What I wrote in 2021

What exactly did I spend time on this year? Hard to say, or maybe it’s just hard to admit that my output this year was all over the place. Let’s sort by topic and see what it amounts to.

Book Stuff

I finished writing this book in summer 2020, and it came out in April 2021.

Was purple the right choice for the cover?

I wrote the sort of book about teaching that I wanted to read — short, personal, aimed more at the working teacher than the teacher-in-training. I thought there were some original perspectives in there, though I think it’s fair to say it’s mostly a synthesis of research ideas.

I wrote a few posts this year that expanded on the techniques from the book:

What is “fading out a worked example” and why would it work and also when?

Good explanations connect particulars to principles

Start class with the good stuff

Making Long Problems Shorter


I was hoping to get started with a second book at some point in 2021, but it never happened. Pedagogically, this was a year of grappling with a million little things, rather than one big one.

Is there a book to be written about whole-class discussion, growth mindset, the equals sign, and math fact memorization? That is the book that (apparently) I am ready to write about teaching, but it just feels like a potpourri to me at this stage.

A Good Eye for Arithmetic

What actually even is a growth mindset?

The Change-Resistance Explanation for Why Kids Struggle So Much with Algebra

A growth mindset is a tendency to explain things in a certain way

These included some of my most popular posts this year, for what that’s worth.

Some questions and answers about whole-class discussions

What People Get Wrong About Memorizing Math Facts


On to the math! Honestly, I didn’t learn very much math this year, though the last few months of the year have been a bit better in that department.

People Actually Really Like Mathematics

Teaching Yourself and Others


Honestly, I know so little about policy. You don’t come to michaelpershan dot com to learn about politics. The best you can say about me is that I’m a dabbler and that I try to react thoughtfully to whatever happens to be causing a fuss at the moment.

Was it a mistake to call KIPP the top recommended charity in the United States?

Teachers are afraid of hybrid learning (picked up here)

What if we ban private schools?

Some basic questions about college admissions

I Don’t Know How To Categorize These

If you trust hitcounts, these pieces were among my most popular. One of them is a would-be takedown of an incredibly popular education figure, another a joke, the last a very brief statement of purpose. I enjoyed writing each of these things but they don’t make it easier to figure out exactly what I’m doing here.

YouCubed is More Than Just Sloppy About Research

All the numbers from 1 to 500, ranked from worst to best by a middleschooler

Where My Cynicism About Education Ends


If you’re reading this, it’s likely because at some point or another I wrote a worksheet that you liked. Or I shared someone else’s worksheet, and you liked it. Or you liked something I wrote about algebra, or whatever. But I spent a lot of time this year writing sorta-funny fiction (or straight up humor) and some of it got published in places.

Is any of this good? I couldn’t tell you. But for completeness, I include it below:

The American Bystander

“I Am Baby, Persecuted in City of New York”


“About the Murderer”

Two Fifty One

“A Mathematical Magic Trick”


“I Am A Mad Scientist, And I Am Begging You To Just Trust Scientists”


For the first summer in years, I didn’t teach. During some of that quiet time I sat down to really try to do service to this essay, something that I’ve been thinking about writing for nearly a decade in one form or another. My teen years were dotted with weird Jewish things that I’m spending my adult life trying to make sense of. Adult religion is so normal. Mostly for better.

“A Time To Die” in Tablet

What am I going for here

I honestly don’t know! Looking back, it’s a lot. But do I regret any of it? Not really. I do wish that I was working on another book. Having a big project is good for me. Having a book is also quite honestly a nice thing for the ol’ ego. Blogging has never really been a “respectable” activity, in the sense that you could talk to family members about it without suffering a paroxysm of shame.

Then again, come to think about it, one of the few times this year that I told someone that I wrote a book, their reaction was to ask how anyone would ever hear about the book, let alone buy it? And then I had to once again shamefully admit that I’m a social media user. So there’s really no way out of the shame of writing. It’s an inherently shameful exercise, and maybe I’ll just try to own that embarrassment in the coming year.

Some questions and answers about whole-class discussions

Some teachers are architects, others engineers. Myself, I’m more of an amateur plumber, in the sense that I have clumsy solutions to issues I’ve created for myself. I show up and start thwacking away at a problem until it’s fixed and then I continue teaching, until I find something else wrong and go thwack thwack again.

This is very much how progress with whole-group discussions has gone for me. I’ve never had a big “aha!” moment that has fundamentally changed how I’ve gone about running a discussion with a group of kids. Just one problem after another that I’ve slowly amassed answers to.

I think that there is value in whole-group discussions. I think part of the assumed classroom contract is that students will be able to share their thoughts and that teachers will care, and I think that’s good. Students probably need practice sharing their thoughts, and over and above any cognitive impact, the social value of doing this is immense — not just that they can divide fractions, but that they’re the sort of person who can divide fractions.

OK, but there are problems with discussion. They all cluster around questions of inclusion, status, participation. So here is a list of questions, along with how I currently deal with them.

What do you do if a kid had a hand raised and was excited to share, but then put their hand down after someone else answered? And then you call on them, and they say “oh I was going to say what [other kid] said?”

I say, “how were you going to say it?” Or “why do you agree?” Or “how would you have put it?” And if they tell me they were going to say the exact same thing then I say, “no two people put things in the exact same way, with the exact same words.”

Basically I don’t want to create a classroom economy where all we value is being first to say something.

What if a kid says something and it’s complicated and you don’t think others heard them?

I’ll ask them to repeat what they said, but I’ll warn the class that I’m looking for someone who will be able to restate the idea — their first words will have to be “[Student] said,” and the goal is to get as close to what the student actually said as possible. I’ll correct them if they start “umm basically what I think.” No! You’re restating. I learned this from the New Visions Mathematics Curriculum and their instructional routines.

What if there are a ton of hands and you don’t know who to call on?

Then I might ask the entire class to express an answer at the same time. This only works for short questions (obviously), but if it’s a question like “and what would you do next to solve the equation 2x = x – 10” and I’m looking at a ton of hands, I’ll say: “let’s all say what we think at the same time,” and then the class will.

Really? How do you make sure they all speak at the same time? What can you possibly learn from that?

I usually find that a quick countdown and a very visible arm motion gets a group to say things all at once. “OK, let’s all say it together, 1…, 2…,” and then I gesture and they speak.

What’s cool about this is that everyone can participate. If pretty much everyone has the same (correct) answer then I get to congratulate the class, it’s a nice social bonding moment. Hey, we all did it! Nice!

It’s surprisingly easy to tell when there’s dissent in the room when we’re all trying to respond as one. Which gives me a nice follow-up move: “alright, there was definitely some disagreement when we all just called out, let’s talk about that.”

How do you make sure that you call on students in a fair way? In particular, how do you call on boys and girls equally?

I always try to switch genders when I’m calling on students to speak. If I’ve called on a girl, I’ll call on a boy next. And so on.

Some of the most cringe-worthy teaching I’ve witnessed is a teacher saying to a group of girls, “hey, girls are a bit quiet back there, what do you have to say?” Ugh. Gross. Ugggggh.

What if only boys are raising their hands?

What, like half the class is raising their hands and it’s all boys?


In that case I might ask everyone to put their hands down, without any explanation, and I’ll switch to cold-calling.

Cold-calling? Doesn’t that make students feel uncomfortable?

Yes, sometimes, which is why it’s important to do it right.

If I’m worried that students won’t have anything to say when I cold-call them, I stop the class and say: “Hold on everybody, I think this question requires some thinking, and I want to give you a moment to think about it.” And after I write the question on the board or whatever, I’ll assign partners and ask students to share ideas about the question with those partners. While that’s happening, I’ll walk around and see how those discussions are going. Often I’ll hear a kid say something and decide to cold-call on them when we return to the whole-group.

If a student is particularly shy or not confident, I’ll interrupt their conversation and say: “I just was overhearing, what you said was really smart and interesting. I’d like to call on you to explain that to the class. Can I do that?”

But this all represents a significant time investment, and sometimes our whole-group discussions are much shorter than this. In those situations, I’ll find myself cold-calling even though I’m not sure what a student is going to say.

What if you cold-call on a kid and they say something wrong? Isn’t that embarrassing?


I used to handle wrong answers in a bad way that emphasized (inadvertently) the student’s failure. Here’s how it went for me:

Me: What’s 3 + 8? Charlie?

Charlie: 10.

Me: Yes, super interesting. Anyone else have something to say? Yes, Susan?

This violates several principles of whole-group discussions that I have. One of those principles is: If you call on a kid, don’t leave until they’ve said something smart.

Another of those principles is: Don’t set up a kid to get knocked down by some other kid.

It’s never fun to say wrong things in front of other people, but a willingness to do so can accelerate learning. So I’m trying to reduce the social costs of wrongness, what people sometimes call “normalizing” error.

The way I do this (and in line with my two stated principles) is in two ways. First, I correct the child myself. Second, I give them a chance to revise. Here is what that above conversation might look like for me now:

Me: What’s 3 + 8? Charlie?

Charlie: 10.

Me: So [looking at Charlie] it’s actually not 10, it’s 11. But how can you prove that it’s 11?

Or maybe “how could you know it’s not 10” or “why is it 11” or “now given that it’s 11, what is 3 + 9” or whatever it is that you’re trying to teach.

But we’re going to stick with Charlie until he says something that everyone in the room agrees is smart, and then we’re going to give him credit for it, and then we’re going to move on.

What if Charlie never says anything right?

You gotta pick that follow-up question until Charlie has learned something or revised in some way. Hopefully it doesn’t take forever, and a few times a year it does and it can be a bit painful. I try not to give up, but you know, no absolutes in teaching.

Why is this all about managing student responses? Isn’t there more to whole-group work than asking students questions and asking them to answer them?

This is very important: no. I try to make as much of my whole-group time about asking questions and students answering them.

Do I give explanations? Absolutely. But I try to embed explanations in questions. Class begins with a question: “What fraction is this shaded piece of the whole?”

And then, after students respond, I say: “Notice that you can write this as 1/2 divided by 2, and that it equals 1/4. And this is true in general. For example, what is 1/3 divided by 2?”

And I think that’s a big part of how whole-group discussions can be engaging instead of a drag. A lot of boring discussions are light on questions for students and heavy on asides and reflections from the explainer. Questions, questions, questions. Let’s actually enshrine that as another of my Principles: Almost everything in whole-group should either be a question or a response to a question.

So, in summary:

  • If you have a ton of volunteers and the question is short, ask everyone to say it at once.
  • The goal is everyone participates.
  • Give yourself rules to make sure you’re calling on volunteers equitably.
  • Use cold-call so you don’t have to rely on volunteers.
  • To prepare for cold-call, ask individuals to think and then give time to discuss with partners.
  • If you call on a kid, don’t leave until they’ve said something smart.
  • Don’t set up a kid to get knocked down by some other kid.
  • Almost all time spent in a whole-group should be spent by students responding to a question.

Thwack, thwack, thwack, thwack.

Where My Cynicism About Education Ends

I think it would be helpful for me to outline precisely how cynical I am about education.

I am very cynical about the impact of wealth on education, and especially on what that means for social mobility. I don’t think education is the great equalizer in American society. I think maybe at one point it was, but now? No. There is competition for whatever is educationally valuable, and those with the resources gobble up those things fairly efficiently. Thanks to widening inequality the bottom 25% of Americans have fewer chances to rise above through schooling just as the costs of not rising are as high as they’ve ever been. It’s not good, very bad, and it impacts education at every level.

I am somewhat cynical about the school curriculum, in particular the school math curriculum. Math is big, and the school curriculum is narrow, and a dozen mathematicians would end up with a dozen different curricula. Sure, every kid should know something about numbers and algebra. But what exactly are we going for in high school? What’s with the onslaught of function types and finicky expressions? But it seems hard at this point to change things in a major way — the stakes are too high, see everything above about widening inequality, we are apparently stuck with the math that we have, more or less.

I am a bit cynical about the ability of math class to keep people from killing each other, as Deborah Ball put it. The gap between some of these social aspirations and the reality of the classroom is just vast. I don’t seriously hope that my teaching helps create informed citizens, or sparks social change, or inspires people to act more kindly with each other…

…but that last one actually gets pretty close to the limits of my cynicism.

Because I’m not at all cynical about schooling. I think that schooling is essential. I think that learning is valuable, really any learning, even if what we’re learning is somewhat arbitrarily chosen. I think it’s good to spend your childhood learning. I think it’s good to spend your adulthood learning. I just like learning. I think a large part of being a kind and good person is being able to continue learning about others and their needs. Learning is good, I am not cynical about it.

And school is a good place for most kids to learn. Highly imperfect, but despite the imperfections I’m not at all cynical about the big picture. Get a bunch of kids together, get adults whose job is to be kind and nurturing towards these kids? I’m not cynical at all about that, this is my job, this is what I love doing. And because I’m not cynical about any of this, I’m pretty intolerant of adults who aren’t kind to children.

And even if I am not very optimistic about “teaching so that people stop killing each other,” I’m pretty committed to being kind to people in the classroom. I think that’s valuable. I think kids just need to be around people who are kind to them. Maybe because it’ll impact them in some way, or maybe just because it’s nice? Not in the future, but right now.

In other words, the kids are here, in your classroom, and wouldn’t it be better if they had a good time instead of a bad one? That’s what my teaching is about.

So, tallying it all up, I’m pretty cynical about the curriculum, teaching for social impact, or social mobility. What that leaves is the classroom, in particular my classroom, where every day I get another chance to do it right or not.