Big Teaching Questions

It’s Tuesday evening.

It’s Tuesday evening. A faculty meeting just ended. I am sitting here with lots of thoughts I need to process. For some reason, I feel less fearful about sharing my thoughts recently. I don’t know if anyone else is going through similar things, but I’m sharing this post to hold myself accountable to this work, but also in case others can see glimpses of themselves and their thinking and feelings in my experiences. Here it goes. Stream of consciousness. No editing. Just writing.

Thought 1: I ended my classes this week. Our last classes were held on Monday and Tuesday. I didn’t know how to end them. I wanted to close the year with some solemnity and definitely not frivolity. I know when I’m feeling the most dark and depressed about the state of the world, I hold two things close. First, the starfish story. Second, it’s showing gratitude to others. Sharing with someone how they’ve affected you, thanking someone for some specific action they took or some role they’ve been in your lives, for helping you grow, or showing you grace. So I talked about these things. And I had students read the starfish story to themselves, and then write an email to: (1) a teacher who you want to thank for their work in online teaching, because students often can miss the humanity of teachers (just as teachers can miss the humanity of students), (2) a person who they haven’t been in contact much during quarantine but they appreciate and want to reach out to and tell them so, (3) someone who called them out and pushed them but helped them grow, or (4) someone in math class who made them feel validated and seen. I wanted to end the year by thinking about community and gratitude. Now that it’s over, I wonder if I did the right thing. I debating having more conversations on recent events (in two of my classes on Friday, we talked… you can read about that here…), but it didn’t feel like a way to bring closure to the year. But after my last classes, it just didn’t feel like closure to me. It wasn’t what the kids needed. And I had the even more horrifying and insidious thought. Maybe kids left with a message I never intended to send but also never specifically disavowed: “when the world feels dark and hopeless, the way to fix things is just to simply be kind.” Since I’ve had this thought, it’s been like an anchor weighing me down. I spent a long time trying to figure out what to do for the last class — and I still don’t know what I should have done instead — but this maybe wasn’t it. Or maybe I’m overthinking things. It just felt off. But then again, everything about the last few months in school has felt off.

Thought 2: Last night I had a revelation/insight which I wrote down and shared with some friends: “The anxiety and inability to have heart stop beating so fast. The repeated pain that Twitter and the news brings me. The tears and exhaustion. The past week has done a number on me. I’m going to try to say something openly and imperfectly. I remember saying a few years ago that I could intellectually understand when I heard poc talk about ‘trauma’ but I knew it was only intellectual and I was never going to be a strong ally until I could understand the word more deeply–because it’s a strong word and it wouldn’t be used without a lot behind it. I think for the first time I’m finally getting there. The weight of oppression feels — not intellectually, academically, but viscerally — heavy. Terrifying. All encompassing. Repeated. Relentless. I’m not saying I’m feeling trauma or know what it’s like to be a black poc. A student today in a discussion used the phrase “radical empathy.” I hope this discomfort and general awfulness I feel stays with me — though I hate it — because it’s allowing me to finally experience radical empathy. <don’t mean to center me-just trying to archive this insight.>”

After typing that out, I remembered I had written this sentiment down a year ago as I was thinking about this work and where I was when trying to grow:


This was in a much longer email to my friend Hema when we were planning last year’s Virtual Conference on Humanizing Mathematics. It took me over a year from recognizing this deficit of mine to actually being able to say I finally get it… I think. And that deficit was truly understanding one word.

Thought 3: I feel like I don’t neatly fit into a category when my school has conversations around race. I’m not white. I’m not black. I’m Indian, and first-generation American. My parents tried to Americanize my sister and me. I don’t find myself aware of daily slings and arrows, not a thousand cuts, not in overt ways, not often. I have a few examples that I can bring up, but not a whole bank of incidents. Because of the privilege I have had through most of my life, I often feel it’s easier to identify as white than a person of color.

I’m also not introspective — probably because it shines a light on things I don’t want to think about. I find it truly challenging to do identity work. I can think deeply about my teaching and my core values and my students, but somehow I’ve gotten away with not doing a lot of deep self-examination in my life. I know I’ve been deeply affected by the way I was viewed by society growing up, and I’m certain racism had a lot to do with it — but I’ve never done the work to think about myself through that lens. I literally only had one friend at school until late junior high. Surprise, surprise: he was also a student of color. I think maybe we were the only two students of color in our grade. I literally don’t think I ever put that together until now. That’s how little introspection I’ve done. I never got invited to birthday parties. But since that wasn’t a thing in my life, I never knew I should be missing them. I was bullied in junior high. I just didn’t know it was bullying because it was so normalized in my life by that time. I honestly wasn’t a sad kid. I just didn’t know any different, so instead of friends, I read books. I know I’m scared to do the identity work to see the ways that structural and insidious forms of racism and homophobia have played a role in my life. I’m a first-generation gay Indian living in America. How could they have not? I’ve clearly had a lot of privilege which has allowed me to get to this point without doing this identity work. But at the end of the day, doing this work, this introspection, forces me to contend with the inner core of who I am and how I see myself. To revise my own definition of myself. It’s easier to just… not.

Thought 4: I recently came off of a zoom meeting with all our school’s faculty (we’re a K-12 school). The anxiety I wrote about above hit me this afternoon. My heart was racing again and I had to lie down in my bed and take a nap. I woke up not feeling any calmer. For the first time, I turned my video off in a zoom meeting. At the start, I heard so many words. Kind words. Sympathetic words. And… I am so tired of words. And so as I heard everything all I could feel was cynical and angry. Give me time and space. Just cancel things. You want to help? Take writing narrative comments off my plate so I can work on healing. I don’t want to know that you know we’re grieving and how things aren’t normal. Just give me something concrete. Just give me something. And at that moment, I realized two things. I wanted them to fix me. I’m broken, and I just wanted someone to wave a magic wand, and I knew they don’t have the power to fix me. I also deeply understood, again at a visceral level, the repeated call that black people have had that sounds like: <<stop talking. stop talking. STOP TALKING. I’m so tired of all the nice sounding talking. So so so tired.>>

I also heard a lot of anger and white people calling for immediate change. Accountability. Demands that we all revise our curriculum this summer. I’m for that also. But I felt such cynicism. Because I just kept thinking “is this performative? is this virtue signaling?” You’re ready and now want everything to change immediately because you feel moved? What about all the people who were at the party demanding change before now? Their voices had been ignored and lost.

And the horrifying thing about my own cynicism is that it’s not like I’ve been one of the people demanding this kind of change for myself or for the school. I’ve been moving along in my personal diversity work, content with doing some work but never getting to the point where I was centering the work. I felt cynical and frustrated listening to people making these statements, even though I have no right to feel cynical and frustrated.

Although I mentioned I often feel white, it was at this moment that I realized all these things I was feeling were what those advocating, crying for anti-racist humanizing curricula, had been feeling for ages. Again, I don’t have any right to those feelings, but in the moment, I had those feelings of frustration and cynicism. I’m grateful — because even though I don’t deserve to have those feelings — I had access to something I hadn’t had before. I was hearing the well-intentioned words that people were saying but from a different perspective, through a different lens, a lens I didn’t have before.

I also was nervous that in the fervor, in the tidal wave of support and sometimes hope that we were going to turn our school into a shining-palace-of-anti-racist-work-so-show-up-teachers-or-get-out, that we were going to do harm. Yesterday I read a tweet that said something to the effect of “if you’ve never talked about black issues in your classroom before, just don’t just come into class tomorrow and bring up George Floyd. Just don’t.” The fear is that if we don’t do this work right, if we rush into things without being strategic and thoughtful, we can do way more harm to students. White saviorism wasn’t really mentioned, but I was thinking about it. Others were probably thinking it. A colleague brought this up, articulated it better than I could have, and I was grateful.

Thought 5: I wanted to reach out to this colleague who brought it up. I wavered and went back and forth on whether to send an email. I wanted to say thank you and I support what you had to say. (I did chime in, in the chat). I wavered because I’m hyperconscious of people who have been doing continual anti-racist work saying they’re tired of words. They’ve been given words over and over. Instead of signaling support, show your support by acting. I wavered but decided to send the email anyway. After writing it, I checked myself. I wanted to show solidarity and that my colleague was heard. But I realized what I wrote boiled down to “thank you” and “I heard you.” I wanted to do better. Without that, the email would have been more about me and virtue signaling. I wanted to demonstrate I really did listen and hear, and I am grateful. So I wrote down what I heard them say, specifically. I still don’t know if I did the right thing by sending the email. But I know I’m now asking the right question: how much of sending the email was about me, and how much about sending the email was about the person I was sending it to? In the weighing, I think I had my answer, and so I sent it.

Thought 6: I am broken. I am tired. I can’t stop thinking about what this all means for me this summer, when all I want to do is heal from this school year. We’re going to be required to do online professional development on remote/blended learning. I’m going to be writing 22 college letters of recommendation. And now I suspect there will be anti-racist readings and professional developments that we’re going to be asked to do, in addition to submitting ways we’re going to alter our curricula. I’m can’t tell you how intellectually and emotionally and physically tired I am. Writing narrative comments on all my students in the next week is a mountain I have to climb but carrying an anchor. But what comes after? That feels impossible.”

Thought 7: I think it’s time to end this post now. Believe it or not, I initially was intending to make this blogpost a list of actions I have started taking, plan on taking, or ideas I have and want to think through before I implement. In other words, concrete ways I’m going to do The Work. I fear that when all these immediate feelings fade away and I’m not being bombarded day and night on twitter and facebook and the news, I may just “opt out.” So I wanted to type some things down to be public in my work and accountable. Maybe I’ll do that post tomorrow. But for today, I’ll have to settle for writing about of my feelings and thoughts, so a month from now, I can try to come back here to a place where I feel destroyed… but ironically because of that, motivated.


At the end…

This is an archive of my day yesterday.

We’re nearing the close of classes with online schooling. It isn’t the end for me, with narrative comments and college letters of recommendations looming. But in terms of meeting with kids, there’s not much left, and I had my plans in order — at least well outlined in my head for some, ready to execute for others. But I felt anxious. On Thursday afternoon, I finished my last meeting, had finished my prep work for Friday, and was in a good place. But my heart was beating, racing, and I didn’t know what it was. That anxiety usually happens to me when I have something impending looming (like a stack of tests I need to grade, or a challenging email I need to write or conversation I need to have) and I am stressed about it. But I had none of that. But my heart was racing. I was a little short of breath.

I tried to relax, but I couldn’t focus on reading. My mind quickly wandered. TV worked.

A few different things had been thrown at me in the past few days. I wrote to teaching friends, as I processed and as a way to vent: “The problem about keeping boundaries in teaching is that boundaries I draw to protect myself often involves saying no to a kid who I can prop up by saying yes. I recently wanted to say no to four requests — some entitled, some respectful. I don’t have much left of me to give. I couldn’t. When it comes to me or them, I pick them. Again and again. As I slowly burn out. Teaching is hard. It will never not be hard. Because we give so much of our selves, emotionally, mentally. I don’t always want to do that. But I (honestly) don’t know how not to.” The same thing happened two weeks ago with college recommendations. I teach two junior classes. All but three juniors asked me for a recommendation. I felt utterly deflated. And honored. If someone could be in my head as I try to craft these, you’d understand the deflation. They not only take me forever, but they are emotionally draining because I want to capture my kids with integrity. I told my classes I had to limit them and I hoped they understood. I tried to be transparent and vulnerable with them about what doing this meant for me, and why I had to limit them, because they deserved that. But when I read their reflections, I couldn’t say no. I thought about the Giving Tree. I’m not that self-destructive. But for a moment I martyred myself.

The next day I woke up at 6:40. to an alarm. I quickly showered so I could check my kiddos nightly work. With online learning, I go through what my kids worked on each day before class to give individual feedback, but also know what we need to talk about together as a class. Although my heart wasn’t racing, I still felt… tight. Wound up. I was off. My kids were doing really strong thinking with hyperbolas and that made me happy. Some kids really struggled applying the quadratic formula for the first time and that made me wonder about my approach this year. I tried to address that by breaking it into two pieces and having them work on those separately — but maybe there was a better way? I woke up earlier than normal because I had an optional meeting I wanted to attend at 8:15am about the finances of our school. Our new head of school wanted to share where we were at — trying to be transparent about the decisions being made by the board and the school. I appreciated that, and her openness to talk about it.

Yesterday evening all advisors received an email saying that instead of meeting in our advisories, we would be meeting as an entire high school to give some time to discuss the recent tragedies involving Ahmaud Arbery  Christian Cooper  George Floyd  Nina Pop. I hadn’t heard of Nina Pop. Her name was misspelled in the email we received. Both of those facts together speaks to something about me, and something bigger than me. I entered the zoom meeting and scroll through 16 pages of faces. More, maybe. Tired, yawning. And then the meeting begins. It was planned to be a 20 minute meeting. It starts with Feel. Reflect. Act. Grow. Repeat. 

Two hours later, we’ve heard the voices of students and faculty. Anger and frustration about teachers not bringing up these current events, and in general black/POC issues, in classes. About the ability to check in and opt out depending on skin color, and whether things should be optional. Calls for people to go to march at Foley Square at 4pm. Kids requested breakout rooms early on, and I was assigned Breakout Room 22 with eight students, seven of whom I had never met, nervous about facilitating a conversation about race that I hadn’t prepared with strangers. My heart sang as my colleague and friend Monika was also randomly placed in the room. We launched the conversation with a focused question, but that didn’t work, so we went broader to “how are you feeling?” Kids started talking. At times, they were discussing with themselves. At times they were asking the opinions of the two adults in the room. One asked our thoughts on ACAB. I had never heard of that and with slight trepidation (should I know?) asked. “All cops are bad” two students responded. It’s a thing, they said. Reductionist. Monika was more eloquent and nuanced in her response. We talked about multiple narratives (it’s complex). The reasons for violence in riots/protests, and if it pushes things forwards or not (it depends). There are no pat answers and easy fixes, everything is layered, structural, cultural, historical. This is one slice, one slide, of a much longer movie. We end with each saying a word, phrase, or something we’re thinking about. I say “over-intellectualizing.” We move back to the main discussion room and I hear our high school principal talking. We’ve gone past first period. I’ve already emailed my kids in my second period class saying we’re not having class and to stay in the meeting. I look and see over 300 students and faculty are in the room. Faculty and students speak. I don’t know how they avoid talking over one another with 300 people, but somehow they do. Outrage. Questioning of the school curricula. Frustration with the statistics around black lives. Calling out hypocrisy. Asking questions about whose responsibility it is to educate kids on race — some say kids are responsible for themselves, some say its the school. Discussions about cultural appropriation. Sharing of feelings. The importance of being called out and of calling out. About the difference between being a liberal and an anti-racist, and being a liberal doesn’t make you an anti-racist. About the conflation between being liberal and being “good.” About being called out and accepting that as a gift. I think to myself that some of these kids must have read White Fragility. A concurrent conversation happens in the chat, twisting and turning with the vocal conversation. I keep silent. I like spaces for kids to talk. I don’t often know what they think about. This isn’t a “conversation” in the sense that we’re talking to find a goal. Right now, we’re talking because people need to talk because they have a lot bubbling up inside. We all have a lot of bubbling up inside. That… that was when I knew why my heart racing yesterday.

Our high school principal ended the meeting before our third period class. It was two hours from when we started. I open my zoom meeting for our Algebra 2 class. Obviously we aren’t doing math today. As the large meeting was winding down, I brainstormed what would make sense and gave my kids some options. They chose to continue the conversation. Unlike in the first breakout room I was in, this conversation was mainly had by kids, where I tried to give them space to speak and I listened. I took notes. They were in the same grade and class and knew each other. They didn’t turn to me for answers. I don’t have answers. I interjected sometimes, and then stepped away. When class was officially over, they were still talking, so I told them they could leave if they wanted or continue talking. Most wanted to stay and so we held court for 20 more minutes.

I was late to a book club I had scheduled during lunch. I emailed the student leader to start it up without me. We were reading Hannah Fry’s Hello World: Being Human in the Age of Algorithms. We were two adults and five kids. The conversation at the beginning stayed close to the book — which also had some themes on race — but very occasionally would go back to something from the discussions the school was having. It was fun and a lighthearted discussion with smiles. We had finished the book, and the scheduled time we had together was done, but we all continued chatting, and the conversation turned into questioning about what teachers think about lots of things. It morphed into an unguarded and vibrant conversation, one that I love having with my friends when they ask a lot of questions showing interest in what I do. I felt close to these kids, and appreciative for them. I don’t know much about what students think about, and looking back I wished I had asked students questions too. It was 12:50 and I had a class at 1:15 so we bid each other farewell. My eyes were literally vibrating at this point. I had been emotionally run raw and I had been staring at my computer screen since 8:15. All I had ingested was a cup of coffee. I heated up some frozen leftover macaroni and cheese and wolfed it down. I emailed a student I was supposed to meet at 2:20pm — an important meeting so I hated doing this — to reschedule.

I entered my last class. At this point I had very little more to give. I had very little left I could discuss. I told kids I had been on zoom all day, and I had been engaging all day, and I needed a 10 minute break to do math and recenter myself. So I did math with them for 10 minutes. And then instead of giving my kids a choice like I did for an earlier class, I made the decision that we’d read something together. I pulled up Francis Su’s keynote address to the Mathematical Association of America — his farewell address as president. A section of this address is on “Justice.” It is centered around this quotation by Simone Weil:

“Justice. To be ever ready to admit that another person is something quite different from what we read when he is there (or when we think about him). Or rather, to read in him that he is certainly something different, perhaps something completely different from what we read in him.  Every being cries out silently to be read differently.”

We read it popcorn style. Someone would read a paragraph or two and then stop. Someone else would jump in. I hadn’t read this in a while. I have the book based on this speech that Prof. Su wrote afterward, after his speech went viral in the math community, trapped at school, unread, sitting on my desk. As kids started reading, I remember hoping it would speak to the events of the day at school. I hadn’t time to review it to see if it did. Everything I was doing today was on the fly. The section did, at least to me. It was longer than I remembered. It took a while to get through, or maybe I just lost sense of time because I was exhausted. When I read, every so often, I forgot words or mixed them around. My eyes were jumping around the text, unable to focus. At the end, I told kids if they wanted space to talk about the events of the day or the piece we just read, we could have it. Or we could call it an end. I consciously tried not to make it sound, when giving the options, like I really wanted to end, so they knew they truly had a choice. We called it an end, and I was grateful. I was empty.

I posted the nightly work for my classes from today. I shared with them some articles, including  this piece on Edray Goins, which I remember having my classes read last year and gave us a lot to talk about. And this keynote speech by Marian Dingle about “centering.” I apologized in my google classroom post for not bringing in more conversations about race, gender, and other -isms into class, and said it wasn’t just the jobs of the history and English teachers (something kids had brought up in the conversations).

I had 45 minutes to lie on my couch and close my eyes. I thought about how much the world has changed since I was in high school. I thought about how much the kids we teach are aware and know and care… and I wondered if the non-POC kids and faculty really cared in their hearts or if they cared because they were supposed to care. I wondered if I cared in my heart or if I cared because I am supposed to care. I felt the weight of guilt — trying to parse what I’ve done to help my kids know they’re “being read” — especially the POC, especially the girls and non-binary kids. I found myself thinking of when I had kids read about a trans mathematician and a queer mathematician and we talked about that in class. Or when I had kids read about a black mathematician and we discussed. And then I thought: wait, maybe we did that last year and not this year? About the ways I tried to encourage the bright girls in my precalculus classes who were outnumbered by boys — to know they were valuable and their ideas were valuable. But maybe it was too subtle, or not enough, or nothing at all. About my intention to have kids listen to a podcast of latinx mathematicians and how I never made space and time for it. As I thought about these things to assuage and exacerbate my own guilt, I clung to certain things as I was hoping to justify I was “good.” Though I’m not white, this was definitely white fragility. And I thought about if and how today would change anything. For me. For our community. Because I’ve been around, and these sorts of days have happened before. And we as a school community get all riled up and passionate. And then a week later, we’re back to the status quo. Or have we? Have small changes been made that add up over time? I remember thinking, maybe one day the fire will catch and maybe we’ll have something sustainable. Days like these are the sparks. You can’t have fire without a spark.

At 3pm, we had a department meeting. It felt incongruous to the day because we had no mention of the happenings of the day. We toasted to colleagues (friends) who were moving on — one to another school, one to blissful retirement. And we did some work together. When the meeting ended at 3:45pm, I moved to my couch and laid down.

A little over an hour later, I hopped onto a zoom call with three colleagues and friends. We have this tradition every Friday. It’s nice to have this normalcy and camaraderie. These are people I need to vent to, but also laugh with, because otherwise I would feel very alone as a teacher in isolation. We talked about the day, processed, a few tears were shed early on, and laughed. We lasted two hours. And we imagined ourselves on a beach adventure together, in person, and committed to making that happen when we could. It dawns on me that this trip is literally the only actual thing I have to look forward to in my life right now. A hypothetical trip to the beach.

This is an archive of my day yesterday.

Distance Learning: Sorting Through It All

Technically I’m still on Spring Break, but this all ends next week, when we go back to school remotely. I’m one of the lucky few who didn’t have to get thrown into the fire immediately, so I’m using this blogpost as a way for me to sort through what I’ve done and what my take-aways are. I’ll be updating this as new things come my way, so I can keep track of everything useful in one spot.

My dear friend @rdkpickle

So my friend @rdkpickle had to start distance teaching already. She’s kinda amazing in all the ways, and so on twitter she shared out how she was doing her lessons — and noted that they’ve been going well. They are low-tech in that they use Zoom and Google Docs, and use a Google Doc as an anchor for the lesson. I love that the doc allows kids who have to miss the lesson for whatever reason (emotional/anxiety issues, having to take care of a sibling, etc.) have a way to keep up.

Before sharing it, I want to say: seeing what she did was the very first thing that I saw that made me feel like: “okay, I can do this. It’s doable.” BLESS. When talking briefly with her online, she was saying right now she couldn’t be all investigatory in the same way she was in class, almost like she was ashamed. BUT very little of we’re doing is going to be like what we do in class. The ballgame has changed (from basketball to some other sportsball!). Right now, for me, the question is can I give space and structure and community to kids where they feel they can learn a few things. And @rdkpickle’s low-tech approach allows for that!

Here’s a PDF her googledoc, which she said I could share. (And here’s the google doc.)



Mike Flynn (helped by Sarah Bent) gave two wonderful webinars on distance learning that he has put online — March 11th and March 17th. (If you only have time for one, I’d watch the second one, but both are great.) They were some of the first things that made me realize distance learning was possible, by showing how to do it through his webinar. (Unlike, say, dry powerpoint lectures on teaching active learning strategies. Ahem. We’ve all been there. I just think over and over, “Physician! Heal thyself!”) My takeaways were both about distance learning and about zoom, so I’ll list them here. Fundamentally, though, the best way to learn zoom is to actually just get a few friends and all try it out together (each of y’all practicing being the leaders/hosts of the meeting).

  • If you can, start the zoom meeting 10-15 minutes early and let kids know you’ll be there. You can just have informal chats like you do before a normal class, and you can use that as an easy way to start building community.
  • You can record your sessions, but if you do that, don’t start recording during that informal chat time. (Right now, since Zoom is overloaded, it’s taking them a long time to get the recorded sessions on their website, FYI. But you can have zoom do a “local recording” on your laptop… so I was thinking if the file were small enough, I could just upload that to a google drive folder my kids could access.) Note that the chat box doesn’t show up on the recording.
  • Talk with kids explicitly about the weirdness of talking on Zoom. There are going to be awkward pauses because we can’t use facial cues and body movement to figure out if we’re going to talk or not (we’re all sort of trained to sort of check before we talk so we don’t start at the same time as someone else). So name that, and say that awkwardness is normal in zoom. You should also mention (and give) lots of wait time — just like we should be doing in our regular teaching.
  • It’s okay if you’re having kids use chat to stop every so often and take a few minutes (in silence) to read over the chat so you can respond to what you’re seeing.
  • The chat can be the “lightest lift” for interactivity, but it’s effective! One tip I got on twitter is that you can ask everyone to write a response to a question, but not press enter until you give the command. Then you’ll get a quick flood of responses that you can go through, and students can also read.
  • You can also set the zoom meeting to have the chat be private – so students are talking to you but not each other… then as you see the responses, you can say “Nice thinking, Jake!” or “If you’re thinking about a parabola instead of an exponential function, you’re going in the wrong direction!” This came directly from Michael Pershan’s experience teaching online this past week:
  • If you have pre-determined questions you want to ask at a particular time during the lesson, have them written in a google doc/notepad, so when you want to ask it, you can just copy/paste them in.
  • Have everyone use their own regular names in zoom (and not emails or userhandles) to make life easier for you.
  • There is a way to include “polls” in your zoom meetings, but I couldn’t figure that feature out when trying it out!
  • You can divide your class into groups (either randomly or pre-determined) and send them to breakout rooms. You can visit any of those rooms and join in the conversations. Each breakout room is given a number when students join. You can have one person in each group (e.g. the person whose last name comes first alphabetically) to create a Google Doc in a Google Drive Folder you share with them in the chat window… And title it “Group 5, March 25, 2020.” Then all participants can write answers in their google doc and you have access to all of them in an organized way.
    • When students are first put into a breakout room, if they’re new to working with each other, start with a non-mathy but quick ice-breaker to get everyone talking (e.g. what’s your favorite pizza topping?) and build a tiiiiny bit of community before diving in.
    • SUPER COOL DISCOVERY: When I did this in Mike Flynn’s webinar, one person in my breakout room showed me a ridiculously cool feature. In any google doc, you can go to INSERT > IMAGE > CAMERA
      And then you just take a picture of your work using the webcam, and it automatically inserts the picture in the google doc!
  • Don’t go crazy with the new technology. There are so many apps and websites. Limit yourself to just a few, like two, for your own sanity and your students’ sanity. Keep it simple and easy — don’t go down the rabbit hole of looking for “the perfect way to do x, y, or z.” Be okay with the tradeoff of having “good enough.”
  • When designing online learning, start with the question “how do we want our students to learn?” Then choose your technology based on that.
  • Screensharing is awesome (so you can set up a google slideshow, and in zoom you can screenshare that slideshow to the kiddos… And you can show kids how to annotate so individuals or the whole class and write/type/draw on a screen you’re sharing (and you can save that).


Desmos Activity Builder 

Julie Reulbach led a webinar on using desmos for assessments, but basically she outlined all the ways we could create activity builders to actually teach content also, and bring students along with us as they navigate the pages, and we talk through what they’re doing. Her resource page is clipped below so you can see what’s there…


But importantly, her page includes links to various activity builders where you can simply copy and paste! Here’s how you copy and paste screens from better activities that your own into your own! They can even have computational layer in them!

Some key tips for creating Activity Builders (but not necessarily for assessments in particular):

  • Steal steal steal screens from other activity builder assessments if you’re doing anything fancy (e.g. self checking, anything with computation layer), because there’s no need to reinvent the wheel right now. Julie has curated a whole list of activities that she takes screens from! And desmos has curated a bunch of starter screens(e.g. “graph how you’re feeling today?”) that you can take!
  • DESMOS NOW ALLOWS FEEDBACK – so you can write a note to individual students.
  • Importantly, let’s say kids are doing a desmos activity or assessment, and you want them to show their work that they’ve done on paper. All you need to do is create a screen which has a blank graph, and instruct kids to insert an image (see sidebar instructions in the image below) and they can actually INSERT a picture of their work! The workflow is a little clunky because they have to take a picture on their phones and then email/airdrop it to their laptops, and then select that file. But it took me only like 20 seconds after I had done it once.

Some key tips for using Desmos for assessments:

  • Have kids log in with their name, but “last, first.” That way when you grade their online assessment, you can sort the responses by their username, and that will match your gradebook.
  • Have a fun introductory “hi there!” screen
  • Have students fill out an honor code/statement screen first if doing a formative assessment
  • After you finish the activity, have two screens at the end. First, a feedback screen so you can find out how they felt it went. Second, a screen asking them if they have any questions or anything they want you to know.
  • If a formal assessment, you should PAUSE the activity at the end — so kids can’t go back and change their answers or share the class code with other kids


Michael Pershan’s blogpost

My friend Michael Pershan has been in the thick of online teaching. He wrote a detailed blogpost about what he’s discovered thus far. I highly recommend reading it! Big takeaways:

  • His school is using Google Classroom (like ours does), so he’s using that to create a system of organization for the kids, with instructions given day-by-day (within a unit):
    He noted: “The most important thing, though, is that each learning activity becomes its own “assignment.” During week 1 I was creating large documents that students were working on over multiple days. This was good in one sense, because I had to post only one thing. But it became very difficult to monitor the progress of kids through the assignment at all. And then it became tricky to modify the plan in the middle of the week by adding on other bits of classwork.”
  • He’s using google classroom to teach kids how to upload their written work. (Note: my kids always submit PDFs of their work on google classroom, so they’re very familiar with this!)
  • To give feedback on google classroom: “Google lets you comment on the work itself via highlighting and commenting, but I’ve found it more useful to give a quick written comment that appears under the assignment itself.”



Lots of great things being shared on twitter. It was so overwhelming that I stopped looking at twitter for a while, but I did save a few things:


What Wasn’t That Useful For Me – But Here are the Nuggets I’ve Taken Away From These

What I have below doesn’t mean these aren’t good for others. It just means that for me, I like to jump in and these things didn’t quite pan out fully.

Alice Keeler had a webinar (“Oh Crap, I’m Teaching Math Online Now“) that wasn’t crazy useful for me because it was a brief overview of many things I already knew about. It was just super tech happy (look at Pear Deck! Look at Geogebra! Look at Desmos! Look at …) and didn’t give me the focus or vision I’m searching for.

Global Online Academy (GOA)’s 1 week course on Designing for Online Learning. Since this was designed to be “big picture” (so it can accommodate people from many schools and teachers of all stripes and many disciplines), I had trouble getting specifics that I wanted to latch onto. Here’s what I did get:

  • They recommended Loom for laptop screen recording, if you were going to be making videos from your laptop. It seemed pretty seamless and easy to use, based on this short video tutorial:
  • The basics of good teaching are still important — clarity and being organized is paramount. Specifically for online learning, they highly recommend:
    • building routines early (just like with regular teaching!)
    • share the “learning goals” at the start of each lesson explicitly
    • don’t get over-excited and share too much… curate what you share and make it super easy to follow
      • using a lot of whitespace and images
      • don’t include anything that isn’t super important — focus on key ideas
      • not using too many fonts
      • everything you share with your students should be “crisp” and “clean” (not “busy”)
  • Be present for students. Create or adopt an online persona. Don’t leave them hanging, but show them continual engagement so they know you’re with them on this journey.

A curriculum is more than a set of papers

I wrote, with my friend Brendan, an advanced geometry curriculum. I was insanely proud of some of it. For those of you who know me, you know I love writing curriculum. It takes time, so much time, but it flexes the best part of my teacher brain. I’m forced to think backwards (“what am I trying to really do here? what matters?”) and requires creativity (“how can I get kids from point A to point B by having them do the heavy lifting, but in that sweet spot where I’m not necessary but their collaboration is? where that moment of invention and surprise is real?”). It is tough, and a lot of what I do isn’t great. But even my worst is better than any textbook I’ve seen.

Back to geometry. A few weeks ago, I met with one of the teachers at my school who is going to be teaching advanced geometry. I shared all my materials with her electronically, but I met to talk through things in more detail. But this meeting reminded me of something I’ve felt acutely for a few years: a curriculum is more than a set of papers.

As I wrote each piece of the geometry curriculum (or as I worked with my colleague as he took the lead), I had so much whirring around in my mind. I knew the intentionality of the questions and their ordering. I knew where kids would stumble. I knew where I asked questions that had no answers — on purpose — to get kids to think. I knew that I included a particular question in order to prompt a class discussion. I knew there were placed I needed kids to call me over to have a discussion with each group individually.  I knew I had included questions which were designed for me to verbally ask follow up questions. And of course I knew which things were hastily designed and didn’t work out so well when teaching.

But as I was attempting to go through my materials with her, it struck me pretty hard how hidden and implicit all those things were in that collection of papers that she had.

A real curriculum needs so much more, if someone else is going to successfully use it instead of me. When creating materials for other people in my department, who are teaching the same material, I started writing comments/notes in Word when I had a teacher move that I had in mind when crafting the problems:

teacher notesteacher notes2teacher notes3

It’s also a good reminder for me in the future. These notes help me and my colleagues remember what I was thinking of when writing my stuff. When I started doing this, I realized how a curriculum is a set of problems/activities with the intentionality behind the problems and teacher moves spelled out

In the past few years, I’ve had the fleeting and recurring thought: hey, I should organize all my geometry, precalculus, and calculus files neatly, and put them online in a systematic order for anyone to access. Maybe all of it will be useful to someone, maybe bits and pieces. I still sometimes think that. But what keeps me back from doing it is that gnawing feeling in the back of my mind: things need to be spelled out so someone else understands the flow and intention of each thing. And how to use it in the classroom. Where to stop. How to start. If there were any important “do nows” that weren’t captured in the sheets. Or knowing that someone was written as extra practice or to reinforce an idea that a class in a particular year wasn’t getting.

Over the past two years, it’s become harder and harder for me to open my feedly app and read blogposts. (I find most of my blogposts through twitter now.) It’s just been hard to find the time, and I get overloaded. And I haven’t had time to blog much either. And that sucks. But one thing I love about blog posts — that you can’t get on twitter/facebook/ed research — is that they often illuminate hidden ideas and bring to life something inert. Like when I read a blow-by-blow about an activity/problem set/ worksheet. Something that shows me the thinking that went into creating it, or better yet, how things unfolded in a classroom. What teacher moves happened? What were students thinking? [1]

If I wrote materials… and had a blogpost about how each day unfolded with those materials… that would be a curriculum at its best in my eyes. Because life is breathed into it. It becomes three dimensional. It involves people. The teacher. The students. And it makes explicit what is happening and why. [2]

Note: Funnily enough, Sadie posted a great piece on the idea of “curriculum” the day after I started writing this one! It is definitely worth a read.

[1] I like writing these kinds of posts — though they take a long time. Here’s a recent one:

[2] Obviously I won’t ever have the time to do this. But it’s nice to fantasize about. An extensive 180 curricular blog. Writing this post also reminds me that I need to get back to regularly reading blogposts.


Inspiration and Mathematics

In my multivariable calculus class this year, we’ve been holding a regular “book club” during our long blocks. (Don’t ask… we have a rotating schedule and every seven school days we have a 90 minute class.) Right now we’re reading Edward Frenkel’s Love and Math: The Heart of Hidden Reality.


In the introduction, Frenkel criticizes the teaching of math:

What if at school you had to take an ‘art class’ in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it. [1] … There is a common fallacy that one has to study mathematics for years to appreciate it… I disagree: most of us have heard of and have at least some rudimentary understanding of such concepts as the solar system, atoms and elementary particles, the double helix of DNA, and much more without taking courses in physics and biology. And nobody is surprised that these sophisticated ideas are part of our culture, our collective consciousness.

So many whirling thoughts came up while I was reading these passages. One thought led to another to another to another. Writing this post is an attempt to start recording them and to get them a little more codified in my mind! It is still going to be a hot discombobulated stream-of-consciousness mess. #sorrynotsorry

I wonder if I asked my kids “what is mathematics?” right now, what they would say. I am doubtful that their answers will include the adjectives and verbs that I personally would say.

I wonder if I asked my kids “what is is going on in the field of mathematics?” right now, what they would say. I’m guessing a lot of blank stares.

I wonder what my kids would say if I asked ’em “what courses exist in college for mathematics?”

I wonder what my kids would say if I asked them to name a mathematician who is alive?

I wonder if the word “mathematics” was changed to “astronomy” or “physics” or “biology” if their answers would be different.

There are ideas that my kids learn about modern physics (in popular culture, in classes) which spark their imagination, blow their minds, make them curious and full of wonderment at the weirdness and strangeness of the world. Special relativity. Quantum mechanics. Quarks and the structure of atoms. They are exposed to these ideas, even if they don’t have the mathematical capabilities or abstraction to attack them rigorously. And these ideas have a powerful effect on some kids. (I know I wanted to be a physicist when I first learned about these ideas!)

But what do my kids learn about modern mathematics — from school or popular culture? Are there any weirdnesses or strangenesses that can capture their imagination? Yes! Godel’s incompleteness theorem. Space filling curves. Chaos theory. The fact that quintic and higher degree polynomials don’t have a general “simple” formula always works like the quadratic formula. Fractals. Higher dimensions. Non-euclidean space. Fermat’s Last Theorem. Levels of infinity. Heck, infinity itself! Mobius strips. The four color theorem. The Banach-Tarski paradox. Collatz conjecture (or any simply stated but unproven thing). Anything to do with number theory! Anything to do with the distribution of primes! But do they capture students’ imaginations? No… because they aren’t exposed to these things.

Where in our curriculum do kids get inspired? Where does awe and beauty fit into things? When do we ever explicitly talk about beauty in mathematics? When a kid has a rush of insight and makes a visible gasp, what do we do in that moment? What has to already be in place for a kid to make that gasp?

We need to expand how we frame mathematics in high school so it isn’t seen as “Algebra I, Geometry, Algebra II, Precalculus, and Calculus.” These course names aren’t mathematics.

We need to consciously and regularly introduce a bigger and more modern world of mathematics to our kids. How? Having kids read when the New York Times publishes an article about a mathematician or mathematical result! Using resources like Numberphile and Math Munch and Vi Hart videos. And… I don’t know.

We need to provide space and time for kids to explore an expanded vision of what math is, and have choice in having fun and playing with this expanded vision of math. (My explore math project is an attempt to do that — website here, and posts one, two, and three here.)

We need to have mathematical lore, stories we can tell students. Galois duel! Ramanujan’s inexplicable genius! What are mathematical stories that can be passed down from generation to generation? (Does a good resource exist for this? Tell me!) [Update: The internet went down when I was going to edit this post by mentioning we need stories and people who aren’t just white men!]

Do we have Feynman or degrasse Tyson-esque figures we can point to? Dynamic popularizers of the subject that have entered the public consciousness?


Maybe what I’m trying to say, if I had to distill everything down to the core, is:

(1) Can we find a way — in our existing schools with our set curricula and limited time — to expand kids notions of what mathematics is by exposing them to notions external to the Alg-Geometry-Alg II-Calc sequence. And if we can do this well, will it help inspire more kids to be interested in mathematics? 

(2) Are there ways for us to keep an focus on beauty, the unexpected, awe, and wonderment in our classes? And find ways to record, highlight, and amplify those moments for kids when they happen? Why I love mathematics is because of all of these moments! Maybe focusing on them would help kids love mathematics?

UPDATE: Annie Perkins has a great blogpost which captures some of the exact same ideas and feelings here. But she’s more eloquent about it. So read itUpdating it here so it is archived for my own thinking on this.


[1] This notion has so many resonances with Paul Lockhart’s A Mathematician’s LamentWhich I highly recommend.



Mulling things over

Tonight at school we had our inductions into Cum Laude (like national honor society) and Mu Alpha Theta (the math honors society). And our guest speaker gave a rousing speech about his life, and how it’s okay to have fear, but the biggest hurdle to doing something significant with your life is accepting the fear and moving on in spite of it. Accept it, own it, be afraid, and then still forge forward.

At the end, he said something powerful. The first thing one needs to do to when leading a purposeful life is to say what it is that you want to do. Articulate it aloud. And that is scary. Making it public so you can hear yourself say it, but also so someone else can hear you say it. So it becomes real instead of this thing that bounces around in your head but never gets out. And so at the end, he told everyone to be quiet, and he was going to say something he wanted to do, and then afterwards there should be silence… and when anyone else wanted to say something they wanted to do — something they would declare out loud — they should stand up and say it, and then remain standing. This was an open invitation to the students in these honors societies, but also to the parents and teachers there as well.

The speaker said: “I want to change the world.”


A little more silence where everyone looked around and felt uncomfortable.

Then a student — one courageous student — got up and said something. And remained standing.

And then another. And another.

The head of the upper school said something. Then more students. Then a parent. Then me. Then another math teacher. Then more students.

At the end, every student made a declaration, and a few adults too. It is scary. But it also showed me how much courage our kids have. Their declarations ranged from showing others that girls can do math and science to spreading love to making people laugh to promoting peace to inventing something to becoming a biochemist to making a mark on the world. Big things and small things, lofty things and concrete things, but all things that share with the room a sense of self and a sense of purpose.

I loved watching this.

I also loved and hated how hard it was for me to come up with my thing. My purpose in life. I said:

I want to make it so that kids see math as an artistic and creative endeavor.

And I meant it. Because you know what has been bouncing around in my head that I have been having trouble articulating? I am now pretty good at coming up with deep and conceptual approaches to mathematical ideas. And I’m okay at promoting mathematical communication. And I’m transitioning to having kids do groupwork all the time, to learn from each other — so I am not the sole mathematical authority in the room.

But all of that said: I don’t think I teach math in a way to shows how it is an art form, how deeply creativity and mathematics are intertwined. And I know that this is one of my charges as a teacher moving forward. It’s going to be an uphill challenge, and one that will likely take me many years to wrap my head around. The hurdles are significant. Having a set non-problem-solving-based curriculum which doesn’t allow time for much mathematical “play,” nor for the inclusion of rich problems with multiple entry points, is the largest hurdle. But there must be ways — activities or units here and there — that can illuminate the artistry and creativity of doing and discovering mathematics. And I want to be involved in finding ways for this to happen. Yes, this happens at math circles. Yes, this happens at math clubs. Yes, this happens at summer math programs. That’s where the love and excitement and understanding of the beauty of mathematics unfolds for many students. But I want to find a way for this to happen in a normal classroom, with normal students, with the normal constraints. That (one of) my purposes.

Projects and Project Based Learning: HELP! AAACK!

What I’m going to ask you at the end of this post: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).


This isn’t a post about something I’m doing in the classroom, but rather me soliciting resources from all y’all so I can do something different in the classroom.

But my basic sentiment at the moment is: AAACK! HELP! AAACK!

Setup: My school is jumping on the Project Based Learning bandwagon. However, no one has been able to give me good examples of what real Project Based Learning in the math classroom looks like. However, no one has yet been able to give me a satisfying example of Project Based Learning in math.

I found this online (thanks twitter) which appears to separate Project Based Learning from Projects:


It’s all very good sounding. But I am a concrete thinker and I haven’t been able to come up with a hundred examples of Project Based Learning. Honestly, I haven’t even seen one that I’d say “hey, this is awesome.”

Also, I am not really good with doing projects in general. I don’t do a lot of them (for a variety of reasons).

So, as I said: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).

Mainly I’m just trying to wrap my head around this. I still am unsure what to think about this move my school is making, and if it makes sense for the math classroom. But for now, I am keeping an open mind.