I created a book with my students’ math writings

Two years ago, I attended Ramon Garcia’s Cultural Responsiveness in Math session at TMCNYC. Ramon did a lot at the session, but near the end he shared a booklet that he created which consisted of his students’ math writings. It was called We Broke it Down. We each got a copy.

It was pretty grassroots, but it was polished. He put a lot of effort into turning his students’ math writings into a professional-looking compilation that he could distribute to not only his students and their families, but also his colleagues and the school community. He took great pride in their mathematical ideas, elevated their status, and showcased this by publishing their names in a book. It was unique and inspiring.

When I saw Ramon’s publication that summer, I had already started thinking having my students do formal writing in Algebra 2. For years I was told — like every teacher is — to incorporate writing into my lessons, but this was different. Through my own writing and personal growth, I was discovering writing’s value when it came to teaching math. (Patrick Honner does a wonderful job of discussing this on his blog.) Discovering this meant pushing myself beyond exit slip reflections and Stop & Jots. Not that those are bad, it’s just that I was beginning to view my students as authors of mathematics and not just students who come to math class and write. This shift made me rethink what writing can look like in a math class and why it should look that way.

Most students — especially black and brown students, like those who I teach — are silenced by math. Their perspectives are ignored. Given the countless tests and standards that rush by, students expected to be strict consumers of math. Problem after problem after problem, they’re expected to be vessels that are filled with all the many wonders that math has to offer. They’re expected to see and experience math as static and unchanging.

Ramon’s book reminded me that math can and should be generative and full of original thinking. It reminded me that my students arrive to class each day bearing mathematical gifts. So while it is true that our students need mathematics, it is also true that mathematics needs our students. It needs their perspective, their ingenuity, their questions, their culture, their stories. More than anything, it needs their voice. I wanted my students to understand this. I wanted them to see that they mattered to math.

So I tinkered last year, found some writing structures that worked well, and hoped to create a booklet (like Ramon’s) of my students’ metacognitive journals. I was determined. I even emailed Ramon to get his advice. But with editing, formatting, and asking students to formally type up math, the project turned out to be way more work than I expected. I had to ditch it.

This year, instead of trying to use a publishing software to create a booklet, which I failed at last year, I wondered if I could create an actual book. I knew I didn’t want to go crazy and have an ISBN, but I did want it to be bound and shareable. I stumbled upon the site LuLu in January, downloaded one of their book templates and played around for a few weeks. It seemed doable and I got excited. Because of a grant, my school offered to fit the bill. I was all in.

So this spring, I set off to compile, edit, and publish my kids writing. While the process was still long (being thrust into remote learning didn’t help matters), the book itself ended up better than I expected because in addition to my students’ metacognitive journals, I included their mathography and math haiku. I also went all out and wrote a Preface and Introduction while asking my school colleague Jeffrey Lowenhaupt to pen the Foreword. With everything, it ended up being 107 pages. It’s called Mathematical Voices, Volume 1.

In the book, I made a point to include a piece of writing from every student. This was important. Mathematical Voices represented my students’ deposit into mathematics, a subject that has for years overlooked them. They all had to be there. In the end, all but a couple made it in, which I was initially disappointed about, but accepted.

In coming up with a title, I purposely included Volume 1 to encourage myself to not let this be the first and only book that I create with my students’ writing. Towards the end of the year, when I was finalizing it, my weekly remote learning themes helped me uncover so many more ways to bring writing into my class. Who knows, if I can do this again, maybe those writing tasks will find their way into Mathematical Voices, Volume 2.

My only disappointment with this passion project was that, because of remote learning, I didn’t get a chance to give each of my students their copy of the book. I ordered 130 copies and they’re all sitting in my apartment. It’s quite a letdown, but I’m hopeful that, come fall, I can put the book where it belongs: in the hands of my students.

While any school year is filled with lots of ups and downs, the 2019-20 school year was like no other in history. There was the Covid-19 pandemic, which unleashed its wrath over our country. It took thousands of lives and caused many of my students unthinkable stress, trauma, and personal loss. Then there was the murder of George Floyd, which triggered protests across all 50 states in an eruption of anger and frustration towards police brutality and the racial injustice that pervades our country. While neither of these two events affected any of the writing included in Mathematical Voices, as I gathered it all before schools were closed, they largely defined the school year and how it will be remembered. Given these extraordinary circumstances, my students proved to be fierce and adaptable learners. They also revealed themselves to be exceptional and determined young people. Because their writing was the calm before the storm, so to speak, I hope that, in some small way, this book captures my students’ lives during this unique time in history.


On being white, teaching math, and seeking racial discomfort (Murd Letter #1)

My school colleague Stephanie Murdock and I are writing letters to each other this summer and publishing them on our blogs. We are both white math teachers leaning on one another to improve the anti-racist stance that we take in our lives, classrooms, and school. This is the first post in the series.

Dear Murd,

Thanks for writing me! I was moved by your letter and would LOVE to be your penpal for the summer. I too have many budding thoughts and feelings that need exploring when it comes to racial injustice. They seem to be growing in breadth and depth with no sign on slowing down. Letting them breath in these letters is exactly what I need. Let’s write to find meaning, to learn from each other, and to be better white teachers.

I feel your hesitancy to wrestle with issues of social justice in your classroom. I hear you. The parallel you made to solving a tricky math problem — the need to dive in without knowing how it will end — was interesting. Knowing you as well as I do, this makes sense. I also find it challenging to bring in anti-racist, culturally-responsive topics into the classroom. This work is incredibly complex and delicate, so out of fear, it is natural to wait until the time is right. And being held hostage by the Regents doesn’t help matters. Instead of discussing the alarming rates at which black and brown bodies are incarcerated when compared to white bodies, for example, New York State would rather us focus on cell phone plans and the cost of t-shirts. Doing anything with a social or emotional conscience requires that we break the rules. By doing so, we have to take risks that may hurt our students in June or earn us a reprimand from our supervisor. This makes it tough.

As a white math teacher, when I actually am bold enough to voluntarily bring up race in my classroom, I often feel that I need to know exactly what I’m going to say and how I’m going to say it. I have to control the conversation. There’s a need to not offend any of my students, yes, but there’s also my subconscious need to protect my image (read: my white privilege). This disappoints me.

I’m realizing, much like you, that by waiting until we — the white people — feel comfortable to discuss and act on matters of racial injustice, we only perpetuate centuries of white supremacy. All I’m doing is affirming my white status while sustaining the resentment that our country has towards black and brown people. As a math teacher, just because I have a mandated curriculum that pretends that racism doesn’t exist, it doesn’t mean I am exempt from speaking out and acting upon anti-racist ideals in the classroom. In fact, as an adult who students admire, appreciate, and rely on so heavily for direction, I feel I have more of a responsibility to lean into my white vulnerability, shoulder the burdens of our racist society, and seek out math that illuminates and fights racism. If nothing else, I owe it to my kids.

But this is deeply personal work that extends far beyond what I do with students. Unlike factoring a polynomial, I can’t leave it at school if I choose to. My whiteness lives in and around me all the time. It’s with me at my dinner table. It’s with me when I read the newspaper. It’s with me when I parent my children. Yet, despite how it blankets my life, I have been socialized not to see it. I have been conditioned to ignore the racist perspectives I hold and actions I have taken. Uncovering its reach and ramifications will take a lifetime. This is humbling.

To this end, I’ve been thinking a lot about how to put myself in positions where I experience racial discomfort. (Writing this letter helped me realize this just now since it is making me uncomfortable.) I know I need it, but figuring out how to do it without being completely overwhelmed and shutting down is tricky. I am social, but I don’t have many friends, so I think our school and my teaching will be huge parts of my racial growth. This seems fitting for a lot reasons, but this letter is getting pretty long, so I’ll cut it short.

I’ll close with some wonderings. I feel that white teachers, like ourselves, at times need exclusively white spaces to discuss racism. I’m not sure most white people can truly confront their racial vulnerabilities and own racism when black or brown people are present. I wonder, would this fly with admin? What would other white teachers think about these white spaces? What about teachers of color, how would they feel? Also, I have a tendency to be pointed and somewhat expressive when it comes to matters of race — specifically whiteness. How do I make other white teachers feel? Should I care if they’re uncomfortable? Should I care if they’re upset with me? Isn’t this how black people have felt since 1619? Isn’t it about time that we white people began to feel racially anxious?

Look forward to hearing back. :-)

Yours Truly,

We white teachers need to be better

I applaud the many rage-filled responses I’m hearing from white people — and white teachers specifically — about the injustices that surround the horrific murder of George Floyd. They’re appropriate and needed.

But I’m about to call out good-meaning white teachers across the country. This includes some of my closest colleagues — and myself.

As a white person in America right now, there is an expectation that I meet this moment with an empathic comment and open ears. It’s trendy. It’s what’s happening. I need to say things like, “Racism still exists, this is horrible” or “We white people must listen more.” If I don’t in some way affirm the rage that is sweeping across our nation, I’ll stick out like a sore thumb. So what do I do? As an educator with good intentions, I tweet about how upset I am and tell my friends and teacher colleagues how terrible this whole situation is. I donate money. I reply to emails expressing my support for a virtual Town Hall at my school. Although I may not have voluntarily brought up race with my students before, I acknowledge the validity the protests in my classes. I try to help students cope. This harrowing moment gives me the opportunity to talk about race openly and support anti-racist causes, and I jump all over it. I stand up for what’s right and make sure that others to see me standing up for what’s right. (For us white people, this last part is critical when it comes to race.)

The problem with all this well-timed rhetoric is that it’s too convenient for us white folks. Speaking out right now isn’t hard. Everyone is doing it so naturally we feel less vulnerable in doing it too. There’s little risk for us. We can be momentarily outraged, ask for deep reflection on the parts of ourselves and other white Americans, but our words and surface-level actions can be completely void of any deep introspection and ownership of our racist American culture and school system. Saying the right things right now means nothing for lasting change in ourselves and the implicit racism that we all carry with us.

While many of us of are engaged allies for our black and brown brothers and sisters, if yet another black man wasn’t killed in the midday sun by a white police officer, if there weren’t bold protests exerting their pressure on us to pay attention, if our white friends weren’t talking about it, then I’m convinced that we would still be sitting comfortably in our white privilege. We’d continue to say that we don’t see color. We’d continue to sit in workshops filled with only white teachers and not even realize it. We’d continue to fail to notice that our department is 80% white and 60% white male. We’d continue to view our curriculum as neutral. We’d continue to overlook the contributions of black and brown mathematicians. We’d continue not bring up our whiteness or race at faculty meetings and, of course, open up our laptop to check email whenever it’s brought up by someone else. We’d continue to remain invulnerable when it comes racial discomfort. We’d continue to be silent.

So, sadly, in three months time, when the protests have died down and the media decides that the appetite for social justice has been satisfied, I fear that we white teachers will think that the risk to speak up is too great. The safety and security of our whiteness will be far more inviting. We’d rather obsess over our Zoom settings and figuring the best question to ask during an EdPuzzle video. Instead of reading, listening, and doing work on ourselves to think courageously about how we are complicit in creating racialized schools, curriculum, and pedagogy, the summer will help us white people to forget about George Floyd. It will help us push Black Lives Matter further away from our minds and classrooms. The anti-racist affirmations from today and tomorrow will be long gone. Our classrooms and schools, however they may look, will not reflect a commitment to racial justice, like they are right now.

I hope I’m wrong. I hope that we white teachers can be better. We need to be better.


Self-graded quizzes and learning how to ask questions

This whole remote learning thing has given me a lot of time to think. Well, maybe not a lot of time, given that I’m trying to plan, teach, and call parents with two toddlers dragging me into a never-ending game of hide-and-seek. But despite this, and the fact that I’m in essence a first-year teacher again, I have been trying my best to lean into this moment and try out some new things.

One of these things has been self-graded quizzes using Google Forms. Amy Hogan uses them a lot and was kind enough to share one of hers with me to get me started. After using hers as an example, I’ve created two in the past two weeks and really like them. I have attached a small grade to the quizzes to encourage kids to do them and take them seriously, but in the future I want them to be gradeless. Because of their self-graded nature, they do take a bit of time and energy to set up, but the flexibility and convenience they offer is pretty sweet. Trying to come up with interesting questions has been fun.

Since I try to leverage student work a lot, I’ve tried to come up with questions that ask students to analyze a piece of student work. Here are two that I conjured up:

As a formative assessment, seeing if my students can find errors in a coherent piece of work is a valuable task, but having the assessment data immediately available is actually what makes these types of questions worth asking. If these were free response questions, it would be a nightmare. I’d have to wade through the mire that is their responses and still wouldn’t have the clean, informative data that the self-graded quizzes give me.

Though I have included a couple free response questions, I’ve been trying to avoid them. Combing through all of their answers to check for equivalent solutions is something I’d rather not do. It defeats the purpose. When I do give a free response question, though, I’m learning how to include in the question what the format of the answer should be. For example:

That worked. Here’s one that didn’t:

The kids submitted all sorts of craziness from “105” to “the answer is 105” to “the remainder will be 105” to “105/x-5.” This turned into me checking through their answers one-by-one, like I would have normally without the use of a self-graded quiz. No fun.

On the other hand, here’s a question I created as a workaround to simply asking students to find the value of csc(π/2):

It’s not a great question by any means (neither are the other two), but at least it’s not free response and it’s a little less Googleable than it otherwise would be. Plus, when combined with the work they submit through Classroom for other problems we do, the question helped give me a loose understanding of what the kids know about radians. Then again, who knows. This is remote learning. Their big sister could be doing these quizzes.

I’m left thinking about how else I can spin my questions. How might the format of the question depend on the math that it’s asking about — and vice versa? What about using response validation? This would take even more work to design, but it is interesting to see where it could go (pun intended). I’m also thinking about using checkboxes in a question with multiple correct solutions and requiring students identify one or all of them. I could also give a multiple choice question, not including the correct answer as one of the choices, but having an “other: ______ ” option where they would enter their answer. This could be a nice alternative to the remainder question I gave above because it would let kids know how to format their answer and could then be easily self-graded by the form.

There’s so much room for creativity in these quizzes that I wish I had more time to explore them. They’re so useful that I’m looking forward to having them follow me back into the classroom, whenever that happens. As for now, it’s back to figuring out where I’m going to hide next. The closet!