My two cents (Week of June 21, 2021)

For each school day of the 2020-21 school year, I will be writing two sentences to capture some of the impressions, feelings, experiences, or thoughts I had that day. This is the 36th and final post in the series.

Monday (June 21)
Sadly, I had to miss the “graduation celebration” because of a wedding in my family. Many students from this graduating class hold a special place in heart, so not being there was especially bitter sweet.

Tuesday (June 22)
I learned today from my principal, via a staff-wide email, that he is resigning as our principal in order to take a position as deputy superintendent of a charter school network. He has been the founding principal of our school for the last 16 years; this is historic news.

Wednesday (June 23)
Being in the building with little to do but write reflective blogposts feels unusual. This afternoon I got up some shots in the gym with Brother D and DeSiervo while casually chatting it up; always leave on a make!

Thursday (June 24)
Completed and posted make up work for my NX students for their journeys during summer school. On his second-to-last day in office, my co-host and I recorded an impromptu and heartfelt podcast episode with the principal.

Friday (June 25)
Alone with the echo of an empty classroom, I packed up my crap for the summer and said farewell; what a year this was. Tried my best to consolidate my gear into a few regions of room 227 and clumsily posted “Belongs to Mr. Palacios – Please do Not Remove” signs on them.


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.


My two cents (Week of June 14, 2021)

For each school day of the 2020-21 school year, I will be writing two sentences to capture some of the impressions, feelings, experiences, or thoughts I had that day. This is the 35th post in the series.

Monday (June 14)
Did lots of outreach to help some of my students make it to the finish line. Prepping the envelopes and labels that will be used to mail my students their copies of our book filled my heart with satisfaction.

Tuesday (June 15)
A quiet day — the low hum of room 227’s air conditioner kept me calm and collected throughout the day as I began to finalize grades, sent more emails to students, and finish a blog post. This afternoon, with remote learning knowing that its days are numbered, it lashed out at me one last time; with the sun in my eyes, I smoothly dodged its noxious thrust and extended grace to a student in need — I consider it my watered-down version of a federal pardon.

Wednesday (June 16)
The 110 copies of Mathematical Voices, Volume 2 arrived and I spent some time in the morning hand-delivering personalized copies to several colleagues in the building who helped make it happen. Enjoyed a reflective and heartwarming conversation with my assistant principal about the year as well as the last five years.

Thursday (June 17)
It felt awfully strange proctoring a Regents exam this morning, let alone doing it in the gym. I happily deposited Mathematical Voices into the unexpected hands of some juniors (including many sophmores I taught last year) who came in to sit for exam.

Friday (June 18)
My co-host and I recorded the last guest-centered episode of the staff podcast this morning. The podcast been an incredibly unique, community-building experience during an weird, unfriendly school year.