Necessary Conditions was published five years ago this Fall. I’m not sure if five years is a long time or a short time, but it’s a natural time frame to reflect on the book (since we evolved to have five fingers instead of, say, four). So I apologize in advance for what is sure to be the most self-indulgent blog post you’ll ever see on this website.
Recently, Necessary Conditions seems to have gotten a second life. I’ve heard of more districts and schools doing book studies en masse than ever before. I know of a handful of teacher prep programs that have been using it for their methods courses. I’m not going to pretend it’s on the NY Times best seller list or anything, but it’s been a slow and steady burn.
And that kind of makes sense: it’s not a small book. It’s not a “Try these three tricks to get your kids engaged!” book. It’s been challenging for me to give hourlong standup presentations about the book, because it’s so complex and interconnected. The book posits a framework of how students experience math over the course of their school career and offers teachers a means to assess and improve those experiences. That’s not a 60 minute presentation. Rather, it is more aligned with my day to day teaching and coaching work. To be sure, I have gotten better at honing in on acute aspects of the book to make it into 60 minute presentations.
There’s a story about P.T. Anderson when he was writing Magnolia. Initially, the movie was supposed to be a nice and short, 90-minute rom-com. But as Anderson kept writing and writing and bringing in more characters, the story became increasingly complex. The final result was a 3-hour web of interconnected storylines (with several more left on the cutting room floor). Necessary Conditions was initially supposed to be nice and short. It was going to be a book about enacting problem-based learning in your class. I probably would have titled it something snappy or generic. It would have been less than 200 pages. Instead, the more I spent time talking to students, it became clear (slowly, over time) that there were untold stories when it comes to books about math pedagogy.
Just about every secondary-directed book about math or math instruction neglects huge swaths of the adolescent math experience. They posit a type of activity, talk moves, etc. And those are helpful. Probably immediately more helpful than a book like NC that posits that even the best of talk moves is a tiny fraction of what will ultimately help students learn math and believe that they are mathematicians.
It’s why it’s been particularly heartening to see the book used in methods courses for pre-service teachers. Without totally realizing it, the book acts as a corrective to my pre-service teaching experience, which was useless. The concept of Academic Safety and how Tasks and Facilitation interact with it is well served by being examined before you are lost in a pile of assignments.
What has resonated the most with teachers?
The concept of Academic Safety was new to many secondary teachers. It’s what helped the book penetrate the market and sets it apart from other math education books. Most often, I get positive feedback on the Active Caring piece. I also get understandable soft pushback from teachers who are overleveraged physically and emotionally from the job.
Only less slightly, the chapter on Assessment (Chapter 10) has made an impact in schools. That chapter opened the door for my dissertation work here in Colorado as a school district wanted to reimagine their assessment practices. The marriage of Anchor Problems and Portfolios in particular has impacted how many teachers operate.
What’s changed since Necessary Conditions was published five years ago?
The laserlike targeting of LGBTQ+ teachers and students and the erasure of BIPOC identity by conservative legislatures and school boards might be the most consequential stories in education in the 2020s. It is impossible to talk about social-emotional safety in schools without referencing laws that cause active harm to students. While discrimination, bullying, whisper campaigns, and violence existed in 2018, legislatures have been enacting laws that specifically target transgender kids. Students are being targeted by bills that require teachers to deadname and out their students. There are schools and districts, such as the one I grew up next to in Texas (Cypress Elementary, part of Leander Independent School District), where you cannot display a pride flag. These legislatures are also targeting curriculum that doesn’t support white supremacy and are removing books from school libraries that don’t conform to a whitewashed version of history. Students of color are being harmed through erasure of their identity. Education companies and non-profits are going along with it.
Necessary Conditions discusses these issues, including race and gender based stereotype threat, but doesn’t imagine a society that would become more violent to students of color and LGBTQ+ individuals. Foolishly, I thought that the successful pushback against the North Carolina bathroom bill in the mid 2010s portended advancement for the LGBTQ+ community in terms of discriminatory legislation. I was clearly wrong.
Less importantly, some of the book already feels outdated. An examination into the Desmos calculator (it has sliders, people!) felt crucial when I was writing it in 2016, but now everyone that cracks open NC probably knows about Desmos. There are other equally effective technology tools that I could have showcased (PolyPad, Graspable Math, etc.). There are also additional task types that I could have included, such as Menu Math and Between Two Numbers.
What’s next for Necessary Conditions?
My hope is that the slow burn continues. It’ll find its way into more, lengthier chunks of time for teachers to digest, such as in a schoolwide book study or in methods courses.
I’m still incredibly proud of the book. I’m going to take this opportunity to high-five myself in a way that I don’t often do. I think it’s the best written book about math education that exists. The compliments that warm my heart the most are when my non-math teaching colleagues tell me that the writing is really good. That’s thanks in large part to Tracy Zager who spent untold hours showing me carefully how to write better. (Haranguing the great Fawn Nguyen to write the foreword was also a huge get for the book.)
What makes the writing of Necessary Conditions different from most math ed books is the centering of the students’ voices and teachers’ voices. Writing about my conversation with Damien (Chapter 1) unlocked a narrative component that is unique to the genre. I learned about research and practice from math education writers; I learned about writing from Anne Lamott. Math and math pedagogy books sometimes include vignettes, but rarely include narratives; fewer still include heart.
I wish I could write a second edition, to get another crack at tackling some of the aforementioned issues. I would probably swap out Polygraph with another type of Essential Task. Alternatively I could create an abridged version with fewer pages. Or a version specifically for methods courses. Maybe one day I will write that sub-200 page book based on solely quality tasks. But it’s going to be hard to transition away from the primary framework of Necessary Conditions.
I still kind of can’t believe I wrote the thing.
emergent math 