My 2018 in Books

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.

 

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I have trouble talking about my teaching

I have trouble talking about my teaching.

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.

Teacher: 

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]

Screen Shot 2018-11-04 at 6.12.03 AM

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]

Screen Shot 2018-11-04 at 6.20.49 AM

Then the same for the 2nd unit in gold. [Updates drawing]

Screen Shot 2018-11-04 at 6.22.44 AM

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]

Screen Shot 2018-11-04 at 6.24.29 AM

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]

 

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Student as author and critic of mathematics

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 handoutrubric, 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!

 

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