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 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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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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#blackbrillance + social justice + problem-based learning

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One of my summer reads has been The Brilliance of Black Children in Mathematics by Jacqueline Leonard and Danny B. Martin (inspired by Annie Perkins). I’m almost three-quarters of the way through it. It is rather dense because it’s packed with research, but I’ve been enjoying it.

Chapter 6 has stood out. It focused on the development of culturally relevant, cognitively demanding (CRCD) mathematical tasks. The authors of the gave this definition of CRCD:

Culturally relevant, cognitively demanding tasks should be mathematically demanding tasks and embedded in activities that provide opportunities for students to experience personal and social change. The context of the task may be drawn from students’ cultural knowledge and their local communities. But, the use of context goes beyond content modification and explicitly requires students to inquire (at times problematically) about themselves, their communities, and the world around them. In doing so, the task features an empowerment (versus deficit or color-blind orientation) toward students’ culture, drawing on connections to other subjects and issues. CRCD tasks ask students to engage in and overcome the discontinuity and divide between school, their own lives, community and society, explicitly through mathematical activity. The tasks are real-world focused, requiring students to make sense of the world, and explicitly critique society — that is, make empowered decisions about themselves, communities, and world. (p. 132)

The authors go on to caution the reader that finding/creating a CRCD task isn’t enough:

It should be reiterated here that task creation is by far only the beginning. Culturally relevant pedagogy necessitates that teachers learn about students, their culture, and their backgrounds. Ladson-Billings (1994) indicates that the teacher must be the driving force to creating a culturally relevant classroom. The contexts of the tasks alone will not necessarily make for the culturally relevant environment. It is the thinking behind the tasks and the actions during the implementation that make them culturally relevant. Without the appropriate set up of the task and the accompanying discussion and connection to the students and/or their communities, the task although created as culturally relevant, will lose its relevance. (p. 134-135)

This all got me thinking about all of the problem-based learning that I did last year with my kiddos. Our focus all year was thinking about, discussing, and solving problems that built on each other. As such, the big ideas of the algebra 2 curriculum were slowly uncovered through the problems. I used a range of pedagogical approaches but mainly leaned on whiteboarding (VRG and VNPS) to foster small and whole group discussions. On top of all this, back in June, I learned of Brian Lawler, who has done work around how teaching mathematics equitably requires problem-based learning. It’s an interesting take and learning from him provided even more incentive for me to improve my PBL approaches. Here are the slides to a presentation that he gave at the PBL Summitt in 2016.

So reading through chapter 6, it hit me that the PBL setting that I’m constantly improving affords my kids frequent, bite-sized opportunities to have meaningful discussions about relevant, empowering mathematics — exactly what I didn’t do last year. I centered all of the problems in contexts typically found on the Regents exams, which surely has its place, but when considering that 90% of my students are either Black or Latinx, it is an issue. The bottom line was that there was a strong disconnect between the problems I curated and my students’ lived realities. Here’s an example from last year’s problems (I could have chosen many more):


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While fairly procedural, it’s a pretty standard Regents problem. Most algebra 2 teachers in New York wouldn’t complain too much about it.

Other than the unrealistic nature of the problem, what I’m coming to grips with is that the discussion we have a problem like this involves just mathematics, not the implications of the mathematics and how it directly affects how my students view themselves and/or society. The challenge I’m setting forth to myself now is to find ways to change the narratives that my problems present to my students that will help us have more meaningful, transformative conversations.

For instance, after combing through the website Radical Math, I found myself thinking about all those payday loan joints that are everywhere in the city, especially in Black and Latinx communities like where my school is located (and where I myself live). With interest rates as high as 400 percent, they help create a wicked cycle of debt that cripples many folks who are struggling to make ends meet — some of whom are quite possibly parents of my students. In addition, they target people of color. I’m thinking that instead of focusing on Bella, Ella, and their mythical interest rates, I could help my students explore about the damaging impact these lenders have our communities through introducing data from the above sources and through a series of problems that they grapple with. It’s not perfect, but here’s an example:


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I’m pretty bad at using math to generate discussions about broader social issues like race. But then again, apart from beyond the white dudes, I’ve never had math problems to catalyze such discussions. I hope I’m better with facilitating discussions about problems like this, to help students see how they can better identify with math. If so, the result could be something important, relevant, and empowering.

This is a long post.

Last thing. The authors shared some examples of these sorts of problems that were created by graduate students who were also teachers. What was interesting was that, after studying the problems, the authors found that “very few of the teachers used race as a basis for their culturally relevant tasks.” Instead, the primary culture the teachers relied on was age. For me, it’s easy to get excited about some other aspect of problem set and get swept away in White culture, so this is a reminder to deliberately seek to address race in the problems and activities I use.

Through all of this, I feel like I’m getting closer to where I need to be, but I’m still left thinking about the many ideas in algebra 2 and how I might address them in the midst of the looming Regents exam.

 

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