what makes a fact a fact, what knowledge itself really is. Are statements true because of evidence, careful reasoning, and refinements that have taken decades or even centuries? Or are they true just because we – the authority in the room – say they’re true?

Over the years I have had the privilege of visiting hundreds of classrooms, seen videos of many more, and talked with over a thousand teachers about the enterprise of teaching mathematics. Nearly all of those teachers share a view of mathematics as a connected body of ideas that logically follow from one another and combine to help us understand the world around us.

But what about our students?

In too many cases, they are just like rally goers, listening to a sage on the stage and believing what they’re being told. Rather than following along and using logic to connect ideas, they are simply falling in line, believing what they’re being told and mimicking it dutifully when asked. The logical coherence and beautiful connections have been replaced by the algorithmic pushing of symbols around on the page, hoping to get kudos in class, the green checkmark when they hit “submit answer,” and an A. They are stressed out, in a time crunch, and just working within the system to please the classroom authority who controls their future.

When we follow tradition, lecturing at students while they passively listen and take notes, the majority of them are not building the interconnected web of ideas we all hold so dear. How do we know this? In one study, a highly-regarded real analysis teacher lectured about properties of sequences. There were five specific connected ideas he aimed to get across; independent observers largely agreed that all five were clear. Students who sat through the lecture, however, couldn’t identify those points, struggled to do so even after reading their notes, and were still unable to do so after watching a video of the lecture.

Of course we have known for decades that there are better ways of teaching than lecturing at students (see David Bressoud’s column The Worst Way to Teach and Freeman et. al.’s meta-analysis for more evidence, and the MAA’s Instructional Practices Guide and the NCTM’s many publications for alternatives to lecture.) Yet another piece about how different pedagogies affect student understanding of mathematics would be a waste of pixels and time. However, in this age of increasing authoritarianism, I think it’s worth paying attention to the impact of pedagogy on developing students’ epistemologies – their views of what knowledge is.

When students’ math experiences largely consist of listening passively to lectures and then working to be able to get the right answers to low-level computational problems on high-stakes assessments, what view of knowledge are we implicitly communicating? Math is a set of steps governed by us, the authorities in the room. What determines if something is correct? It’s not the logical edifice of mathematics, the reasoning and critical thinking we prize. It’s us. We’re teaching them to believe what authorities tell them.

Think of it another way. What happens in a math classroom when the instructor gets something wrong? If knowledge in the classroom is governed by logic and reasoning, anyone who sees the error would point it out, the problem would be corrected, the instructor would get over the mild embarrassment, and the class would move on.

That happens in some classes. But in too many places, when the sage on the stage says something that isn’t true, those in the room – including some who know better – continue lapping up the authority’s supposedly infallible wisdom¹. Sound familiar? At least in this one way, many math classes are similar to authoritarian leaders’ rallies.

How did we get here? While it’s easy to point fingers – at teachers, students, rally goers, and politicians – the harder and more productive path is to critically examine the systemic structures that led to these behaviors. When it comes to the teaching of math, teachers aiming to develop students’ critical thinking, logical reasoning, and deeper understanding are fighting against some powerful forces. Overloaded curricula, assessment policies, students’ prior experiences & attitudes toward mathematics, some colleagues’ and administrators’ views of teaching, and deeply held cultural beliefs all push them toward more didactic, authoritarian methods.

When we challenge those norms, teaching in ways that help students see mathematics as beautiful, interconnected, and logically grounded, we are also helping build a view of knowledge that is more resistant to authoritarians’ siren calls. We are doing our part to protect democracy.

Of course the list of reasons people are swayed by authoritarian leaders is long, and how we teach mathematics is not near the top. However, it’s worth examining – both individually and collectively – how the interactions we have with students and the choices we make in the classroom every day can either support authoritarian tendencies or serve to protect us from them. Teaching mathematics better can not only help students succeed, it can be part of the resistance, protecting our democracy from authoritarians now and in the future.

Acknowledgement: Parts of this post were drawn from a TEDx talk I gave in 2019; the ideas benefited from conversations with many colleagues and friends.

Author’s Note: This is an intentionally provocative post. What do you think? Can how we teach math impact how our students view knowledge, and how they respond to would-be authoritarian leaders? Join the conversation at MAA Connect.

Dr. Dave Kung serves as Director of Programs at TPSE-Math and as a consultant as a mathematician without borders. He has worked in the intersection of mathematics and equity as the Director of Policy at the Charles A. Dana Center at The University of Texas at Austin, and as Director of MAA Project NExT. He also works closely with K-12 and higher ed organizations, especially concentrating on equity issues in mathematics. Kung was awarded the Deborah and Franklin Tepper Haimo Award, the MAA’s highest award in college math teaching, for his work at St. Mary’s College of Maryland. He resides in the DC area, coaching local teachers, playing violin, and running – occasionally alongside his partner and daughter.

¹ For some women and faculty of color, such moments can play out differently, with a single mistake proving disastrous for students’ sense of trust in their instructor. Authority is a privilege some have access to more easily than others.