Teaching Ethnic Studies: Number Theory Edition

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.

Do you know about Srinivasa Ramanujan? He was an incredible mathematician who’s way of studying math did not fit the standard white normative way & was thus disregarded by many. Imagine the contributions he may have had if his professors & other mentors saw his way of understanding mathematics as brilliance rather than arrogance…

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?! 

Have you heard about the Lebombo bone? It is the oldest known mathematical artifact dating back to ~35,000 BC! According to The Universal Book of Mathematics, the Lebombo bone’s 29 notches “may have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar.” 

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?

A Short Story About Me, My Mother & Tracy Castro-Gill

There is currently a letter writing campaign going on to support Tracy Castro-Gill, you can read about the ask in my last post and Tracy’s post. We are also doing a video campaign! Upload your video here.  Current deadline for video: May 29, but it may be changed once we get a date for the postponed executive board session that will determine. See more information at the end of this post.

I was not originally planning to share this email given how personal it is. But my partner reminded me that it is important I do, because it’s easy to fall into the political aspects of all of this work & forget the human element of it… So, enjoy this small glimpse into my childhood & life. I hope it challenges you & helps you think about those who have impacted your life.

I still remember this day: It was my 8th birthday, I wore my fanciest Indian outfit, as was traditional in Indian culture, on my birthday. Some kid on the playground asked me if my dad was a terrorist, why I hated America, and if I wanted to walk around looking and smelling like a terrorist, eating terrorism for lunch (he was referring to the okra baji & roti my mother had made special for my birthday since it was my favorite) that I should just go back to my country.

Hello Board Directors,
I am writing to urge you to overturn the demotion of Tracy Castro-Gill, our loved and esteemed Ethnic Studies Program Manager. As I’m sure you know by now, she has impacted the lives of hundreds if not thousands of educators and in turn, thousands to tens of thousands of students. At this point you have received emails regarding her amazing, honest, and community oriented approach to her work. You have been told why the false claims are evidence of the lack of integrity of our district, not Tracy. So my email is to share with you about my personal story and experience with Tracy.

A little bit about me.
My name is Shraddha Shirude, I am an immigrant, Indian American womxn, a 2nd year high school math educator, a member of the Ethnic Studies Advisory Group, a CRE Coach, and the lead of my Racial Equity Team at Garfield HS. None of these things were ever things I thought I’d be as a young person.

I grew up in an immigrant home where my father tried his best to make us American. He believed the lie of the American Dream and falsely thought that the Model Minority would benefit us. My mother however, was smarter than that. My mother fought to get us to participate in Indian culture, only speaking to us in Marathi so we wouldn’t forget, making us Indian food for lunch, and celebrating holidays through the eyes of Indian culture.
My father detested this, not because he was a bad man who hated his country, but because he had begun to believe his country was the reason why he was rejected and talked down to at his job. My mother was a stay at home mom, so perhaps racism she felt was limited to the grocery store trips and PTA meetings (not that she was ever invited to these). Or perhaps she had a stronger relationship to our culture and was wiser to the lies of the American dream. I’m guessing it was the latter, she was an extremely wise person.

As a 2nd grader, I began to feel the impacts of racism when 9/11 hit. My family was suddenly a target because we were brown. I began to hate my culture and wanted more than ever to stop being Indian. I still remember this day: It was my 8th birthday, I wore my fanciest Indian outfit, as was traditional in Indian culture, on my birthday. Some kid on the playground asked me if my dad was a terrorist, why I hated America, and if I wanted to walk around looking and smelling like a terrorist, eating terrorism for lunch (he was referring to the okra baji & roti my mother had made special for my birthday since it was my favorite) that I should just go back to my country.
That day I went home and shouted at my mother and told her I didn’t want to be a loser anymore and that I wanted to be an American. I can’t imagine how much her heart broke and how hurtful my words were. Things were different from then on. Not for the better, but what did I know? I was being colonized in school and it was working.

My mom, sister, & me at my sister’s wedding reception in 2017.
This is one of the few pictures I have where we are all dressed up in Indian clothes.
It was one of the most Indian experiences & memorable moments of my life.


Fast forward about 17 years. I’m a first year teacher. My mother is on her last days. I’m sitting there trying to learn everything she wanted to teach me, but it’s too late. She tells me all she wants is for me to be happy and be myself. I told her I was and I am (both are not true). She knows I’m not being truthful but smiles and says okay, just like she has all of my life.
Fast forward a few more months. This is when I meet Tracy. I tell her I’ve read her blog in search of answers and I’d like to be a part of this movement. She says “that’s great but what do you want to do?” I have to think about it. I respond by saying “I want to help kids not go through what I did and stay connected to their cultures.” She takes me on. Teaches me personally about ethnic studies, provides me with resources, I sign up for the Ethnic Studies Summer Institute but get wait listed. However, my experience the few times I worked on Ethnic Studies work was so intense that I show up the first day 90 minutes early anyways and cross my fingers that I’ll get in. Yes, all that during the summer after my first year teaching. Good news, I got in!
I meet hundreds of educators & community members and find dozens of mentors. My mindset is right. I have support. I have friends. Everyone encourages me to be happy and myself. And reminds me that my true self lies in my history and ancestors; my pre-colonized self. My life changes forever.

Ethnic Studies Leaders at Northwest Teaching for Social Justice Conference
(Left to right) Jeff Stone, Tracy Castro-Gill, Jesse Hagopian, Lisa Rice, Wayne Au, Shraddha Shirude, Usana Jordan, Kaitlin Kamalei Brandon


Since meeting Tracy, I have taken the lead in writing the Ethnic Studies math framework, teaching Ethnic Studies 101-3 and Racial Equity Literacy 101-3 as part of the anti-racist training series that Tracy created in partnership and collaboration with many many educators. I have helped to write Black Lives Matter at School curriculum. I have lead workshops in conferences and at colleges. And it was all because Tracy saw me and knew my potential. She didn’t see me as a new teacher, a naive immigrant, an eager wannabe, all things I have been told by colleagues and supervisors to explain my “incompetence” over the years. Turns out it was actually that I was no longer okay with whiteness and that scared people.

Tracy fights to allow everyone to thrive every day. Tracy fights to have everyone at the table. Tracy fights to provide support for all communities, students, parents, and educators. Tracy has always put others first. Fighting off death threats and putting her livelihood on the sidelines to be a true leader. I am ashamed that I have to send this email at all. But here I am. Putting my story out there for you to read and feel and use. It is the way of whiteness to force us to do things that cause us pain in order to fight it off. So my question to you is, are you willing to break the cycle of white supremacy culture that is at the heart of the Seattle Public Schools agenda? Or will you as a board member, allow for boxes to be checked and the hard work to be bypassed? We will continue to fight the fight and Ethnic Studies will come to Seattle one way or another. But the real question is, what side of history do you hope to be on? I hope it is the side of true, radical, educational justice for all.

Thank you for denouncing the lies and holding our district, Diane Debacker, and Superintendent Denise Juneau accountable to their white supremacist actions and upholding the honest work of Tracy Castro-Gill.

Best,
Shraddha Shirude

Video Campaign information:


These videos will be compiled into one video of support and may be edited for length of time. By submitting a video you agree to your name and video to be shared in context of supporting Tracy Castro-Gill and Ethnic Studies in Seattle. 
Please help by submitting a video of support! It can either be you reading your letter of support aloud or a short video that says your name and community role / position and then  “I believe Tracy is truthful and has integrity, and that she collaborates and leads well. Because of this she has moved ethnic studies forward.”* 

It is important that you do your video ASAP and submit it in time for it to be edited together. It doesn’t have to be perfect! Thank you for supporting Tracy Castro-Gill.

Use this checklist for both videos

  • Record video horizontally (phone or camera)
  • At the beginning of your video state your name and title / community role
  • Speak slowly and clearly
  • Use a tripod or have someone record you
  • Have someone hold the letter or tape it to the wall so you are looking at the camera and not looking down at a paper
  • Record in a quite place and close enough to the camera so your audio is easily understood
  • Here is a quick reference guide to help you film your video
  • You do not need a dropbox account to upload a video, just a way to record yourself and a support for Tracy!

*This statement is in direct response to what her employer is saying she lacks. 

¡Ayúdame! Ethnic Studies in Seattle Needs You! — Thoughts on Racial Justice from an “Activist Teacher”

If you follow this blog and my work, you know that I am on paid administrative leave and have been under investigation for allegedly violating several policies. Recently, I was informed that my supervisor, Dr. Diane DeBacker, made a formal request to HR that I be removed from my position as Ethnic Studies Program Manager […]

¡Ayúdame! Ethnic Studies in Seattle Needs You! — Thoughts on Racial Justice from an “Activist Teacher”

walk the walk

If my work has impacted you in any way…. Please read through Tracy Castro-Gill’s post & then write to our school board members stating your support for her. I would not be the educator or human I am today, without Tracy. Her leadership, support, & friendship are what allowed me to help write the Ethnic Studies Math Frameworks. Additionally, when the Framework originally went viral, I did not take the brunt of the racism, threats, or personal attacks. Tracy took all of those in stride, with absolutely 0 support from her employer, Seattle Public Schools. You know, the district checking off their “woke” box on the backs of educators, like Tracy, who have been facing threats and being traumatized; and not just by strangers but by the very institution (Seattle Public Schools) that claims & appropriates our work as their own.

It’s time we as math educators step out of our comfort zones & support racial justice more intentionally. It is not the fight of our humanities educators, it is for all of us. Please don’t just like this post or send me an email or Tweet or share on Facebook. Actually walk the walk. Send the email to the board members. Share why removing Tracy is just another act of institutional racism. She is not the first to be put under fire. But we can break this trend of perpetuating systems of injustice by removing the change makers & anti-racist leaders from positions of power. This movement has never been about Tracy, although people in power try to make it seem that way.

This fight is about Ethnic Studies, our Black & Brown communities & most importantly, about true Racial Justice & Freedom from White Supremacy.

Please make your voice heard. Please support our team. Please show up to support Ethnic Studies. Please send your statements about why Tracy should not be removed & why doing so perpetuates white supremacy & allows Seattle Public Schools to continue being a racist institution.

Dear Privileged,

I'm sorry for all the tech.
I'm sorry for using videos.
I'm sorry for all the frustration.
I'm sorry for using multiple platforms.
I'm sorry I didn't reach out right away.
I'm sorry I reached out too much.
I'm sorry for the lack of communication.
I'm sorry for not responding right away.
I'm sorry for not explaining enough.
I'm sorry for explaining too much.
I'm sorry for the confusion.
I'm sorry for the frustration.
I'm sorry for the anxiety.
I'm sorry for the depression.
I'm sorry for not being more flexible.
I'm sorry for not having detailed policies.
I'm sorry for the grading policy.
I'm sorry you're feeling overwhelmed.
I'm sorry we cannot do school like normal.
I'm sorry we are in a pandemic.

I know this isn’t what you signed up for. It isn’t what anyone signed up for when they were born human.
Racism, misogyny, homophobia, ableism, classism, and other discrimination are not what anyone signed up for when they were born human.

I appreciate your advocacy during this pandemic about inequity.
Please reflect on why it took a pandemic that affected you & your family’s normal for you to feel concerned about educational justice.

I'm sorry if I have caused discomfort.
Feel free to add to the list of apologies I owe you.

Take care,
Ms. Shirude





Math is Life. Life is a story. So why aren’t we telling stories in math class?

I kept putting off starting this blog because I couldn’t muster the energy to introduce myself and tell people what I’m all about. Which I guess is what a first blog post is supposed to be about. Then I realized, I’ve never done things “the way they’re supposed to be done”, so why would I start now…? So I’m just going to start here. Wherever I am today and share what’s on my heart. If you already know me, you’ll understand where this is coming from. If you don’t know me, but want to, you’ll follow along and eventually understand. If you don’t know me and are here to judge me or whatever else, okay, I don’t need to explain myself to you either. So I guess the conclusion is, here is my first post. Think of it what you like:

I love math. I love teaching. I love people. I love God. I love justice. All of these things are intertwined with one another, believe it or not. Many people tell me I have a strange relationship with math, because I speak about math as though it is somehow human.

One time a student said to me, “Ms. Shirude, why do you teach math?” I responded by saying “Because Math is LIFE.” I meant it mostly as a joke because the students at the time had been messing around saying “______ is life!!!” all week. I don’t remember what the pop culture context for this was anymore. But I really do believe that statement.

Math is EVERYWHERE. Literally. Like, I don’t know how anyone can go through their life and not see math. But then I realized, I think I look at math very differently than others do. I believe this is what makes me so uniquely qualified to do what I do (teaching & writing “woke” math). I find that it is this perspective, not my degrees, careers, or how many books I’ve read that makes my students also start to love this subject.

This is an awesome book if you need some examples to understand why Math is LIFE.

Also, I love to tell stories. Everything I talk about has the context of a story. Even my lessons. Every unit starts with a story. Every lesson starts with a story. Every conversation I have with a student, becomes a story. Just like math, STORIES are everywhere.

This is why I believe math and ethnic studies fit together so well. Both are parts of daily human life, every single day. When I hear reluctance with incorporating ethnic studies into mathematics, it is often from teachers and others who would like to focus on teaching methods over meaning. While there is a time and place for methods in a math classroom, I believe centering ourselves in meaning and stories gives life to what is seemingly (historically would be a better word, if it weren’t still the case today) a lifeless topic.

This is an incredible book to help you tell some stories about math history!

Let me be clear, I am NOT suggesting that we do not teaching methods in math class. In fact, without methods, we would not understand math as well as we do. Methods are what allows us to have common language and understanding around steps to arrive at a problem. In graduate school, we had an entire course series called “math methods”. Granted, I didn’t feel like I learned much from this course series given there were only 2 math educators in my cohort… *story for another time*

Methods are important. However, we do not need to center methods in class. We need to center stories. By centering stories in math class, we center humanity. When we center humanity we bring life back to mathematics.

Every single day, I hear at least one person say “I’m not a math person”. OMG. STOP IT. I hate this phrase. And I know so many math educators who do as well. But what’s the point of hating it, if we don’t look at why so many people say this? Given that, I decided to start asking people in my life (coworkers, friends, family, strangers) why they felt like they weren’t “a math person”. The most common response I get is, I just don’t like it or I don’t know, it just never really clicked for me. Being an educator, I, of course, have a follow up question to their response. Which classes did click for you? I hear a range from history to art to science to PE. When I ask why, they say things such as because I get to talk to my friends or I like expressing my thoughts or it’s interesting/fun to see things work.

The best part of teaching ethnic studies in math class is that students get the opportunity to feel connection with math. If you read those responses, you can see that each person is sharing their connection with the content! The students who have not liked math or even hated it, now have an opportunity to see their humanity in it. After all, it is only when you dehumanize something that you can be so cruel to hate it, or worse yet, erase its existence from your mind.

So, no more of this “I’m not a math person” bullshit. Let’s start re-humanizing the math classroom to build a love and passion for mathematics and in turn, for humanity.