I was really pleased with my reading habits this year. I read more than I ever have. In 2017, I read 26 books. Given some demanding life commitments that I knew I had this year, in January I set a goal of reading 20 books. As of right now, I have finished 30. Yay me! (And thank you NYPL for being amazing.)
So when I read Patrick Honner’s post Books I Read in 2018 where he summarizes his year of reading books, I was inspired to write this post. He also inspired me to request On Writing Well from the library. Thanks Patrick!
Most of my reading this year revolved around race. This continued the trend from last year as it’s something that has been on my mind a lot. In addition to reading about race and getting closer to my own whiteness, I was more conscious of the race of the authors I chose to read this year, ensuring that authors of color made up a large percentage of my reading.
Nonfiction | This is usually where I live when it comes to reading. The most impactful were:
Messy by Tim Harford. I’ve always believed that disorder and randomness are highly underrated. This book helped me to better see why.
White Fragility by Robin DiAngelo. This was probably the most thought-provoking book I read this year. As a white man, it helped me understand how my own ignorance and privilege has contributed to our racialized society. Written for white people, it was unapologetic and bold.
Teaching to Transgress by bell hooks. Chapter 10 was probably the most important chapter of any book that I read this year — and maybe ever.
Goodbye Things by Fumio Sasaki and Essentialism by Greg McKeown. During late summer and early fall, I read a string of books centered around living with less. Less stuff, less ideas, less commitments. Both well-written, these were two of my favorites.
Born a Crime by Trevor Noah. Easily 5 stars. I knew next to nothing about Apartheid, so (once again) my ignorance was on full display here. I savored Noah’s superb storytelling all the way to the end like a good meal. I was sad that it had to end.
The Subtle Art of Not Giving a F*ck by Mark Manson. This was such an engaging book from start to finish. This is technically a self-help book, but it didn’t feel like it. It’s more of a reality check; it’s woefully pragmatic and I love it.
Between the World and Me by Ta-Nehisi Coates. While I haven’t finished this yet, I already know that it’s special. Both vivid and powerful, he shares a lived experience in a way that feels like an obligatory read for anyone in this country.
Fiction | I told myself that I wanted to read more fiction as compared to last year. I succeeded! Last year I read 3 books and this year I read a whopping…5. I’m trying to get better. Notable were:
The Hate U Give by Angie Thomas. This really made me think. It took me to places that I never knew I always needed to be. It transformed something that’s in the news every day — young black men who are targeted by the police — something tangible for me. Reading it was a visceral experience. I read it before the movie came out and still haven’t seen the movie, but I want to.
Americanah by Chimamanda Ngozi Adichie. I read this near the end of the year and the timing was perfect because it tied together so many social issues and stereotypes. It centers on one African woman’s journey in — and out of — American culture. Plus, the writing was stellar.
The Curious Incident of the Dog in the Night-Time by Mark Haddon. Having taught several autistic students through the years, and never making an effort to truly understood their experience, this book was fascinating and informative. It provided such a clear and unadulterated look into the perspective of an autistic young person.
Part of the reason for this is that teaching is so damn complicated. This makes it hard for me to have conversations about how my students learn — especially to teachers that I don’t know. Sometimes I just avoid talking about myself because I fear the incoherent answers that I’ll provide to the questions about what I do every day with my students. This got much worse last year when I started teaching through problems.
To get better at talking about myself, my classroom, and my students, I’m going to simulate such a conversation. I’m speaking to a fellow algebra 2 teacher. The scene opens when I make a comment about how they’ve set up their units.
Me: I like how you’ve structured your units. After your review unit, you start the year with exponential functions? That’s interesting.
Teacher: Yeah, it’s only the third year we’ve taught the course with the new standards, so our math team likes starting with exponentials and then diving into logarithmic functions. We then go into polynomial and rational functions and end with stats, probability, and trig.
Me: I like that. The standards place a huge emphasis on exponential functions now…it’s good to get that off the ground early. This is also my third year teaching with the new standards. There’s so much content in algebra 2 that I’ve run out of time each of the last two years. I couldn’t teach it all.
Teacher: There’s so much! How do you do your units?
Me: [Feels uneasy] Umm…I don’t have units.
Teacher: [Confused look on face] What do you mean?
Me: I suck at doing it, but I teach through problems.
Me: It’s confusing, even to me. All the topics that were in my traditional units are now all mixed up…but it a way that helps bring them closer together. Instead of having discrete units where topics are isolated from one another, the problems allow for the concepts to be easily interleaved, spiraled, and married in ways that I found hard to do when I had units. I’ve realized that a lot of what and how students learn in math class can be studied nonlinearly…and that’s what my classroom reflects.
Teacher: So, wait, are the kids just solving random problems? How do they learn?
Me: Sort of, but I think a lot about how I sequence the problems. I’m very intentional about which problems kids do and when they do them. So while on the surface the problems may look random, underlying themes and concepts from algebra 2 emerge for students through the problems over time.
Teacher: … [still confused]
Me: Here, let me show you what I mean. In a typical math class, the units are sequenced and taught linearly. [Gets paper and begins drawing] For example, take four units from the school year. Traditionally, when we finish with one unit, we move on the next. [shows drawing below]
Instead of using that model, I interleave the topics, skills, and vocabulary from each unit to span the entire school year. My old units are now parsed. Think of the first unit in purple as broken up into smaller pieces and spread out over the course of the school year. [Shows drawing below]
Then the same for the 2nd unit in gold. [Updates drawing]
And so on with the remaining two units. Notice that some pieces are bigger than others. In the end, it might look something like this: [Updates drawing again]
One of my goals in using this model is that, since students are frequently revisiting key ideas from the units, it helps with retention. With all the units mixed up, it makes it harder for the students to remember what they’ve learned…but that’s the point. It’s messy by design. That said, I build coherence by thoughtfully sequencing problems.
Teacher: Hmm…I’m wondering how your lessons look?
Me: Well, I typically assign them 3-5 problems for homework. The problems aren’t “practice,” as homework is traditionally viewed. They are more like puzzles or explorations that I ask the kids to do before class. It’s not expected that they understand and speak to all of the problems when they walk into class…I fully expect them to have questions. I also expect them to do individual research to help them figure out the problems. And because of how concepts are interleaved, the problems are usually all on different concepts — and have roots in different units. We don’t typically study one idea per day as is customary in math class. Instead, we study several ideas — and sometimes they are not directly related.
Anyway, we’ll spend the entire period discussing the homework problems in small groups and as a whole class. I have large whiteboards all over the walls that help with these discussions. Students are fully responsible for putting up problems and trying to gain a better understanding of them together. If they cannot (or do not) put up meaningful work to drive our thinking for the day, then they don’t learn. Also, I put few constraints on how the discussions look and feel. The kids typically move about the room freely.
Teacher: So where do you come in?
Me: Most days I help students make sense of the problems while in small groups. I also sequence student presentations of solutions for the whole class discussion. Equity of voice is important here — I keep track of who presents and how often. I also step in with direct instruction on the problems when it’s needed.
On other days, usually 1-2 times per week, things will look more like a traditional lesson where the problems focus only on one key concept. I consider these my anchor experiences that usually focus on high-leverage concepts (like sequence notation or logarithms). I also bring in Desmos Activities all the time.
Teacher: I wonder, where do you get the problems that you use?
Me: All over the place. I steal most of them from other teachers online, but I do write some myself. Those suck. I use Regents problems, too.
Teacher: How did you learn about all this?
Me: Two summers ago I attended the Exeter Math Institute. It blew my mind. As an immersive PD experience that pushed me beyond my comfort zone, it helped me completely reimagine what math teaching and learning can look like. It was different and challenging. It was led by a teacher from Phillips Exeter Academy who used one of their problem sets with us for a week. Exeter has pioneered the problem-based model that I’ve adopted…and they are well known for their problems — they’re tough, but they’re rich. I have included a couple of them in the problems that I give my students.
Teacher: This sounds interesting…I would love to see it in action.
Me: You are welcome any time. I must say, though, there are tradeoffs to using this model. Lots of them. First, students generally don’t like it…at least initially. Giving them so much control and disrupting what they know to be “math class” causes plenty of frustration and discomfort. And they are regularly confused and don’t always leave each day with a “clean” answer or understanding of a problem or concept. This can be hard for everyone — them, me, their parents. Last year, I wasn’t prepared for the amount of dislike and pushback I got. Second, since students learn content nonlinearly, it’s a mess for me to plan and sequence. Also, each day can be somewhat unpredictable because what we do each day is largely dependent on students’ independent work before class and the motivation to drive learning during class. Our discussions can suffer as a result of kids not doing their part…which happens A LOT. What makes this worse is the fact that I’ve never met another public school teacher using this approach…so I haven’t been able to critically bounce ideas off anyone. This makes it very hard to improve. I miss co-planning. There’s more, but, yeah…[awkwardly changes the subject]
I’m hoping to improve my students’ journal writing experiences this year. After learning about problem-based journal writing from the work of Joseph Mellor and Carmel Schettino, last year I created/stole a fancy handout, rubric, and told the kids to go write.
I was hopeful for more, but the kids ended up only writing one journal entry. This is totally a result of me assigning in the late in the year, yeah, but mainly because I was too lazy to actually read through them all. I pitifully underestimated how long it would take to read what was essentially 120 essays. English and history teachers out there, I can now finally appreciate your workload. I feel for you.
Fast forward to this year. I’m ready to step my game up. I’m primed to better position my kiddos as authors of mathematics. I tweaked the handout, rubric, and my introductory talk with kids about writing and why it is important — even in math class. Through the journals, they will be formally reflecting and thinking about their own mathematical thinking in a deep-ish sort of way. Just like with the Mathography, I’m pretty sure they’ve never done this before.
One of the key differences this year is that instead of me being the authority figure on providing feedback and grades (and putting this onus on myself for reading ALL those journals), I am forming six editorial boards in each class. Each board will be a yearlong grouping of students who will peer-review the journals.
I got this idea after I read The Art of Problem Posing by Stephen I. Brown and Marion I. Walter this summer. After they’re turned in, I will distribute 4-6 journals to each editorial board, who will use the rubric to do a blind-review (I will remove all names of journals) to discuss, assess, critique, and give feedback on the mathematical writing of the authors. I will have final say on all marks, but I will fully expect integrity, honesty, and fairness from the boards. And by reading through and analyzing so many of their classmates journals, I hope that their own mathematical writing gets better over the course of the year.
I’m really hopeful that they’ll get to write four journals over the course of the year. What’s really cool is that after each round of submissions, each editorial board will select one journal that they read to be published at the end of the year. By “published,” I mean featured in a compilation that I will print out in a little booklet in the spring. It’ll look and feel professional…like this one that I came across at TMCNYC this past summer from Ramon Garcia who teaches at Borough of Manhattan Community College Adult Learning Center:
By the end of the year, I want every student to get at least one journal entry published.
I’m not 100% confident in any of this, but I am very excited. At a minimum, I know it can’t be any worse than last year!
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?