Reflections on my students’ math penpal experience

You’re lucky to overcome your weaknesses, especially one so fundamental. Mine is so hard to overcome despite how easy it seems. Little mistakes or a lack of understanding can shift a problem entirely. It’s been my issue for a long time and basically became a habit. Anyways, one of the weaknesses I’ve successfully overcome is fractions. Besides the occasional mix up, I’m golden.

Some of my favorite topics in math would be the classics. I’m thinking of things like basic arithmetic. Why? Because they are not as complicated as the present lessons. Despite the lessons taking more of time, it takes up a lot of space in my precious books. Those pages can be filled with stories or fan-fiction, not factoring or distributing. Still, I’ll take distribution any day, factoring may seem easy but there’s so many different types that I can’t keep up. No. Just no.

One of my students (in a letter to her math penpal)

Last August, before the school year began, I wrote a blogpost on the notion of mathematical penpals. It was essentially a public plea to see if anyone was interested in trying out the idea with me. My thinking was that we’d come together, have our students write mathematically-themed letters to each other throughout the year, and possibly have them meet on Zoom at the end of the year. If you’ve read wonderful book Mathematics for Human Flourishing by Francis Su, I imagined our the students’ letters would be, in spirit, like the ones between Su and Christopher Jackson.

Despite my excitement for the idea, I dampened my expectations. We were in the midst of a pandemic with no vaccine in sight. Teachers everywhere were fastening their seatbelts for a school year unlike any other. The idea math penpaling would have been outlandish even in regular circumstances, let alone the one we found ourselves in. I hit publish on the post and waited.

How many people responded to my plea? A heartwarming — and surprising — 17.

I emailed everyone to see if we could establish partnerships. Most teachers were from the northeast, but there were a few from places like Illinois and Minnesota. Thankfully, Sarah Furman and I found common ground in terms of what and who we teach and decided to give it a go. Sarah teaches Algebra 2 in upstate Michigan and the differences between our students (e.g. race, geography) was a huge draw for us. She’s a 21-year vet who is thoughtful, reflective, and eager.

We had plans for the students to write each other every 4-6 weeks. That didn’t happen. The logistics of an unpredictable school year kept us guessing and caused longer-than-expected gaps between letters. We were in-person one week and remote the next. Our students were all over the place. So were we. In all, our students ended up writing two letters to their penpal. I’m very proud of this.

And the actual exchange of the letters? How did that work? After pairing the students up, we hoped that the letters could be handwritten and mailed to each other, just like old-school penpal letters are. That also didn’t happen. Who was I kidding?

The letters turned out to be a combination of handwritten and typed correspondences. Students who hand-wrote their letters scanned them and sent them to us. Students who typed it shared it with us. Because of the remote learning mess we found ourselves in, we didn’t even attempt to mail them. Instead, we just dropped them in a shared Google folder and called it a day. The other person retrieved the letters and distributed them to their students. It worked out well.

Outside of logistics, one of the more interesting challenges about the experience was figuring out engaging and worthwhile prompts for the students to respond to in their letters — especially when it comes to mathematics. Some of the math-themed talking points I threw at the kids included:

• What is your earliest memory of math or learning math?
• How do you learn math best?
• What parts of math are challenging for you?
• What is/was your favorite topic to learn in math? Why?
• Tell your penpal about our A Mathematician and Me assignment. Share your mathematician and why you chose them.

The main goal of this project was to build community between students through letter writing and mathematics. I’m not sure to what extent Sarah and I achieved this, as students may have viewed it as one of the many random things that happened in a crazy year, but it was a lot of fun trying. For what it’s worth, Sarah and I both observed the genuine interest and enthusiasm amongst the students when the letters “arrived” and when it was time to reply. That counts for something, right?

We both agreed to try this again next year. We’re hopeful that the experience will be more meaningful for our students, allow them to write more letters, and just run a lot smoother. I’m looking forward to this and have many wonderings. Like, how might we safely connect our students over social issues and current events? And how might mathematics be a vehicle for this? What about problem solving and problem posing? Could we have students jointly solve problems through their letters? How might students debate mathematics through their writing? Could their letters make it into a future volume of Mathematical Voices?

So many juicy questions to sit on.

A fascinating subplot of this experience is that, in all of our planning and organizing for our kids’ math penpaling this year, I’ve still never seen or spoken to Sarah. It’s strange, but I kind of like it that way. It’s as if she and I have been penpaling about penpaling. It’s fitting. And beautiful.


Mathematical Voices, Volume 2

Last year my Algebra 2 students and I created a book using their math writings from the year. We called it Mathematical Voices, Volume 1. I wrote a blog post about the experience, which was birthed at a math conference I attended several summers ago. The goal of the book was to lift up my students’ mathematical ideas, perspectives, reflections, and creative writings in a way that was purposeful and public. I saw it as their contribution to mathematics.

Because of the pandemic and my students being ripped away from me in March, there was a serious lack of closure to the school year. This was compounded by the fact that I wasn’t able to give the book to its authors and rightful owners: my students. Despite my disdain and incertitude about how the year ended, the book excited me because of what it represented.

My delight for the book lingered all summer. I even boasted about it to my new students on Zoom on the first day of class this year. Although it was one-of-kind, it felt like something bigger. So, despite being remote, I implored that we were going to create a Volume 2 and it was going to be amazing. Frankly, I knew no better — I was simply riding the wave of a new school year.

Sadly, that bright feeling got buried once the darkness of this school year revealed itself. As we trudged our minds and bodies through the fall and winter months, my lofty plans for compiling Volume 2 got pushed waaaaaay down on the list of priorities. While their writing was therapeutic for me, a soothing balm for the wound created by remote learning, a coping mechanism for interpersonal gulf created between my students and me, I found myself merely surviving for a good part of the year.

Though the idea for Volume 2 got buried and lay dormant for most of the year, it never died. When spring arrived, bringing a COVID vaccine and hope along with it, I caught my second wind. In early April, I slowly began combing through the kids’ writing from the year and drafted a manuscript. I started this process a month later than I did last year and figured it would be a crunch to finish it by June, especially with the cumulative stress of 15 months of remote learning weighing me down. I ended up spending the entire month of May (and part of June) hunched over my computer in order to complete it. The result was beautiful.

The overall structure of the book is the same as last year. Much of the sections are the same; included are the students’ mathographies, metacognituve journals, and math poetry. To spice it up, though, I made some changes.

First, with the guidance of my co-generative dialogue, I scaled up our math poetry assignment to include Fibonacci poetry, free verse poetry, and math raps/spoken word poetry. Last year the only option was haiku. This was a major upgrade because of the ingenuity it fostered amongst the students. I also included a new section for the A Mathematician and Me task from February. I attribute this task to my dear colleagues Stephanie Murdock and Brother DeVeaux, who came up with it early in the year. And after writing many open, antiracist letters to each other last summer and fall, I asked Stephanie to pen the foreword, which she supportively did. The last change was unrelated to writing and instead came in the form of drawings. They were based on an assignment near the end of the year where I asked my students to make a hand-drawn sketch or collage representing their year in math class. Their sketches are sprinkled throughout the book. Despite all the writing they did, sometimes art can say things that words cannot.

In addition to what physically appears in the book, what I came to appreciate about this anthology in its second iteration is the collaborative nature of it. It is a joint effort between my students and me. I compile it, yes, but my students do the heavy lifting with their writing. All but a few of my Regents-bound students are included in it and, this year, one student even helped design the cover. In my eyes, this all amounts to us producing something together. It’s communal, symbiotic. It’s their voices, but our song. In this way, Mathematical Voices embodies the decentering of authority and the flattening of hierarchies in academic contexts, which includes the pages of a book. It’s a co-created solution that bows emphatically to our collective humanity and shared responsibility we have to learn from each other and grow. I am proud of this.

In a school year filled with relationships built around Zoom, virtual handshakes, and all things Google Classroom, creating a physical book seems strange. All the work that my students submitted this year was digital, but yet here is a physical manifestation of their mathematical selves. Unlike everything else from the year, you can hold it. You can touch it. You can pick it up and give it to a friend. You can read it without straining your eyes. Viewed from the perspective of a mathematical function, this year’s inputs should not have yielded this particular output. There is great deal of symbolism in this paradox that I have yet to fully wrap my head around, but do greatly appreciate. Thankfully, unlike last year, I was able to mail each of my students a copy of our book.

When thinking about last year and Volume 1, what I realize is that this year it wasn’t just about lifting up, validating, and publicly circulating my students’ math writing, it was also about finding a way to document this once-in-a-lifetime school year. The book strives to capture our persistence and refusal to let remote learning win. In many ways, the reflections and other writings function as a mathematical time capsule for me and my students. By bounding their thinking and printing their perspective again, I hope this edition serves to chronicle a most unique school year in a most unique way: through mathematics.

In the end, despite not being able to share a physical space with my students and feeling estranged from teaching and learning, my only hope is that Mathematical Voices, Volume 2 can serve as a humble reminder – at least to myself – that my students were not mere screen names or profile pictures this year. They were humans. Behind the screen and on the other side of that email was a young person. A young person with a story. A young person with thoughts, feelings, beliefs, ideas, struggles, and triumphs. A young person, who, in many ways, I’ll never know. By the time they get to see their name on those pages, our paths, both mathematical and otherwise, will have diverged. With our humble book, which represents our final attempt to repossess a school year co-opted by COVID-19, my only wish is that it honors them in a way that I was never able to on Zoom.


Some learnings from Carter G. Woodson and The Mis-Education of the Negro

The minister had given no attention to the religious background of the Negroes to whom he was trying to preach. He knew nothing of their spiritual endowment and their religious experience as influenced by their traditions and environment in which the religion of the Negro has developed and expressed itself. He did not seem to know anything about their present condition. These honest people, therefore, knew nothing additional when he had finished his discourse. As communicant pointed out, their wants had not been supplied, and they wondered where they might go hear a word which had some bearing upon the life which they had to live.

Carter G. Woodson, The Mis-Education of the Negro

Some colleagues and I have been reading The Mis-education of the Negro by Carter G. Woodson for a few weeks. Published in 1933, the book is a timeless indictment on anti-Blackness in our country and, more specifically, in our schools.

A major theme of the book is Woodson’s calling out of “highly educated” Black folks for doing things that work against the collective liberation of the race, included himself. As a white person discussing the book in the company of at least one Black educator, there are times that I’ve been made uncomfortable with our talks. It kind of feels like I’m part of a conversation between Woodson and other Black folks, a conversation I have no business being a part of. In this way, reading it on my own has been enlightening, but has made me question the cross-racial setting in which we’re studying it.

To deal with this personal dilemma, it’s been helpful for me to look inward and find ways to place myself in the crosshairs of Woodson’s criticism. For example, after coming across the passage I cited above, in which Woodson critiques Black ministers and how they show up for those they serve, I couldn’t help but draw connections to white teachers who serve Black and Brown students, especially in large numbers. In other words, teachers like myself.

The context of Woodson’s challenge, at least how I interpreted it, is how schools of religion have indoctrinated Black ministers with the values of white supremacy. This conditioning shows up in their interactions with their congregation. In his words, these schools “followed the traditional course for ministers, devoting most of the time to dead languages and dead issues.” He goes on to highlight an example of such a minister and says, “He went off to school, and when he came back the people could not understand what he was talking about. Then he began to find fault with the people because they would not come to church.”

This raises a stockpile of questions for me. Most directly, as a white teacher who teaches an overwhelming majority of Black and Brown students, how has my lived experiences, education, and continued professional development prevented me from interacting with my students in meaningful ways? Also, how has the euro-centric model of teaching and learning conditioned me to not center Black and Brown joy? How has it erased Black history from my instructional framework? How have I been trained in and perpetuate a system of deficit thinking that preys on Black and Brown students? How has it permitted me to downplay and then ultimately ignore the intellectual and emotional endowment of my students? How has it blinded me from comprehending gender and sexism? How has it separated me from my aging white body and mind and keeps pushing me, with every passing year, further and further away from the young people of color I serve? How does where I choose to live and do my business affect how I understand my students and the communities they inhabit? How has all this removed me from, as Woodson calls is it, my students’ “present condition”? How has it removed me from their realities?

In the end, I bring these questions with me into spaces that I occupy with students — and it shows. It shows in what I do or say, but also in what I don’t do or say. With these questions in mind, I’m not all that different from the Black ministers that Carter G. Woodson is calling out. Many of my students are disengaged, alienated from the content and class, or simply don’t come to class at all and, when this happens, I question their commitment to getting an education. It should come as no surprise, then, why many of my students leave me seeking a word which has some bearing on the life which they have to live. They’re not getting it from me or my pedagogy. My life and training as a teacher thus far has inescapably divorced us from reaching that point.


Paying Homage to Malcolm X

On Wednesday, May 19, several of my colleagues and I went to Ferncliff Cemetery in upstate New York to visit the grave of Malcolm X. It would have been Malcolm’s 96th birthday.

The idea for the visit was birthed after we read The Autobiography of Malcolm X in February. It was part our school’s book/podcast club. Having learned so much about him and discussing his impact, we decided that paying homage to him on his birthday would be a fitting thing to do. Seven of us carpooled and made the 35-minute trip.

While there, we spent some time standing around his grave, reflecting. We shared our learnings, our feelings, our shortcomings. We imagined a world where Malcolm was still alive, still evolving, still advancing his antiracist beliefs. We gave thanks for his truth-telling and revolutionary spirit in the face extreme violence, enraged white supremacy, and death. Living to the meager age of 39, we acknowledged that his life was far too short. We affirmed his gifts to not only to Black Americans, but all Americans. Just like Malcolm, we vowed to keep learning and to be critical of ourselves and the world around us.

While there was a sprinkling of people around us, it felt like we were alone. We had Malcolm all to ourselves. While we talked, he listened. He also told us a few stories and wished us well on our journey. It was powerful. The moment transcended our school, our students, and our professional bonds. I’ve been at my school for five years and it was one of the proudest moments I’ve had as a member of our community.

Admittedly, I didn’t know a lot about Malcolm before we read his autobiography. Reading it was informative on many levels. After we finished it, I wanted more of Malcolm so I picked up Black Minded: The Political Philosophy of Malcolm X by Michael E. Sawyer. I learned of Sawyer and his work after watching him discuss Malcolm at The Schomburg Center’s The Mother Tongue: The Philosophy of Malcolm X event in February. Black Minded was a dense and challenging read, but really helpful in getting closer to Malcolm and the nucleus of his thinking. I finished it this week, coinciding with our trip to Ferncliff. It left me with a lot more to share and feel than I would have otherwise. The Dead are Arising is on my summer reading list.

Despite living and working so close to his gravesite for many years, most of us didn’t know Malcolm was buried right underneath our noses. How did we not know he was here? Some of us drive past him every day and had no idea. Several people also spoke of the simplicity of his gravesite, expecting something with more grandeur given his stature. When I think of how society blacklisted Malcolm during his life and ostracized him after his death (it took over 30 years for him to get a postage stamp after his death, my gosh), the modesty and obscurity of his gravesite surprised me at first, but not after I gave it a second thought. The stark difference between his grave and that of Martin Luther King, Jr. tells the story.

As we were getting ready to leave, more people began to arrive and a larger community formed. We opened up our circle, they opened up theirs, and suddenly we were speaking with perfect strangers. We were from all walks of life, all there to honor a man who moved us. We shared our connections to Malcolm and filled our hearts with a shared respect for the moment. We’ll probably never see those people again, but our transient companionship couldn’t be denied. They gave us water. We took a picture together. After about 15 minutes, we headed towards our cars. I felt whole.

Though our team departed his grave the same in number, we were far bigger than when we arrived. Thanks, Malcolm.