Each year I begin my classes with a Number Theory unit. Number theory is a critical part of mathematics that has historically been left out of public mathematics education. Why? Some say because it is complex mathematics that can only be understood once one has an understanding of “practical” math. I had a colleague ask me “Why are you teaching them number theory? That’s a 400 level college course I didn’t even take until I hit my master’s program. They’ll think your class is hard right from the start…” I disagree. I did not see number theory in this way. The study of number theory is the study of the properties and relationships of numbers. This is critical for students to be taught at an early age because this is what sparks the curiosity that is mathematics! Number theory helps us to understand questions like “why do we count the way we count?” “are there other ways of counting?” “what does it mean when I say my birthday is on January 27th?” “How do I know when January 27th will happen each year?” “what is a year?”
Ethnic studies is about more than just multicultural history, it requires us to literally change how we see, think, and feel about the world.
To answer these questions we turn first to number systems. Why do we count in a base-10 system? What is a base-10 system? I brought the kids back to elementary school when we used base-10 blocks & we talked about how those work and what it actually meant. So many of them were having aha! moments and brilliant realizations about what they had done 8-10 years ago in early elementary math! This told me something huge: it wasn’t that the students didn’t know. It’s that they didn’t get a chance to process deeply enough to use that skill beyond its taught usage: learned helplessness. Learned helplessness in the context of math learning is the idea that students will only perform a skill based on what the teacher is asking them to do. It is a direct result of the “I do, we do, you do” model of direct instruction that is taught as “good math instruction”. This results in students only being able to use a skill the exact way a teacher teaches it, so when they are asked to use their “math skills” from prior math learning, they don’t know what to do and will wait until the teacher tells them exactly how to use it in this particular context. Limiting the students’ ability to actually gain any value from learning the math content at all.
Once we were able to learn about base-10 & what it really means, we jumped into learning about other base systems from around the world. This is where we began to address the unit’s ethnic studies theme: “Origins, Identity, & Agency”. We ended up looking at the ancient counting methods for about 8 different civilizations and studied very brief histories about each one. Students were then asked to try counting in those based systems and boy, they suddenly found it to be very difficult. It was mind boggling to many students that anyone would choose to count in base 60! And based 2?! Why would anyone do that?!
Nonetheless, they persisted and practiced converting back and forth. We did this to help understand the idea of dimensions – a critical skill for understanding geometry. We used number theory to help us understand what 100, 101, 102, etc. mean. The students were able to explain the difference and similarities between 101 versus 71. And viola! They’re understanding bases – a skill normally taught in algebra 2/precalculus when we begin to teach logarithms. Who knew, teaching using base-10 blocks & math history would actually help us to understand logarithms…
Now you might ask me, what does all this have to do with ethnic studies? You’re sitting here talking about modulus and logarithms, that’s just math… And this is my point exactly.
The last thing we discussed in this number theory unit was modulus; another supposedly “advanced” mathematical standard. I definitely did not learn modulus in K-12 education and most do not learn about it in their undergraduate programs either. I started by using the phrase “circular counting”. We had already talked about different base systems in history, so we started this conversation by talking about different base systems in the modern day. At first students struggled, then I started probing them with questions like “hey, what day is it today?” students responded by saying “Tuesday” I told them I didn’t understand. They looked at me confused and I just kept asking them to explain what they meant by “Tuesday”. Finally a student threw a Friends (TV show) quote at me (LOL). “Ms. Shirude, like Joey (Friends character) says, Monday, one day; Tuesday, two day; Wednesday, what? What day?; Thursday, third day!” I laughed and said, “Oooh so Tuesday is the 2nd day? I thought it was the 17th day.” And the kids then realized I was talking about the month and started to see what I was saying! We count in modulus all the time! It’s how we measure time! I’ll give you an example: 15(mod 7) = 1mod (7). How can we understand this practically? Well, let’s say the first of the month starts on a Wednesday & there is an event that’s happening on the 15th. What day of the week will the event be held on? Well, each week has 7 days (mod 7), 2 weeks is 14 days, so we are left with a remainder of 1 or 1(mod 7). So we can safely say that the 15th day of the month is a Thursday without actually taking the time to count it out!
Now you might ask me, what does all this have to do with ethnic studies? You’re sitting here talking about modulus and logarithms, that’s just math… And this is my point exactly. Whenever we talk about centering our focus on our students, and specifically students of color, white supremacy gets in the way and fools us into believing that we must somehow stop talking about “advanced” math or “theoretical knowledge” because all “those kids” want is practical applications or easier math to just graduate. And no, these statements did not come from some horrible outright racist people. These are statements said to me by other educators who care about racial justice and many that are in fact people of color themselves. These are ways in which internalized white supremacy affects our understanding of our own communities. To be completely honest, these are thoughts I had as I entered the career. My first year, I had a colleague who was thoughtful enough to check me one day when I had alluded to this very claim. I have since then worked on dismantling that internalized white supremacy to really see my students for who they are, not what I expect them to be.
Ethnic studies is about more than just multicultural history, it requires us to literally change how we see, think, and feel about the world. Woke math means waking up to see our own internalized white supremacy, waking up to see how we perpetuate white supremacy in our daily engagements in the math classroom, waking up to the idea that the reason the mathematics world is filled with white men is because we have allowed ourselves to believe that only a certain caliber of human (wealthy, white male) is capable of truly understanding how the world functions, thus allowing that caliber of human to control everything.
The key to my success with this unit was changing the narrative of who is a mathematician. Reminding students that they are mathematicians, that their ancestors created the study of mathematics, and the purpose of mathematics is to observe the world and rationalize its mysteries is the work of ethnic studies theme 1: origins, identity, and agency.
I will leave you with this question: how will you dismantle white supremacy norms in your next unit?