The Anti-Sentence

Ask teachers to fill in these two blanks:

1. Math is ___________________________.

2. School math is ___________________________.

I’m willing to bet that sentence #2 is the anti-sentence of #1. When I did this with a roomful of teachers, one teacher shared out loud that she had nothing for the first blank—nothing—but for the second, no hesitation: “School math is required.”

That’s what made me say it out loud, twice in one day—to the 60 or so people in that room and again to the driver who took me back to the airport: math should not be a required subject in school.

Of course, I work full time for Amplify, and our math product is Amplify Desmos Math—one I believe in and am excited to share. I live in this space: Since math will remain a requirement, here’s a damn good math curriculum.

I had it good as a teacher. I had my principal’s trust that I would do my best to serve my students and their learning of mathematics. I had fertile soil and viable seeds. It was my job to provide nutrients and prune, to grow our mathematical garden of big blooms and glossy green foliage. The work was never-ending, but so was the reward.

Outside the classroom now, I’m reminded that progress is molasses slow. The Common Core State Standards came out sixteen years ago. Sixteen. Our most recent nationwide overhaul is old enough to drive.

The forever war. We are still fighting over direct instruction versus problem-based learning. Still. The math wars started in 1821, when a Harvard grad named Warren Colburn published an arithmetic book with the radical premise that children should discover ideas before drilling them—and we’ve been fighting about it ever since. But of course we have: when every child in the country must take a subject, every decision about how to teach it becomes a decision imposed on millions of kids—so of course it’s a battlefield. Meanwhile, the best teachers I’ve watched do some of both, because children are not a position paper.

The theory parade. Every few years (decades) a new theory arrives to explain what we’ve been doing wrong. In math alone we’ve marched behind constructivism, discovery learning, productive struggle, growth mindset, etc. Learning research matters—but it never ends, and theories fall in and out of favor. I’m afraid to say anything in case it got shelved last Tuesday. Some of the parade wasn’t even math’s fault: learning styles came and never left—long debunked, yet still baked into most early childhood classrooms. The research churns; the kid in period 3 who’d take raw spinach over fractions is still sitting there.

The acronym graveyard. I just can’t. There could be a game show made entirely of educational acronyms—Who Wants to Be a Millionaire? but without lifelines, because no one you’d call could help you anyway. California keeps an official list; on it, SED has three different meanings and the state seems fine with that. Every new initiative arrives with its own litter of acronyms, and the acronyms outlive the initiative. I’d rather save my RAM for the kids’ slang. I once replied to my son’s text with LMAO, and he wrote back, “Do you even know what that means?”

The math that doesn’t math. A teacher shared this with me three days ago, her voice full of defeat: the class period is perpetually shorter than the lesson. But the deeper problem isn’t the missing minutes—it’s what the shortage does to her. She teaches afraid: afraid of falling behind the pacing guide, afraid of not covering what’s on the test, afraid that the minutes she spends letting kids actually think are minutes she’ll pay for in April. Nobody handed her that fear on purpose. It comes standard with a subject everyone must take.

So, yes: if I ran the world, math would not be required. It would live with music and painting and poetry. In that world, we do math because we want to. It relaxes us—and it tugs at us, too, to come back to it right after the dishes. The coffee shop posts a problem of the week on the chalkboard, right between the mochas and the lattes. The bartender with his bartending ears shares a new problem he just overheard from the couple at the far end.

But I don’t run the world. Math is required. So how do I keep moving without getting swallowed by the noise? Here’s what that would look like if I were still in the classroom.

Number talks and visual patterns. I mention these warm-up routines often in my talks. Whatever curriculum my district grants me, I’m starting class with these routines, alternating them every other day. It’s the IMMEDIACY for me: walk in and do math, get it right or almost right, get it wrong and learn, share with the class—ah, Bethany’s way is pretty cool; oh, Miguel, slow down and tell me how you see it again.

The 5 Practices. I first blogged about this book over 14 years ago. It's the INTENTIONALITY for me. Plan the lesson with Gabe in mind: his hand will go up three times before you finish your first sentence. Plan with Cathy in mind: she'll likely have the answer before you pose the question. Plan with Joey in mind: he'll probably come in 15 minutes late, and how are you going to get him started? Plan with Amy and Brent in mind: rumor has it they fancy each other—pray the random grouping separates them. However you plan, read the teacher's guide only after you've done your own thinking. The curriculum writers don't know your kids. That's why the guide is something you fold into your planning, not the other way around—you're the professional in the room.

Building Thinking Classrooms. I'm definitely on board, but that doesn't mean I read it like scripture. It's the FLEXIBILITY for me: there are 14 practices, each nuanced and cross-pollinated with the others. There are haters out there; they even have a hashtag. That's where your noise-cancelling headphones come in. Focus on doing one or two things well. When they become second nature, layer in the next, if you want.

The UDL classroom. Rachel Lambert gets full credit for educating (and humoring) me in all things UDL—an acronym, yes, but this one has earned its plot outside the graveyard. It's the ACCESS for me: I don't know a framework with a deeper research base whose whole premise is mathematics for all kids. It's also one of the heaviest lifts, and a high-quality curriculum should be shouldering most of it for teachers. Does yours? Shameless plug, but I warned you at the top that I live in this space: Amplify Desmos Math lessons are built on UDL principles, and showing teachers all the parts genuinely makes me happy.

Non-routine tasks. I was unwrapping a stick of butter and said to my son, “You know, if new research came out that butter causes cancer, I’d still be eating it, just as much.” He nodded in approval of my death by butter. It’s the BUTTER for me: non-routine tasks are to my teaching what butter is to my cooking. But you know that about me already—I always talk about this, no need to dwell here. Ha! Instead, here’s a newer gift, one I got from James Tanton:

How many triangular numbers are less than or equal to 100? In general, how many triangular numbers are less than or equal to a given value N?

Requiring math is what turns it into school math. I can’t fix that from where I sit, and neither can you. But here we are anyway, teaching—the most honorable and humble of the servant professions—and doing our best with what we have. So stay steadfast. Smile and wave politely at the next shiny thing as the parade passes. You are grounded in something the noise can’t touch: the resolve to do what’s best for your children, so that they might fill in the first blank someday. Math is beautiful and joyful.

Update:

From Kerri Zitar, a reel on playing the notes versus playing the music.

From Raj Shah, a video the Global Math Project folks made ten years ago. (I saw this back then and my one word was/is: beautiful.)