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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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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Why am I all about chalk and t-shirts this summer?

I need to let this out of the bag.

This summer, I have had two things on my mind more than they probably should be:

  1. using sidewalk chalk
  2. buying t-shirts

Why? Hang on.

First here’s some of what I’ve done with the chalk:

And these are the t-shirts that I have bought:

Through both the chalk and shirts, I’ve found myself publicly advocating for math like I never have. Obviously, I’ve always been a proponent of math in my classroom, but now through what I subtly wear and create on the pavement in my neighborhood (and around my school), I’ve found myself attempting to transfer this passion more broadly…to the general public.

With the awakening of my social conscience during these last few years, I am more mindful of the damaging stereotypes and inequities that exist in and around the culture of learning math. Far too many people in society are put off with math as being a cold, lonely subject that is reserved for the elite. The reasons for this vary, but, as a math teacher, I think I am really coming to grips with the responsibility I have in reversing this trend, even if most of my effort goes unnoticed. There’s something bubbling up inside me to find and create small, practical ways to promote math as an accessible, friendly science…that go beyond the scope of my classroom.

It’s a very steep mountain to climb, but the hope with both the sidewalk math and my new t-shirts is to promote equity, access, and exposure to math in unique ways and to spark meaningful conversations about math (potentially with perfect strangers). Along with this comes helping to shift the mindset of how other people (young and old) view learning math and their own mathematical value.

I’d like to think it has worked…as both the chalk and shirts have elicited reactions from people I’ve encountered this summer. Two other teachers even liked my t-shirt so much that I went ahead and got them one. I guess that’s a good thing.

Come to think of it, this is really no different from Sara VanDerWerf’s call for math teachers to identify themselves evangelists.

 

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