The Mathography

During the first week of school this year I assigned a mathography. It’s essentially a math biography and details one’s relationship and life experiences with math. This was a new idea to me and my colleague Stephanie Murdock put me on to it in the spring. She learned about from Wendy Menard’s NCTM session in D.C. earlier this year. Here is Wendy’s handout.

After assigning it, I figured it would take me forever to read them all (~120). So instead of getting overwhelmed and trying to cram them all within a week and probably not remembering anything about my students, I promised myself to read them a little bit at a time in bite-sized chunks. I wanted to slowly digest them, to really savor them. Each day, I might read a couple in the morning when I got to school and also just before I leave for the day. Maybe I squeeze in another during lunch. And because I want the kids to know that I read them and that their story matters, I write a healthy, thoughtful comment on each one (thanks Google Classroom). My goal is to read and comment on each mathography by the close of the first marking period. I may not make that deadline, but I don’t really care now because they’ve been so interesting.

Now that I’ve read a good number of them, I failed to anticipate the closeness that I would feel with my students as a result of the assignment. I’m learning things about my students that I would have never found out before. When I look at my students (some of whom I even had last year), I actually see them through their relationship with math. I can welcome who they are in our classroom because I actually know who they are now. It’s wonderful. And not only is it what they write about that tells a lot about who they are, but it’s also how they choose to write. For example, a few students submitted poems and fictional stories as their mathography. They beamed with artistry, were pleasant surprises to the pool of personal narratives that I expected, and told me so much about those particular students in ways that beyond what their words did.

I’ve always tried to pride myself as someone who works hard to get to know my students. But I’ve never done it through formal writing, like this. What a huge difference! Come to think of it, because writing plays an important role in my personal life, I understand the power of reflection and written word…and it only seems natural that I experience it with my students. That said, I’m so disappointed that I didn’t assign this to students earlier in my career.

Also, it was clear from their writing and from their reactions to the assignment itself, that my students had never formally reflected or wrote about their relationship with mathematics. This has been refreshing for them and me. And exactly why it’s so important that I assign it again next year.

I’ll close by sharing excerpts from some of the mathographies that I’ve read so far.

  • Math is like an ocean. The deeper you get into it the more harder and challenging it gets. Although it has different layers just like math has different concepts, if you look at it in a big picture it is really just one concept all together as one.
  • I’ve always had a constant battle with math. Whether it was counting money, telling time, or measuring something, math never seemed to be on my side. Since I was a kid, I would classify myself as “not a math person”. I wasn’t terrible at math, I was actually quite good, yet I never enjoyed it. My teachers also tended to teach a certain way which didn’t allow me to find my own way to solve problems. Math only got worse from there.
  • In the 8th grade it was the best, my love for you could have burst through my chest. [line from a poem]
  • When first introduced with mathematics, I was not thrilled with the idea of learning through numbers. At the same time it was a new learning experience, so why not give math a try. I ABSOLUTELY HATED MATH. My brain exploded when face to face with math. There was simply too much combinations of numbers at once. I gave up on it and just turned my mind to Science and History during my elementary school days.
  • Being an Asian, we’re usually stereotyped with being good at math. Also known as a subject I can’t ever get a good grade in because exams stress me out to the point I fail or score really low on. I hope to understand all math concepts at one point in my life but right now it seems like a stretch for me.
  • In English, I can annotate and understand the central idea. In history, I can study the important dates and find out why they’re significant. When it comes to Math, you need to understand each concept thoroughly and if you miss a step it’s automatically wrong.
  • My earliest memory of math I would say would be in kindergarten. I attended school in Mexico. I lived with my grandma for 3 years. I was about 5 years old. I remember going to pick eggs every 2 days with my grandma and she would count with me every egg we picked in Spanish. Every chore I did with my grandma would require counting out loud. I have to thank my grandma because if her I leaned my numbers pretty quick.
  • Math isn’t just a subject, it’s an experience.
  • As time passed things just got harder. I got less and less star stickers on the board for correct answers as I watched people get every single one of them. I have always been jealous of those people that just understood math with no problem. How did they get it so fast? That’s the main question I always use to ask myself. There were times where I felt like there was something wrong with me or I felt like I was never going to understand. No matter how fast I ran or how much I tried to avoid math I couldn’t get rid of it.
  • The bane of every math teacher’s existence is when a student asks why. Why are we doing this? How does this relate to our life? How will it affect us? To this day I still haven’t gotten a clear answer and why is it that most teachers can’t tell me why. They all have the same answer “I don’t actually know. Search it up and tell me tomorrow.” It’s ludicrous to think that someone who has devoted their life to a job wouldn’t actually know why they’re teaching a subject. Then there are people who say “their job is just to help us pass the test or the regents.”
  • I don’t recall any specific positive memories with math from my early childhood. My classmates were angry at the attention I received, and some of the teachers assumed my family gave me the answers.
  • When I came to the United States at the age of 3, I only spoke, understood and wrote Spanish which is why ELA was difficult for me the first 5 school years. However, the numbers stayed the same, they didn’t change their meaning, one continued to be uno, two continued to be dos, three continued to be tres etc.
  • For most of my years, math has not been so much of a satisfying experience, it was thought of something that I just had to do. I can only hope that in the future, math continues to surprise me and that we can find peace with one another. Maybe one day, math will find its permanent and pleasant place in my life.  
  • To me the whole concept of math and what math is completely confusing. I understand that I’ll need math in my life to keep track of my money and all that good stuff but there’s some topics in math that I just don’t understand how I’ll ever apply what I learned in those classes in my life beyond school. Classes like geometry, trigonometry, and calculus make no sense to me to be completely honest. When will I ever need to find the circumference of a circle or the Cos off point A in a right triangle? You see where I’m coming from?

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I have fewer desks than students. On purpose.

There is a growing number of shared public spaces that are popping up all over the world.

 

Cars, bikes, motorcycles, and pedestrians are forced to govern their own behavior. They have to make eye contact and acknowledge each other’s presence. There’s an inherent faith that folks will slow down and pay attention to each other. I bet they even greet one another way more than they would otherwise. It all makes for a more trusting and human experience. And, from what I’ve read, the number of injuries in these spaces has even decreased significantly.

Why can’t we operate on the same principle in our classrooms? Can we somehow use shared space in our classrooms to create a more personal and humanistic learning environment? Call me idealistic, but I’d like to think so.

That’s why last week I asked the custodian at my school to remove several desks from my classroom. I wanted to ensure that I had fewer desks than students. I didn’t want each student to have their own desk. Instead, because I have the room set up in groups, I have intentionally removed 1-2 desks from each group — but left the seats. The result is 6 groups of 4 desks with 5-6 chairs each. Here’s an example of one group:

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It’s a small change (unlike removing all street signs from a busy intersection), but the idea is that in order to navigate their group’s space, students must purposely engage with one another on a regular basis. It creates a more communal learning environment and helps them take ownership of their workspace (and our classroom). It can get messy because they rub elbows, get in each other’s way, and have to constantly negotiate how they should use the space. But in the end, I 100% welcome these inconveniences. (Honestly, living with the ungodly congestion of NYC, my kids probably don’t even realize these things.) They create a greater degree of collective energy each day. Ultimately, my hope is that they will be more mindful of each other, to be more present.

A side note: This line of thinking is also reflected in the large whiteboards that I began using last year to de-front the classroom. These are communal spaces around the walls of the room that students used to publically display their thinking at any time — unlike having one greedy board at the front of the classroom that screams for attention (and a lack of optimal engagement).

In some ways, I see desks as imposing segregation on my students (and me). Despite being organized into groups, desks still create distinct social spaces for students to think individually. There’s a clear end to my space and a start to yours. Can this subconsciously establish a greater sense of independence from others in the classroom? Tables would probably be the best physical solution for helping create a more personal, humanistic classroom, but I doubt that I’ll ever convince my principal to get me those.

 

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The case for disorder in the classroom

I’m going to go ahead and say it.

I think there needs to be more disorder in our classrooms.

By disorder, I don’t mean kids throwing chairs and running amok. Instead, I’m thinking about those instances when teachers give students largely unstructured time and space to land on their own ways of thinking the content. Those instances when the teacher, by design, fails to impose a rigid learning structure on student learning.

This is not a popular idea. It goes against pretty much everything teachers are told must happen in their classrooms every minute of every day. We must have structures, routines, and systems. We need tidiness. Students need to learn concepts linearly, there must be an obvious beginning, middle, and end to everything. It is our job to provide managed, predictable spaces for our students to work together and exchange ideas. For if we don’t do these things, our students’ will be distracted. They won’t learn. Unless its art, a mess is not welcome in the classroom.

Now I’m not saying that there’s no value in structured pedagogy. There is. I have lots of structure in what I do with kids. This includes approaches that range from “traditional” teacher-directed lessons to instructional routines to Desmos Activities to debate-oriented strategies like Talking Points. These are great and serve a purpose. They work to establish outlets for students to explore concepts in safe and dependable ways.

Yet with all the value of structured time, I would argue that messy, unpredictable time is equally important to our lessons and student learning.

By consuming ourselves with algorithmic structures, we teachers sometimes take away opportunities for our students to face problems openly. At times neutralize their brilliance and rob them of their natural inclinations — both intellectually and socially. By giving my students pedagogically less and expecting more individually and collectively, I’ve realized the importance of allowing my students to own their learning — to own our classroom.

For example, it’s now a regular thing for me to give my students a set of carefully constructed problems, whiteboards, and random groups as a means to learn new concepts. They are free to do whatever to understand the problems, including each other and the internet. If it was up to me, I’d even let them leave the classroom. Nonetheless, they are out of their seats for the entire period. I will aid with the math, but I indirectly encourage struggle. I’m there to help, but mainly around to support them to summarize and reflect on their work. It is their energy will make or break the room. It’s on them.

The result is often an untidy and confusing classroom. The uncoordinated, ambiguous, and disoriented learning environment it creates relies heavily on the cognitive diversity in the room. It’s an intentionally unpredictable and flawed approach, but something I’m learning to be good with. For me, it’s worth the tradeoffs.

Rarely does it end in rainbows and butterflies. But that’s kind of the point, though. Often times the kids walk out more confused than when they walked in. We might not get to an answer, let alone a correct one. This usually means that they don’t like me for a while (sometimes all year), that I won’t be on their list of favorite teachers. But in long run, it’s my belief that their discomfort will not only help my them understand the responsibility they have to themselves and their classmates when it comes to learning, but also the responsibility they have to make our classroom go.

Formal schooling sucks the instincts out of our kids. I teach high school and by the time my students get to me, they’ve internalized the classroom as a place where the teacher is supposed to direct their every action. They lose their ability to sense-make because they’re only concerned with “doing school.” They would probably stop breathing if I told them to (and then run to the principal’s office).

So while we thoughtfully select safe and comfortable approaches to student learning this school year, let’s make sure we don’t deprive our students of something they desperately need, which to experience disorder and be pushed out of their comfort zone. This means that they’ll be more tension, messy interactions, and awkward moments in our classrooms. And this will most likely require us to be pushed out of our comfort zones. And that’s a good thing.

 

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Math ed conferences: let’s leave the host city better than we found it

This week at TMCNYC18, I had a very brief conversation with Michael Pershan. It was literally 4 minutes long. While short, it spurred some pretty deep thoughts for me…and a dream. (If you know Michael personally, or read his writing, then you know it is not uncommon for him to blow your mind.)

In the spirit of teacher math ed conferences, we talked about the nature of these growing set of gatherings. They’re everywhere nowadays, big and small. We, teachers, go to a designated location — usually by plane or car, but not always — stay in the area for a few days, learn, network, and collaborate. Sometimes we have breakthroughs, sometimes we struggle to find a session to connect with.

Though all of these professional experiences at the conferences, we naturally adopt the city and its many local communities as our own. We interact with locals, enjoy their local food and attractions, plan group outings, create memories, bond. Whether it is mathematically or socially, we generally take away a lot from being immersed in the host city.

But what do we give back? What’s left after we leave? What remains after we use the community for our own needs?

It’s a simple idea that I hadn’t thought about until Michael and I chatted this week.  Perhaps inspired by our localized TMCNYC experience, we talked about why giving back the local communities (even if the conference itself is local) that we occupy for multiple days would be a worthwhile thing. How can we have a positive impact on the host city after we leave it? While it is unconventional, considering the exceptional amount of mathematical energy that exists at these conferences coupled with the fact that we’re all in the field of education, organizing such a contribution seems fitting. So why not? Let’s change the narrative about who benefits from these conferences. It need not be only us. These conferences afford us a great opportunity to acknowledge the privilege we have as math educators and use it to positively affect a local community in a very unique way: to leave a host city better than we found it mathematically.

But how? What would such a contribution to a host city look like?

We didn’t get this far. Remember that I said it was a four-minute conversation? AND that it was a dream? That said, I sort of imagine that this “contribution” would be integrated into the conference itself, like a session or series of sessions. Those folks who attend the session(s) would go out into a local community. Or not. Maybe the local community comes to the conference, like a panel discussion. Maybe we invite students. Maybe a small group of local attendees tackles some of the logistics and planning before the conference starts. Math on a Stick comes to mind. These all seem like really big ideas. Maybe too big, I don’t know.

What I do know that there are so many thoughtful and creative math educators out there (if you’re reading this, that means you) who attend these conferences. And I know that they would be about this life. They would want to give back. They have ideas.

After I shared sidewalk math (here and here) as a My Favorite on day 1 of TMCNYC, Michael suggested that that could be an example of a thing we use to give back to a host city. We could hook up with a local who knows a deserving (possibly underserved) community and then go tag up part of the neighborhood with sidewalk math. Someone at the conference called it guerrilla math. It seems very, very doable. And one that would present a local neighborhood with a cool, useful mathematical exploration AFTER we leave. Having been lucky enough to attend three math ed conferences this year, two of which were local, I’m going to hold myself to proposing this session at a conference in the near future.

Thanks Michael for helping me dream.

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Teaching is personal

We are invited to teach information as though it does not emerge from bodies.

~bell hooks, Teaching to Transgress

Often times I hear the phrase, “separate your personal and professional lives.” Of course, this catch-all phrase assumes a dichotomy and that separating our personal and professional lives is actually possible. It makes the issue a matter of black-and-white. It’s as if our home and work lives are completely distinct.

I can’t speak for other professions (I’ve only ever been a teacher), but I’m more and more convinced that this just isn’t so for teaching.

Teaching has always felt like a profession that does a great job of blurring the lines between the personal and professional. The work we do in the classroom is so humanistic in nature. We are in the business of helping other humans better themselves through learning. We help them uncover new ideas, connect it to what they already know, and reflect on why it matters in the long run. For me, these are the types of human interactions that require my full self to do effectively.

Similarly, my last post hints at how my professional life has influenced my personal life. I probably wouldn’t have made the decisions about buying custom t-shirts and using sidewalk chalk to make accessible math for my community had I been a construction worker or a dentist.

Back to teaching, I suppose we can help students uncover objective facts neutrally. We can attempt to “remove” ourselves from the delivery of content. We could teach by focusing only on the purely academic (see definition 2) side of things. But by doing so, we disregard every human in the room. And teaching is very, very personal work. Every day in my classroom, there are over 30 wildly diverse personalities converging. This convergence is an explosion of knowledge and social and emotional tendencies that cannot be forced to do anything that’s worth doing. Over the course of a school year, somehow I must learn who my students are as learners and people. I must plan for them, their dispositions, their vulnerabilities, their cultures, their identities, their families. I must somehow leverage all this human capital for the betterment of everyone present. I’ve realized that this happens tortuously slowly, like a tugboat pushing a barge. But at the same time, it also happens collectively and in unison. In a recent talk, Patrick Honner so eloquently said that teaching “brought me back to the edge of human knowledge…and it’s not lonely out there, because we’re out there together.”

Because we are bound to our students on this adventure to better ourselves each day, how can we be expected to be mindful of our students’ personal lives, their lived experiences, if it is expected that we forget about our own once we welcome them into the classroom?

Who I am as a person outside of the classroom universally affects what I do inside the classroom. If I am teaching genuinely, my two “lives” are inseparable. Do I forget this at times? Heck yeah. When I do forget it, I say and do things at critical points that separate who I am from the situation. Usually, my decision is one that dodges conflict and that allows everyone to sit peacefully in their comfort zone. I don’t challenge the given.

As the inherent leaders of our classrooms, acknowledging and embracing our personal lives and attitudes in the classroom is critical to its ultimate success. This happens when we plan before students arrive and during class on a one-on-one and whole class basis. Most teachers don’t even realize it when it’s happening. Justifyably so, many of us (myself included) place much of our energy on addressing our students’ needs and forget about our own selves in relation to that work. But just like our students, we too have personal histories, interests, identities, and biases. These features are deeply rooted in who we are as people and, consequently, who we are as teachers. As important and involved as teaching is, I’ve found that it demands that I purposely recognize, and integrate, my personal self as part of the process.

As teachers, who we are matters. A lot. In fact, whether we like it or not, our personal lives are already part of our professional lives. If we can do our best to welcome that into our practice by design, while it won’t make our work any easier, it may make what we do with students more relevant and forthcoming. Maybe.

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