Author: samjshah

My First Day, 2018 Edition

I had my first day with kids this past Thursday. We had only 30 minutes with each of our classes, so I went back and forth about what I wanted to do. Some years, I like to get them in their groups and we start right away. I have a compelling question or *something* that starts the first unit, and we charge ahead. When I do this, I’m thinking “I want kids to see what we do every day in class. We do math. We work together. We don’t waste time.” [1] Kids seem to enjoy that. They are usually revved up and excited to start, even though we’re all a little sad that summer is over. (Okay, very sad.) But there’s energy in the air.

This year I decided to do something different. A colleague of mine did this for a class we both co-taught years ago, and I really thought it would be a great way to start this year.

Part I: The Initial Card Sort that Sorted My Kids Into Their First Groups

I said hello for literally only one or two minutes, and then I shared the activity we were going to do for 15-20 minutes. We were going to do a puzzle-y card sort to figure out who was grouped with whom. But in order for the class to be successful, they all needed to work together. I projected a sample card. I said anyone is allowed to use a calculator. But some of the cards might require some laptop assistance. So they had a little laptop symbol on it.

card1.pngSo in this case, for example, I knew almost none of my kids would know what binary numbers are, but using google they could find a converter online that would say this was actually “170.”

Each card had a kid’s name written on back. So each kid got “their” card. And their goal was to find others who were in their group because their cards formed a logical group. Here’s a sample group to show you what the cards looked like and how they link:


See if you can tell what the link is among these four cards…

I’ll give you a second.

I will reveal the answer in the next line, so don’t keep reading until you are sure you want to know.

Okay, the link is the number “ten.” So 10! is the number of seconds in six weeks. When the kids type those equations into desmos, they will see the number 10 show up. Neon is the 10th atomic element. And “X” is 10 in roman numerals.

You can see why kids are going to need each other and the class is going to have to work together. Because until someone recognizes that “ten” is a category, these all seem very unconnected. But as soon as you know someone’s card represents “ten,” then things like the neon symbol or the “x” make sense.

I’m kinda proud of these, so I’ll show you another:


The theme? “Pi.” The first one is circumference over diameter, the second is a recipe for pie crust, the third is an approximation for pi, and the fourth is a world record holder for reciting the digits of pi.

(If you want to download my cards, here you go: Group Card Sort! And the explanations are Group Card Sort Explanations.)

I only had allotted 15-20 minutes for this. I had no idea if this would go quickly or take forever. In all four classes I did this in, I was able to get them to finish in 20 minutes but only through some careful prodding/help. If I were a bit more hands off, I could see this easily taking 40 minutes and it being time well spent. But alas, I didn’t. Here’s how I intervened:

  1. After 7 minutes, I stopped everyone. I asked who knew what they had. A few people did.
  2. Throughout the time, I gave a “few” hints where I could, but mainly I was acting as facilitator to help others help each other. So for the pie crust recipe one, I had the person go around asking if anyone was a baker (or I would shout out to the room if anyone liked to bake, and had them come to us).
  3. When someone wasn’t doing anything, I had them go help others. They might have been confused about their card, but they could help others (and get help from others).
  4. Sometimes when a kid “got it” but still had some uncertainty, I would put them out of their frustration and tell them they got it. If I didn’t have time pressure, I wouldn’t have done this, but it didn’t ruin the activity or anything.
  5. After 15 minutes, with my proddings and connecting, kids were doing pretty well. So I stopped everyone and had people who knew what their card represented be quiet. There were always three or four people who were stuck. So I had them share their card or write their puzzle on the board and see if anyone could figure it out in the remaining few minutes. (We wrote the different “solved” categories on the board, so sometimes they could figure out their card by seeing what it might be.) They gathered, talked, and some classes barely finished in time and others didn’t. I didn’t focus on that. For the ones that didn’t get them all in 20 minutes, I quickly went through the explanation of the remaining few cards.

It was really fun for me to watch, and I saw kids really getting into the puzzle-aspect of things. The first time a kid figures out their card and finds someone else with the same thing, it’s just a wonderful feeling. It honestly feels impossible to kids at the beginning. They literally start looking for anyone with the exact same card as them, or if they have a picture they’re looking for other people with pictures. But as soon as they realize it’s more challenging and more interesting, I get to see how they react and what they do. Do they sort of back down? Do they go help others? Do they hope someone comes to them? My big goal was having kids realize they can’t do this alone and most cards won’t tell you what they are so you need to hear about others and help others.

Oh! One big thing. I realized in the first class that kids were just kinda sitting with their cards. So I made a rule that until the card sort was over and everyone in the class figured out their cards, no one was allowed to sit down — not even when using their laptops. This actually got kids up and moving. It was a small thing, but I know it was super helpful to making this a success.

I wish we had time for kids to say hi to their first group and do a little group norm setting, but alas with only 10 minutes left, I had to transition.

Part II: New Years

So I totally saw Howie Hua’s first day post and was in love. It was positively inspired. Often times, people post awesome things they do in their classrooms that are awesome but just not me. When I read this, I felt: “OMG THIS IS ME!” He celebrated new years with his classes. Here’s one of his students’ videos/tweets:

And it really got me thinking. The first day IS my new years. My life doesn’t go in January-December cycles. It goes in September-August cycles! And it was the perfect time for kids to make a new years resolution. They had 90 seconds of thinking to come up with something.

new years.png

Then after 90 seconds, I threw up this screen, obliquely referencing the Maurader’s Map from Harry Potter (but opposite-ish) and I had them recite this pledge:

no bad.png

Then I gave each kid a baggie that I prepared. In it was a super fancy piece of origami paper, a mardi-gras necklace that someone had a zillion of and was throwing them away, and a noisemaker I bought from amazon. It mabye took me 45 minutes to put these all together. But totally worth it. For some reason, I believe that being given your own personal goody bag is way more exciting than having someone pass out necklaces, noise makers, and origami paper individually.

I then handed out party hats too (but those had to be returned to me). I actually always keep a stack of party hats in my office, and when it’s a kids birthday, I give them a hat, candy, and we sing a short birthday song. As I said, this idea of Howie’s fit me!!! Anyway, kids had to write their name and their resolution on the origami paper which I collected. (Later that day, I put them together in a ziploc bag and hung them visibly in the room so this doesn’t become a thing we did but wouldn’t return to. I was thinking I’d give them back to kids after the end of the first semester so they can see how they’re doing on their resolution. But I might have another brilliant idea. Who knows!) As soon as the bags were out, the noise makers were making noise. And that was a lovely cacophony of BWWWAAAPP and BAAAAAAAA noises. (That was also why I had kids pledge to do no evil with what they were given… *grin*)

In any case, I was standing at the front of the room when they worked on writing their resolutions. When they were done, they had to bring up the resolution to me and wait at the front of the room with me (with the necklace, hat, and noisemaker). After 2-3 minutes everyone was up. And then… we took a class picture, all decked out, blowing on the noisemakers and just being amazing. And oh yeah, we also took a class boomerang (which is an app that lets you take a 2 second video and plays it over and over).


The boomerang was my favorite part because kids were jumping up and ducking down and doing fun things. And I kind of am obsessed with boomerangs. So there’s that.

I think I’m going to get these photos printed and framed, and hang them up in the classroom. I don’t know what to do about kids who were missing  (there were a few) or who transfer in after some schedule change, but maybe I’ll list them missing on a caption instead of some awkward photoshop job?

Our first day together. (I did post the boomerang video and our class photograph on the google classroom site in case any kid wanted it.) [2]

And then it was the end of our first 30 minutes together. I was really happy with how it went. I like the feeling that I left each class starting the year with good vibes. Thanks go to my chemistry teacher colleague and friend for the card sort idea which I made into something my style (with my kind of clues!), and to Howie Hua for helping me make a memorable moment to start the year.


[1] We do a lot of the logistics things in the following week. They read the course expectations at home and fill out a “get to know you” google form which also asks them questions that require the expectations to finish. And then each day or day, I talk about one or two things I want to be explicit about (like how to write me an email, or that’s it’s okay to go to the bathroom and they don’t need to ask, but they do have to discretely let me know they’re leaving if I don’t see them, or that they need to bring a waterbottle to class because they can’t leave to get a drink).

[2] I just realized this photo could be fun to have up on the screen on parent night, when parents/caretakers come in two weeks to hear me talk about our class.




Start Of Year Edition: Even More Things I Want To Highlight From Twitter

A few months ago, I had “liked” so many tweets but I wanted to archive them somewhere so I wouldn’t forget them. So I wrote a post. I don’t have too much time, but I want to do that again. [Update: Okay, I might have spent a few hours compiling this. But I’m so glad I did.]


A lot of people use four 4s as a way to get kids thinking. I liked this idea of having a sheet and kids using post it notes to fill in the missing ones. It’s compact. I might use the small post-its, and have kids use a different color post-it if they have a different solution than the one posted. It might be good to keep in a public hallway for everyone to work on, or maaaybe in my classroom (if a group finishes something way before everyone else but I don’t want them moving on yet). But four 4s is all over the web, so I might need to change it to 5s or 6s. :)


Ummm. Oh, okay, @mathequalslove had a tweet which showed she already thought about how to create a first day activity around this, along with amazing facilitation notes. Yay!


@abel_jennifer tweeted out saying she was going to be bringing math kids on a (multi-day?!) field trip to NYC and wanted to know what mathy things kids could do here. Many people responded, and so she compiled the responses in a google doc. I never take my kids on field trips. I should. (Maybe as a reward for completing the four 4s challenge?!)


@stevenstrogatz linked to Harvey Mudd’s math department goals. It’s beautiful and shows they worked collaboratively to generate a shared vision. Our department has done this too, though we need to refer back to it and see where our strengths and weaknesses are so we can move forward.



@mrdardy shared his geometry curriculum with someone looking to explore new ideas for their class. He shared the book he wrote with them [which I highly recommend checking out!]! And in that folder, he has an awesome short paper he writes called “How to Succeed in Geometry.” However it is soooo not specific to geometry. It’s amahzing and most of what he writes is true for my kids also. I should look at this when revising my course syllabus this year!


@zimmerdiamonds posted a nice open-middle problem that I think I could use this year with my new Algebra II class.


@Caitlyn_Gironda gave a presentation on making AP calculus more engaging, and she shared her slides, but also a set of folders filled with great activities! Because she’s aweeeesome. I need to look through these before teaching my (non-AP) calculus class this year!



I love this question. The activity is here. I could see it being used for a first day challenge. I wish there were like 10 of these, instead of just one, with different “levels.” That probably exists somewhere. Ooooh, or maybe after kids do this, they create their own to challenge other kids. This could be a groupwork task, where at first they solve this together… but then the work together to create something complicated that stymies other groups! <3


I always forget where I can find desmos activities made by other teachers. It’s the desmos bank. The link is here:


@mathycathy posted how she had some students’ desmos projects printed on canvas to hang up in her room. It shows her kids how much pride she has in their work! But more importantly to me, she shared her project, which is kids making a pet house in desmos. The activity builder for it is thoughtful and kids learn about lines just by playing with them! I think I could modify this to add in other kinds of graphs (parabolas, square roots, etc.) for Algebra II.



@cljreagan posted a problem she used in her precalculus class on the first day.


I wonder if I could do this for my standard Algebra 2 kids, actually?! Start with them working with whatever approaches they could come up with, individually. Then after a minute of individual thinking, they share their thoughts with their group. Then the group works together. Then finally, graphing! And a discussion about why the graph might look crazy in the places that it does!




A terrific teacher: is, says, does, does not.

I think I might want to do this for a terrific student also. The teacher I look up to most in my building does something like this as a way to build class norms. This wouldn’t involve the refining and consensus building that she asks for, but I might use it anyway. I could transcribe them into a draft teacher poster, and then talk about ones that might be problematic for me (based on either who I am, what I can do, or things I philosophically disagree with) and be transparent about those things. And then I can have kids look and see if there are anything on the draft student poster and see if there are similar things they want to discuss/refine/change. Then I can create a final version to hang up.


This idea. It reminds me of something I used to do called “Path to Glory” (which I heard about so long ago and I don’t remember from whom…) where I asked kids to fill out a 10 question True / False test … but they weren’t given the questions. They just had to fill out the answers.

Then they all stood up. And then I read the questions and kids decided whether it was true or false, and then those who got it wrong sat down. And we’d continue on the PATH TO GLORY (the last person standing).

I always incorporate this on the last day of my calculus classes, and the T/F questions are questions about the kids in the class or me. It’s cute, and I think special to me. Because it shows my kids I know them and listen to them, and it’s a community closing activity. (It could be a community building activity too.)



This slideshow requires JavaScript.


@eulersnephew posted a google doc with a ton of amazing quotations about mathematics that he’s been compiling. The tweet thread then led to this wikiquote page with quotations about mathematics. And he linked to a google drive folder that @MrCoreyMath shared with lots of posters of mathematicians and what they work(ed) on (modern and old time-y). He also has a poster with a lot of questions students can/should be asking themselves when they solve a problem or are working on a problem.


@joelbezaire posted a great challenge. He gives his kids this chart, and asks them what the relationship is between the four variables. Then when kids think they know, they go up an add a line (which then gives more data for kids who might not see it). He created these exercises (called Variable Analysis) and they are here (along with more about how he facilitates it).  pic15.png



The post of his activity is here. I watched a documentary of the MIT Mystery Hunt, and there was an awesome communication activity in it. Watch this video (11:19-13:50). I think it would be hilarious to watch kids do this.


This quotation:

And this quotation:



@allison_krasnow shared this site with great collaborative activities for students. *Swoon.* *I’m in love.* To whet your appetite, here’s a screenshot of what awaits you:


Which of course reminds me of Play With Your Math by Joey Kelly and CiCi Yu (twitter for site: @playwyourmath), which I will also screenshot to whet your appetite:



Sara Van Der Werf does an amazing “name tent” thing at the start of the year (I’ve done it and enjoy it!). But I always struggle in the moment to come up with good questions. @averypickford shares questions he uses for student interviews which could make good name tent questions. The questions he’s going to use this year are:
“What was the last movie you saw or book you read that you really enjoyed or had a lasting impact? If I gave you enough 💰 to live comfortably w/out going to school or working, what is 1 thing you’d do with your time? What is something you’re particularly good at? What do you think is important for me to know in order for you to be successful in this class?”

@algebrainiac1 shares her questions in a blogpost.

@JennSWhite tweeted that she does:
Day 1: If you could be any creature real/fictitious what would you be & why?
Day 2: What is the sure-fire way to lift your mood/spirit?
Day 3: If you could have dinner with any person alive/dead who would you pick & why? What would you eat?
Day 4: What superpower would you want?

@Riehlt says: “”If you had three wishes, what would they be?” I got this from a school phycologist and used it for many years. It really gives insight to what they value and has revealed all sort of things; hardships, illnesses, deaths, body image, family conflicts. A few rich, fame, etc.

@EmilySilman asked kids to finish this “If math were an animal, it would be _____ because _____” or “If math were a food, it would be _____ because ______.”


Just because cool!



@JennSWhite posted this picture from the second day of her classroom. A group activity:

When people asked for more information, she shared the puzzles and the solutions! It was inspired by @nomad_penguin’s post here. And links to Mark Chubb’s post which talks about things to consider if doing activities like this in your classroom.



@a_schindy posted some posters she hangs up in her classroom about the behaviors/traits of a mathematician (from Tracy Zager’s Becoming the Math Teacher You Wish You’d Had). And, importantly, how she had a conversation about what was on the posters, which she blogged about here.



@BearStMichael shares his classroom norms and his thinking about how to introduce them/start the year. This is a must read. Full stop.



Edutopia tweeted a sweet way to end a particularly harrowing or energetic class or challenging discussion. It’s a video, so you have to go here to see it. It’s called “the three As”  (appreciations, apologies, aha!s). The purpose is the reflect on the day and the dynamics. Kids stand in a circle and just say an appreciation, an apology, or an aha moment!


@Lisa99Bailey posted these pencils she made for her kids. Here’s the original tweet so you can see what she wrote on them bigger. Other people, in the replies, also added “Be Original” and “Be Inclusive.” I think I’d want to do this randomly on a day that had nothing special so it was truly unexpected.


And @MrsDi, in the replies, had a great idea to spread the love: “Super cool! How about on the next batch you have the kids each write an inspiring message and put all those pencils in a classroom-share location? Or… trade with the classroom next door?”


@davidwees posted this


and shared the isometric drawing tool that NCTM has for creating stuff like this!


@bowmanimal tweeted out a great blogpost he wrote about changing how we think about assessments. It is fantastic. An excerpt:


Years ago, maybe at PCMI, I also heard of a great quiz idea. Partner kids up to take a quiz. And they have to do it silently, and write notes to each other to help them communicate. They’ve made all their thinking visible for you, and they have each other to rely on. I can’t believe I’ve never done this.


A number of  years ago, I did a random act of kindness day. We didn’t do content, but we wrote thank you cards to people in the building. I haven’t done that recently, because other teachers have taken to doing that in other forms, and it felt like it wouldn’t be special if I did it. But if I end up doing something like that again, @allison_krasnow shared @MsCummins12’s blogpost about reading How Full Is Your Bucket with her kids. I really liked the idea. I think if I did a random act of kindness day, I might read the kid with books, have a discussion, and then have kids plan random acts of kindness that aren’t thank you cards. What are ways we can be kind that takes a different form? And then their homework will be to actually execute those acts of kindness.


@HankReuling posted this great puzzle (a sangaku!). It took me a page of work to solve. But then I saw someone replied with three lines of work. But that didn’t take away from the sense of accomplishment I had! Have fun playing with it!



@DavidButlerUofA posted a display / game he does with kids called “Numbers and Letters.” I had seen the British show Countdown on youtube on which this is based. I love this as a display, and there is a random element to it which is eggggselent!  It might be fun to get a moveable whiteboard to the front entrance where we have this up, and encourage caretakers and kids alike to engage (and the younger kids can take a short in-school field trip to work on this together as a class). Maybe have a jar of starbursts for anyone who contributes an answer?



Sara Van Der Werf @saravdwerf compiled all her week 1 activities here. I’ve done some of them and am a fan.


Look at these. I’m in love. From @solvemymaths (post, post, post, post).



@rwhite_teacher1 created “extension cards” for kids when they have finished early. The google drive folder is here. I don’t quite know how I’d use them in class, but I like the sentiments. It might be more for me to remind me about ways I can ask kids to extend their work.



This is one of my favorite @benorlin comics. I want to show it in class early on.



A public WoDB bulletin board space!


And, in case you were wondering, there are actual fancy posters you can buy too! My department head just ordered them for us!!!


@rundquist wrote “Don’t just ask what they learned, ask what they unlearned.” It’s a great exit ticket question.


I’m teaching Algebra II this year and I remember how this vocabulary in particular used to be tough for kids. The only change I might make in this is not have the equation equal 0. Kids like to set everything to 0, and that’s crazy. I don’t want to reinforce that.



@davidwees posted a neat set of pictures to think about exponentiation and logarithms, using the Connecting Representations instructional routine I learned in my TMC17 morning session. To see the images/tweet, go here.



@glennwaddelnvhs posted a google doc compiling all the great exit ticket questions that people have come up with!


@TracyZager tweeted a 2-page PDF of great questions to help kids utilize their own intuition when problem solving. A random snip of that PDF:



@mpershan tweeted about using Anna Weltman’s Loop-de-Loops! in class. I’ve always wanted to do that! It’s a great exercise in generating mathematical questions. His class came up with these:

And AMAAAAAZINGLY, Lusto created a beautiful interactive webpage for this.



Transformations: How Our Class Moves The Needle

[This is my contribution to The Virtual Conference of Mathematical Flavors. To see what that is all about, and read other great blogposts that take a zoomed out view of their classrooms, click on that link! The fundamental question that the conference has people musing on is: How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?]

When introducing this virtual conference of mathematical flavors at TMC18, I went through a little rant about how much was expected of us, and how much we expect of ourselves. I went on a mini-rant about this:

Here’s the thing. We all are told to do a thousand things in our classrooms.

Build risk-takers. Have kids work collaboratively. Provide rich tasks. Utilize Vertical Non-Permanent Surfaces. High five kids each day. Do random grouping. Call on students with the Popsicle Sticks of Destiny. Instill grit in our kids. Develop growth mindsets. Provide formative feedback and alter our lessons based on it. Do Standards Based Grading. Engage kids with project-based learning. Obviously we have to do lagging homework… or… is it no homework? Be sure to interleave concepts so you can make it stick, amiright? And make sure kids have facility with technology.

But the thing is: we don’t all do all of that. It would be CRAZY to do that.

We pick and choose what makes sense to us based on where we are, who our kids are, what we decide our goals are for our kids.

And by doing that, we are actually shaping what kids think mathematics is all about.

I came up with this conference because I was genuinely curious. Every day I see all the little pieces, the beautiful flotsam and jetsam that people post on their blogs and on twitter about things they do in their classrooms. But each person has a different flavor, and each person’s classroom has some sort of impact on their kids and how they think about mathematics. I wanted to see how people thought about the work they were doing on a broader scale.

And I was relieved, because I have no idea how I’d answer that question myself. And if I were hosting the conference, it would be gauche for me to also contribute to it, right? I’m the organizer! But then stupidhead Rebecka Peterson — who clearly forgot that I asked her to keynote and now she was being super mean  — tweeted:


Followed quickly by another keynote speaker and consummate jerk:


And so, bullied, I felt compelled to write a contribution to the virtual conference. But the hard thing for me is that I don’t want to profess my classroom moves the needle on how kids think about mathematics when I’m not sure it does. I know what I intend to do, but with so many intangibles, how do you know if it actually worked? So I started thinking if I had any evidence that could help me figure this out and I realized I have the perfect thing. It’s totally biased, but for some subset of kids, it can help me answer how I move the needle. You see, I historically have taught a lot of juniors, so I’ve written a lot of college recommendations. And when I agree to write one, kids have to fill out a questionnaire. Those reflections often tell me how our class has had an impact on the kid. Now granted, these are reflections from kids who asked me to write a college recommendation — so a total skewed sample. But I’ll take it. Because even though I don’t know how our class affected a lot of kids, I can say with some confidence I know how it affected some kids because they chose what to write about. I’m going to find some old reflections and see if I can’t maybe come up with a thesis after seeing them. [In case the gallery isn’t showing the student quotations, I’ve included them at the very bottom of this post, so scroll down!]


This slideshow requires JavaScript.

I’m so glad I went through those (and others). It helped me see there are three main things that I think our time together has an impact on. Again, not all kids… I know I’m not one of those life-changing teachers that entire generations of kids will remember… but for some kids, our time together has changed them in some way.

  1. Our class helps kids recognize the importance of sense-making and drawing connections as the heart of what mathematics is all about. And in that, there is excitement and beauty.
  2. Our class often provides a shock for kids, where they are initially unsuccessful and have to undergo some sort of transformation that pushes them, that I help them along, so they can see they are more capable than they thought. (In general, I try to push kids to do something juuuust a tiny bit past what they think they’re able to do.)  Often times, this aspect of the class leads to kids telling me how they learned to believe in themselves and have confidence in their own abilities in a way they hadn’t before.
  3. Our class helps kids recognize the value that others students have in their own learning process, and that working collaboratively can be much so much more fun and much more generative than working independently. With the combination of all our knowledge, we can do so much more than we could do alone.

So here’s the tough part of the question — but also the whole point of the conference. How is my class designed so it can move the needle in these ways? What do I do to make this a reality?

Who knows?!

But I guess if someone was going to get close to the answer, I’d probably have a better shot at it than you, since you know, it’s my classroom and all.

  1. I write my own curriculum. I do this because I want my kids to be mathematicians (as much as I can do in a school setting with a list of topics I need to cover). I don’t know how to do this with a textbook. I write curriculum because I don’t know how else to get across the insane interconnectedness of everything that mathematics is, that I want them to slowly build throughout the year a large woven superstructure and at the end of the year recognize “Whoa, yeah, we did that. My teacher might have been a guide, but we did all the heavy lifting.”

    In general, I start with them playing around with a problem or an idea, and then they start to codify and see a structure, then they try to articulate in words (and diagrams! and with examples!) why their approach/algorithm/solution works, and then I tend to ask questions that extend their understanding or force them to relate what they’ve done to something they’ve done before.

    And central to this superstructure is one question: why. For many of them, our course is the first time they have to do that regularly and deeply. (I’ve come to realize how incredibly challenging and anxiety-producing this can be for kids who have never done this before.) And for some of them, this real understanding opens up for them a sense of beauty and interconnectedness that they didn’t quite see before.

  2. I am a “warm demander.” I only heard this term a year or two ago, I think from Sara Van Der Werf, but I think it suits me better than any other lingo I’ve been exposed to.

    One quotation: Warm demanders “expect a great deal of their students, convince them of their own brilliance, and help them to reach their potential in a disciplined and structured environment.”

    A second quotation: “Warm demanders approach their students with unconditional positive regard, knowing students and their cultures well, and insisting that students perform to a high standard. Students have told researchers that they want teachers who communicate that they are ‘important enough to be pushed, disciplined, taught, and respected.'”

  3. I have kids work in groups almost every single day. I try to build a classroom environment which is both relaxed and focused. I let things just unfold and don’t try to put time pressure on kids — each class is different and will get through things at different paces. What this looks like, if you walked in, would be groups of 3 (and maybe one of 4) sitting at tables working on a packet. When the packet is pushing them, kids will be talking a lot and there might be some frustration that comes before excitement when someone has a breakthrough. Sometimes when they are working on more formulaic practice (seeing if they can apply what they just learned to more problems, which may change slightly in difficulty but not much), there tends to be less noise and chaos. Music often will be streaming softly from my computer (from a playlist kids have created). I will be walking around checking in on groups, asking some probing questions for groups who seem to know what they’re doing, giving hints to groups which are genuinely stuck. And occasionally, I’ll bring us all together to talk as a whole class about places people were getting stuck and to help tie some things together.

    To be successful, with a few exceptions, kids need each other in my class. And I try to make clear that most classtime will be groups working towards collective understanding. That means you’re thinking not only of yourself but your group members. What are their needs? And they’re thinking of you, and what you might need. When kids are at home, they can put their focus on their individual understanding.

    But I don’t just expect this to happen. I have kids talk about what they need in a group, and what their strengths/weaknesses in groupwork are. They often make a list of group norms. Sometimes we do a bonding activity. I have a way for groups to check-in with each other and have honest conversations about how things are going. At the beginning of the year, I try to give explicit feedback to positive things I see people doing in groups (“I really love how you asked X if he felt like she understood…” or “I love how you all are leaning in and listening to each other” or “I totally see that you’re getting frustrated about not quite getting it, but you haven’t decided to ask for help yet and you’ve kept on trying different things… that’s awesome.”) So kids can really learn how to work together, I keep groups together for four to six weeks. At least for me, I’ve found this gives my kids enough time to develop real relationships and get into a rhythm.

    Most importantly, though, working in groups (especially ones that feel safe) lowers the cost of entry into mathematics. Kids aren’t talking aloud to the whole class and feeling totally self-conscious. They are working with two or three other kids so it’s less scary to say “I’m confused.” And the flip side is true. When working and there’s a moment of celebration and kids might think (gasp!) math is cool, it’s more okay to share that excitement with those who have been on the journey with them. It also is just more fun when math can be a social activity, where emotions can be shared. Frustrations, elations, and everything in between. And since the bar is always set a bit higher than they think, these emotions are important.

Now it doesn’t always work. My classroom doesn’t always work. This isn’t a recipe that I can follow mindlessly and transform what every kid think about math. It’s just the best I have right now. I remember some years ago I was teaching two sections of the same class where I was using the same curriculum, I was being a warm demander, and I had kids work in groups. One class was filled with joyful mathematical noise and the other was a slight and occasional murmur. Night and day, though everything else was the same except the kids. I truly struggled that year. And that’s the thing. My mathematical flavor — the thing I do to move the needle and change students’ perceptions about math and who could do it — was delicious for one class but just meh for another. Which is why I keep on iterating and changing and trying new things. Because no two classes will be the same.


In case the little gallery isn’t working above, here are the student quotations:


TMC in 2018: a personal reflection of where we are

Super rough draft thinking…

Last summer at the end of TMC17, there was a flex session on diversity. That brought up a host of questions that made us realize: as an organization/conference, we don’t even know who we are. That was both terrifying (do we not?!) and exciting (we get to tease out our core values!).

Here’s the thing. The conference runs pretty darn smoothly and appears organized to people attending, but that all comes as a result of a handful of people on the committee working on certain individual tasks (usually alone, sometimes with one other person). And Lisa, our amaaaaahzing Lisa, keeps her eyes on everything and does the bulk of the infrastructure/logistical work that makes the conference actually happen.

But — and this may come as a surprise to y’all — I’ve been on the organizing committee for a few years, and never once in that time did we all get together in person or on a google hangout to have a discussion. Mostly the committee members worked on their individual tasks and we would occasionally send an email out or ask a question… most people knew what they were working on, but didn’t know what everyone else was doing. And honestly, there probably wasn’t a need. The conference was successful in that it, for many attendees, provided something that they didn’t get in other places professionally, and people were on the whole happy.

So when that flex session on diversity came up, it opened my eyes to something. We were doing the logistics of recreating the conference from year to year. But it was now year six, and although still organized by math educators for math educators, we (as organizers) were still considering ourselves to be a ragtag conference that we cobble together. Maybe I shouldn’t speak for everyone. I should probably say…

… at least that’s how I looked at TMC until then. It was perhaps a vestige of the thinking when it all first happened in 2012, and we were cobbling everything together from scratch (here’s the original website that I put together but don’t even remember putting together!: TMC12). And perhaps it’s because it was just a merry band of us making spreadsheets and organizing ourselves in dorms and trying to read contracts and figure out what they meant and fumbling around trying to make things work over the years… it just felt like we weren’t professional conference organizers. We were just trying to make things happen as best as we could. And so that was enough. I thought we’re volunteering our time for this… so who could ask for more? 

But the flex session made me realize we are not that anymore. We can’t be that anymore. Because the conference is real and sustained and impacts people. That’s it: we were responsible because we were putting things together and what we did impacted people. And it was clear that for all our work to be welcoming, we weren’t always being successful. Jenise Sexton wrote in 2017:

So when I walked in the Dining Hall of Holy Innocent Episcopal School along with around 200 other participants, I wasn’t surprised to see like 4 or 5 other brown skinned people. But that evening I received a DM from another participant which read, “Where are all the black people?”

In that moment, reading that message, I realized it wasn’t my role to be the sole representative. It isn’t supposed to be normal for me to be the only black face in the room.

And in the flex session, people had lots of questions about how things happened to make the conference what it was. How did we think about registration and who can attend? What outreach do we do? Who chooses the keynote speakers and how do they get chosen — and does diversity (in any form) come into play? How do sessions get selected/accepted and organized? Why do we really want diversity, and what kinds of diversity are we even talking about? What is diversity anyway?

People cared about this. And conversations (good conversations!) happened at TMC around this. Marian Dingle wrote wonderfully about it here (“Yet, I don’t feel that I was able to fully let my hair down at TMC. For one, I was a first-timer, and the few people I “knew”, I only knew through Twitter. For another, I was one of a few black women, which although not an unfamiliar situation, still was not comfortable.”) and I’m glad that she was selected to be on the TMC Board this year. [1]

And this is precisely where I started to realize we were responsible for answering these questions. We had to think more than simply about logistics and getting the conference to run smoothly. We had to think about what the conference really was, and what a vision for it was. We can’t hide behind “don’t expect too much from us… we’re just putting this thing together on our spare time!”

And from this, Tina (with me as a trusty sidekick) took the reins on coming up with a mission statement for TMC — asking for input from all constituents (anyone who attended TMC, the committee, the board) and then asking for more feedback from the community during a Global Math Department session before it took its final form.


That was a huge step forward for us, I think. Because it helped us define our core values as best as we could, and then refine them. It is perfect? No. But does it give us a place to start working from? Yes.

Now let’s fast forward to TMC18. Another flex session on diversity. And the first question that comes up:

Why do we value diversity as TMC? The mission says “we value diversity” but it doesn’t go deeper. We need to go deeper. 

And in this hour and a quarter, many things got raised. Some of my key notes:

  • We are at a place where TMC is a grassroots organization whose grass has grown too high. We are just starting to grapple with how to deal with that mindfully, inclusively, awesomely.
  • Do people see diversity as important for TMC because: (a) diversity helps TMC (it makes TMC stronger), or (b) we want to create a TMC that’s valuable for all math educators?
  • We all blog and tweet to connect with people, and sometimes it is comforting to connect with someone like you in a way other than just math — such as in terms of race or sexual orientation. “If white people/cis people can find it, I should be able to find it too.” [One thought that was thrown out for those who want to connect in safe spaces at TMC was to form “homerooms” or “affinity spaces.”]
  • “It’s not just about inviting people, it’s about what they’re being invited into.”
  • As math educators, we know that numbers can be powerful. But the number of people of color attending TMC each year might not be the metric to use to measure us with “diversity.” We want to be careful not to try to “get” people of color (or diverse participants) just for numbers, to make us feel like we’re filling a quota and doing the right thing. We don’t want diversity to be trendy — to make ourselves feel better, or so we’re trying to make the “picture” look better. Maybe other metrics (more qualitative) are better. [What we do at TMC? Action steps we’ve taken? Things like pronouns on tags. Sessions. Keynotes. Big and small. We tried some these things — what can we measure? What does success look like?] Numbers don’t speak; they lie in a vacuum when given without context.
  • We need to be more strategic than being generally welcoming (which we do really well). We need to be specifically welcoming.
  • If TMC is going to double down on addressing diversity and encouraging participants to engage, it needs to build that into the schedule (perhaps by having a diversity/equity strand in the program, and perhaps other ways to encourage conversations around these issues).
  • TMC and the #MTBoS are intertwined because the #MTBoS is the primary pipeline for people coming to TMC. So one possible thing that could happen is that people could start having more sustained and organized discussions about diversity and equity in the #MTBoS. One idea was about having a regular chat (e.g. #MTBoSequity) and having it center around shorter things like articles/blogposts instead of books. Questions were raised about twitter being super public and challenging to have those sorts of conversations — and the idea of having semi-private discussion boards or not-saved-video-conferences similar to Global Math Department were raised. (Tina just blogged about the idea here.)
  • Having people write their pronouns on their nametags was a way TMC forced people to confront diversity in a small way. Someone asked if there were other small things like that that we could do.
  • We have a lot of people at TMC who are supportive of the ideas of diversity. 

In the flex session, people asked a lot of questions about how we plan the logistics, just like last year. How are the sessions chosen? How are the keynotes chosen? How does registration work? At heart, the reason these questions were asked is because people were interested in seeing if there was intentionality in how they were being done. [2]

And that to me is where we need to go next as we think about organizing TMC. Intentionality. I wrote earlier that:

I’ve been on the organizing committee for a few years, and never once in that time did we all get together in person or on a google hangout to have a discussion.

TMC is at a place, at least to me, where we have successfully figured out many of the logistical aspects of putting the conference together. We were able to do that as a committee without being a cohesive whole — we could work in our little silos. However we’re at a critical juncture as an organization. We need to figure out how we can ask big questions, have sustained and challenging discussions that push us, have a process for moving from discussions to making decisions so we can move forward, and come up with a clear and shared vision that we’re moving towards. 

After writing that, I only have one word that comes to mind: overwhelmed.

After TMC18, the committee and the board did all sit down together. We had four hours. And though we could have used four more, I was proud that we identified that we needed a way to communicate and have discussions, and we are in the beginning stages of learning how to do this all virtually and asynchronously. In the few weeks since TMC18, we’re actually starting to do this. It’s a lot we have to do, and we don’t have a roadmap on how to do it. It would be way easier to just go back to how things were done. But that’s not in line with what we want to be. Earlier, I wrote:

The conference was successful in that it, for many attendees, provided something that they didn’t get in other places professionally, and people were on the whole happy.

But I wrote that to reflect my thoughts then. Now I see that this is problematic. Is that a good metric of success for us? Who gets counted in the “many” and what does “on the whole” really mean? We have to be intentional to make sure that everyone feels at home and that we are working towards our mission of reaching “all learners.” Which means we need to think about teachers who are feeling left out. When we’re thinking about the conference as a whole, who are we designing it for? Is it for people like ourselves (those on the organizing committee/board)? [3] Or do we need to start de-centering ourselves before asking this question?

As I said: overwhelming.

I don’t know how this all will happen. I know it won’t be easy, and it won’t be quick. I’m imagining years. [4] And honestly, a big part of me wants to shy away from all this change. Those who know me know that change is really hard for me. I’m a little  (big) hobbit who likes to live in my little hobbit hole. But I also know that if I were one of my students who came to me for advice on all this, I would say to them “doing what’s easy is not always doing what’s right.” And I’ve never been scared of hard work.

I should conclude by saying these are just things I’ve been thinking a lot about. But they are my thoughts. They aren’t fully formed (rarely are my thoughts fully formed), and certainly not cohesive. But more importantly, they aren’t official thoughts of the committee or the board. I don’t really even know if other TMC organizers will agree with my thinking about this! But I promised @BeckyNftP I would blog about the flex session around diversity, but the only way to keep that promise was to embed that in the much larger thing that I’ve been mulling over in my head.

[1] Please don’t ask me what the Board does and what the Committee does. Remember when I said ragtag? These are things we’re still figuring out.

[2] And things were being done.  Those selecting the keynotes or organizing the conference program did think about bigger picture things. But they took that up on their own, not because they were working towards a shared vision we all had.

[3] As TMC started, it had to be. That’s why it was started! For a small group of #MTBoS people to meet in real life. But now we have to ask the question if our answer is still the same?

[4] We’ll probably need at least a year just to figure out how to communicate with each other semi-effectively.

Desmos Pre-Conference 2018 Recap

This is a quick blogpost that I’m using to recap just some of the information from the Desmos Preconference before TMC18. I was dealing with some other stuff when I returned from TMC, and then I had to take a short few-day jaunt to see my parents/aunt/uncle. Now I’m finally home and starting to do things like write college recommendations and think about my new class for next year (Algebra II). But I’m afraid if I don’t take the time to reflect on some of what I took away from the conference, I will not end up using it. But at the same time, I feel like it’s so much stuff that to do it comprehensively, it will take too long and that’s keeping me from starting. So here’s my pledge: I’m just going to do what I can, and not worry about being incomplete, and then I’m going to #pushsend.

Tonight, I’m going to #pushsend on the desmos preconference day.


I went to one session, led by Heather Kohn, David Sabol, and Mary Bourassa. These three desmos fellows shared how they use Desmos in the classrooms. Here are a few gems:

  • Heather often creates handouts to accompany activities. For example, for Will it hit the hoop? she has a spreadsheet for kids to fill in (e.g. “Predict, Screens 5-11” “Analyze, Screens 12-19” and “Verify, Screens 20-26”). 
  • I shy away from doing cardsorts (or even short activities) on desmos because I tend to have some groups finish way earlier than others. But this would happen even for paper cardsorts! So here are some tips. First, just so all groups start at the same time, you can pause the activity on the first screen (which you can have be an introductory screen). When everyone is ready and logged in, you can then unpause the activity which allows everyone to start at the same time. More importantly, you should create a slide after the cardsort/activity which links to another activity or has some extra practice for those kids to work on. And for extra fun, you can have this slide be a “marbleslides challenge.” But one tip is to use the teacher dashboard to pace the activity to the slide before the challenge, so that you can make sure kids aren’t rushing. (You can check in with the first group done and ask them a few questions to make sure they’re getting things.)
  • You can do a Which One Does Belong on Desmos (example: go to and enter 5CK W7N). Have kids vote on which one doesn’t belong. You can then display how they voted! If no one picks one, after they finish and you discuss, you can have them go back and everyone has to pick the one that wasn’t picked… and then explain why that last one might also “not belong.”
  • David was worried about how kids will access desmos activity knowledge later. There’s a lot of digital work and verbal work in class, but then things aren’t archived. So here’s a great example of how David deals with this. He used Andrew Stadel’s “Math Mistakes with Exponent Rules.” On day 1, he used the first day PDF to have kids work the problems in class. Then on day 2, he screen grabbed the second day PDF and made a desmos cardsort (sorting them into true/false) and used the dashboard to showcase wrong answers and have class discussions. Also, after the cardsort, he had a screen that said: “Make a FALSE statement that a classmate may think is actually TRUE.” Then that night he created — using what kids wrote for their false statements — a paper copy with all these FALSE statements (sometimes there’s a true statement that a person wrote!) where kids had to identify the errors!
  •  A great question in a desmos activity is to show a lot of work/visualizations/etc. and write: “What would you tell this student to reinforce what they know and correct their errors?” If the student work has some nice thinking and some subtle not-so-good thinking, this often will lead to solid class discussions.
  • Mary uses Desmos occasionally for assessments. There were only a few questions, but they involved deeper thinking (e.g. given a graph of part of a parabola, can you come up with the equation for the parabola?). The presenter asked her kids to do all their written work on paper handed out for the test. Yes, students could revise their work/answers based on what they saw on Desmos, but that had to be reflected in words/notes/changes on the written paper. So a student guessing-and-checking on desmos with no supporting work will not garner credit. (For students who finish early, put a screen with marbleslides challenge.) One big note: make sure that at the end of the test, every kid goes to a blank last screen, and then PAUSE the activity. That way kids can’t come back and rework problems or show other students particular questions on the assessment.
  • Rachel K. (attending the session) said that she often had kids project their laptops up to the airplay and lead the class through something they found/built/figured-out on the Desmos calculator, or will have one kid lead a desmos activity on the big screen.
  • I often worry about how to lead effective discussions on activities that kids are doing. For pre-existing Desmos built activities, there are “teacher tips” that help teachers figure out what to focus on and how to facilitate conversations. But more importantly, whether Desmos built or random-person built, every activity has a teacher PDF guide (Click on “Teacher guide” in the top right hand of the screen for the activity.) You can print this out and use this to help you come up with a specific list of things you want to talk about, and stop at those places (e.g. questions, places to pause, etc.)
  • After the session, I talked with Heather about this feeling I had when doing long activities with Desmos. Although I was constantly checking the dashboard, and walking around listening for conversations, I often felt useless and bored and like I was doing something wrong because I wasn’t … doing much. She let me know that she also feels this, but that’s part of it. Letting kids engage. But I realized that some of my best classes (without desmos) have me circulating and listening but not doing too much beyond that. I was “being less helpful.” So I think I just have to make sure that when I’m not doing much, it’s because kids are doing good things mathematically and conversationally, and that’s because I’ve orchestrated things to be that way.

As an interlude to this wall of text, here’s my favorite nerdy math picture from the day.

20180718_141146.jpgYes, indeed, you see a 3-4-5 right triangle, and a visualization of the oft-taught “Pool Problem.” In Starburst. My kind of math manipulative!

For the remaining two sessions, I worked on playing with Computation Layer and refamiliarizing myself with it (I spent 3 days earlier this summer spending huge swaths of time on this… a huge shoutout to Jay Chow who helped immensely with this). Having CL experts in the room and granting myself three hours to play with CL was amaaahzing. I first reacquainted myself with some of the basics (a lot of which I had forgotten, but it came back fairly quickly) and then I decided to start trying to “desmosify” this calculus optimization activity.). I didn’t get too far in, and so far this is no better than the paper version of the activity, but I am proud of what I was able to do with my CL chops! (You can see what I made here.)

The keynote session was given by Robert Berry (the new NCTM president) and he gave an overview of the recent NCTM book Catalyzing Change (which I have bought but haven’t yet read!), talked about some big picture NCTM things (advocacy, membership, financial health), and then told us what has been happening on the ground level. He ended his session talking about technology and what excites him about that. He said that “Technology that supports and advance mathematical sense-making, reasoning, problem solving, and communication excites me” and that “Competence is about being participatory in mathematics – with each other, with the teacher, and with the mathematics.” He then said technology can be used for good or evil based on how technology affects the following things in the classroom: 

  • Positionality [how students engage with each other, their teacher, the curriculum, the technology, etc.]
  • Identity [how students see themselves]
  • Agency [how students present themselves to the world? how do we create structures for that to happen?]
  • Authority [“shared intellectual authority”]

His latest NCTM President’s Message is precisely on this. Also, Robert is a totally awesome guy.


That’s me on the left, him in the middle, and friend and TMC keynote speaker Glenn Waddell on the right.

Lastly, Eli (founder of Desmos and super nice guy) showcased a new desmos feature for teachers: SNAPSHOTS. You can read about it here, but what I love is that it allows teachers to facilitate discussions more thoughtfully in line with the 5 practices. (I’d love any help finding or coming up with problems at the high school level that work well with the 5 practices… Most examples that I’ve seen are at the middle school level so it’s been hard to wrap my mind around how to find/create problems for a precalculus or calculus class that might make this approach work super well.)

My favorite slide of his was:


Eli keeps things simple, which allows me to read slides like this and think: “wait, in what ways does my teaching do that?”

And with that, it’s time to #pushsend.


The State of the 2018 #MTBoS (to me)

Every so often, I like to take reflect on where I think we are as a community of math educators who collaborate online. Usually after attending TMC — a math conference run for and by math educators. But please forgive me in advance. This is the ramblings of someone writing late into the night and someone who isn’t revising. Musings, at best.

Taking Stock Previously

May 2009: Why Twitter?
November 2009: How BlogBuddies Became Friends
July 2012: 40 Choose 2 First Dates, or Initial Impressions of TMC12
March 2013: Some New Things On the Interwebs & HOLY COW What is Happening!
June 2013: My Thoughts on the #MTBoS
August 2013: TMC13: The State of Things For Me
July 2014: Teacher Growth, the MTBoS, and TMC14
July 2015: My Thoughts about the Evolution of the #MTBoS: 2015 Edition

But I haven’t taken stock for a while. Partly it was because I didn’t see much change in 2016 from what I wrote in 2015. And then I made a decision to consciously avoid jumping in the numerous conversations that happened during and after TMC17, although I had lots of thoughts. [1] So now it’s time to take stock again.

Taking Stock and Making Predictions: Teacher Leader Edition

The biggest thing by far that I’m noticing is that people in the community are becoming (and seeing themselves) as teacher leaders.

When I started teaching a bit over a decade ago, I didn’t see many pathways for classroom teachers to have huge impacts on math education. (That wasn’t something I was looking for, to be clear, it just wasn’t something that I saw in my world.) In the past five years, as social media has fueled things, our classrooms aren’t silos anymore and our practice have become more public, and as this community has grown bigger, I’ve seen the rise of various pathways that teachers can become teacher leaders.

There are many ways people can become leaders from within the MTBoS community (for example, Annie Perkins/Megan Schmidt/Dan Anderson/Justin Aion inspire playful mathematics through art for so many math teachers. And people are planning and running mini-TMCs and tweet ups. New things like Desmos’ Computational Layer come around and people like Jay Chow become the expert teacher of us teachers who want to learn it. There are always people running and presenting at the Global Math Department.) That has actually been something I’ve found true since the early days of the MTBoS. It’s just that there are more and more of them now as the community has grown. I’ve found that the MTBoS provides numerous ways for people to gain their voice as a teacher leader. Tweeting is one way, short and sweet. Blogging is another. And TMC also gives some opportunities for honing a face-to-face voice (from the short and sweet my favorites, to the 30 or 60 minute sessions, to the six hour morning sessions). In a small community which attempts to be supportive and people try to raise each other up, it is easier to identify and amplify your voice, see that others find what you have to offer valuable, and gain confidence in yourself.

But we now have community members that have become recognized as teacher leaders outside of our MTBoS community. For a long time, there was Dan Meyer who fit this definition. But now there are a group of people who are in that category — MTBoS people who have kinda broken out of the MTBoS in terms of their impact on math education. Fawn Nguyen is always traveling to give talks! Julie Reulbach publishes a post and almost 10K people get it in their inboxes! John Stevens and Matt Vaudry published a book around their approach to the classroom that resonates with people! Heck, so many books are out now or coming out now by MTBoS people *cough* Christopher Danielson! Chris Shore! Edmund Harriss! Denis Sheeran! Wait, so many white men! In any case, I’ve compiled a list of all MTBoS books that I know about here.) [2] In fact, there are now a small group of MTBoS people who seem to be making the conference circuit giving keynotes. There are so many people who are now presenting or even keynoting regularly at NCTM and other conferences. And there are a lot of MTBoS folk who are on NCTM committees. (I don’t know if I’m in the minority or majority, but I see NCTM as acting as a pretty great partner to this online math teacher community.) And probably most exciting to me, I’m reading more and more tweets of people in the community taking on math coaching roles for districts, or becoming department chairs! Teachers who love math teaching leading math teachers! The MTBoS cultivates internal leaders who then can become leaders more broadly. A lot of that has happened in the past three years.

I have done a lot of thinking about the rise of the teacher leader, and what even a teacher leader is. These thoughts started in 2015, and became more solidified as I started talking with Julie Reulbach in 2018 about her TMC keynote address which is specifically about teacher leadership. (YOU SHOULD WATCH IT!) I came to the conclusion that I personally would define a teacher leader broadly… as someone whose work has a positive impact on kids outside of their own classroom.

So that includes sharing materials/lessons with other teachers, supporting other teachers when they’re down, writing a book that changes someone’s practice, running (non-sucky) PD which pushes participants forward in their thinking about teaching, creating spaces and structures for teachers to reflect about their practice (ahem, shameless plug for The Virtual Conference of Mathematical Flavors that I’m hosting right now!), tweeting out answers to questions people ask, writing blogpost reflections about your classroom that inspire others, whatever. As Julie said in her talk, teacher leadership is not a ladder you climb. (I think it used to be.) You don’t have to leave the classroom to have that broader impact. And that a tweet that hits someone at the right time might be way more impactful and useful than a book. [3] This isn’t something “new” but it is something that I think people in the MTBoS are starting to be aware of.

With the smaller things we’re doing (cheerleading each other, having book chats online, pushing people to think about diversity and equity in their classrooms, etc.), we used to think of it as just helping each other out. But there’s a reframing that is happening. We’re doing the same things we’ve always been doing, but people are starting to recognize that this work is the work of a teacher leader. That, “OMG, I am actually a teacher leader… wait, no way… I am not… but… maybe I kinda am a little bit?” It might slowly be entering some MTBoS folk’s understanding of who they are. And that’s pretty awesome. There may be nothing different in what people are doing, but I sense the beginnings of a shift in how people are interpreting what they are doing. (And acknowledging and really accepting that what they are doing has real value to people.)

It’s like — I don’t know — I see the pathways for teachers to become leaders as numerous, crisscrossing, and some pathways are only just beginning to show themselves. Maybe vines on a trellis is the image that I’m trying to go for? All I know is that there are now a zillion different ways for someone to have a positive impact on kids outside of their own classroom… and the existence of the internet and the online math teacher community is making that even easier. I predict that there will be some cool ways people figure out how to have an impact outside of their classrooms that we can’t even image. Who knows? Find ways to get involved with new (math) teacher training programs — or create resources to help new math teachers? Argh. I literally can’t come up with good ideas… but that’s precisely the point. Who could have predicted 5 years ago that there would be a math space in the Minnesota State Fair?! I suspect in 5 years there will be a number of different awesome pathways that people will carve out for themselves to become a teacher leader in a way that aligns with their passion/interests that I totally wouldn’t have anticipated today. Which means we’re at a cusp. We’re still trying to figure out what precisely teacher leadership can look like. We have a number of examples that have emerged. But we’re likely going to see a bunch more.

We have people who are in math ed and also part and parcel of our MTBoS community. Specifically, I’m thinking of Lani Horn and Tracy Zager. Their books Motivated and Becoming the Math Teacher You Wish You’d Had tout the work of people in the MTBoS do and outline pedagogy that most everyone in the community can rally behind. But also their work also engages deeply with the idea of identity and status. And importantly, although in the past I saw certain beams of light here and there emerge about the idea of identity and status in the classroom (in the vein of complex instruction), this kind of thinking is becoming much more normal in the conversations that are being had in the MTBoS. More and more, I think people (myself totally included) that the basis of an awesome classroom has to be rooted in consideration of these things. Thinking about “how to teach completing the square,” for example, isn’t just about scaffolding and conceptual development of the idea. Being able to do that well is also predicated on building an atmosphere in the classroom that the scaffolding and conceptual development can happen within. I think more and more people (myself included) are starting to recognize this. Like Lani and Tracy do, I predict more people in math education are going to start engaging with our community, as they will come to see us as a powerful resource, and we will engage with them if we see them as an ally in our classroom work.

In general, the MTBoS conversations aren’t entirely consumed with content or sharing resources anymore. It hasn’t been that for a while. Broader discussions about identity, status, diversity, equity, social justice are now more commonplace. Not everyone is engaging in these conversations, but they’re happening and I bet this is going to turn into another pathway that the MTBoS will be creating teacher leaders that are recognized outside of the community. And I’ve seen that these conversations of identity, status, diversity, equity, social justice have been turned back onto us. Not just things to consider for our classroom community, but also for us to consider as an online math teacher community. Right now there is a small but growing recognition that we can’t brush these conversations under the rug — for the sake of our students, and for the sake of our own community. 

I don’t quite know what to make of this… but there are a ton of #MTBoS classroom teachers that have left the classroom to work full time at Desmos or Illustrative Mathematics. I went to dinner with a group of IM people in Cleveland recently and there were only two people at the giant table who I wasn’t friends with from the #MTBoS. Similarly, I know a lot of the people working at Desmos (and I heart them all!). Although I don’t know what to make of this, what I can say is that these people are working at places I believe in, and that will have a large-scale positive impact on math education. And I probably can say that if it wasn’t for the MTBoS, many of them might not have this opportunity that they decided to take.


This post feels incomplete. I feel like I have so much more to think about and write. When rereading this post before I #pushsend, the ideas seem inchoate, and somewhat incoherent, to me. I can’t underline anything and say “THIS. THIS IS WHAT I’M TRYING TO GET AT.” Usually when I sit down to write something like this, all the blathering helps me refine my thinking and gets me to clarify what I really think. And at some point, I usually hit upon that thing that makes me feel excited and like I have found something TRUE and A REAL INSIGHT. But I am not leaving this post feeling any more lucid. No big insights emerged. So I suppose I leave this post as late night musings, as I started it as.


[1] If you don’t know what this is all about, but me being all cryptic has piqued your interest, you can get a flavor of it by reading these two posts: here and here.  This moment was important for me in one huge way. It highlighted how scaling up the online math teaching community without a central authority could lead to problems with intentionality/messaging/impact. How does a decentralized community with community-builders who are volunteers grow bigger with a coherent set of values and vision and positivity that are not only agreed upon but also enacted? Where intentionality in things that happen have a place? I don’t have answers.

[2] In 2015, I noticed there were “brands” (for lack of a better word). I still see that. The number of people with a narrow/specific idea/vision and a coherent voice that really resonates with people is growing. These people are gaining a lot of cache outside of the MTBoS. Often times, these “brands” are related to projects that were just gaining traction in 2015 (like Visual Patterns or Open Middle or Which One Doesn’t Belong or Clothesline Math or …). Conferences, books, at the MTBoS spread the word of these “brands.” And now from their rising popularity in 2015, they’ve become something bigger in math education. And with that, they carved out one pathway of “teacher leadership” that didn’t really exist before. But a number of people seem to be following it in some form. And that’s cool to see.

[3] But what I like about the MTBoS is that, taking my definition of teacher leader, it’s all a community of teachers who are trying to support each other. And so in the ways we all prop each other up, push each others’ thinking, share resources, etc., we all are having a positive impact on each others’ classrooms and each others’ kids. And so we all in small ways can consider ourselves teacher leaders. I love that it’s not a zero-sum game.

I wrote this and it doesn’t quite fit above, but I didn’t want to delete it. So I’m sticking it at the bottom of this post here. When I started teaching, I wanted to become a “master teacher.” That was my goal. Feel like I know I’m an expert in what I’m doing. I have since realized I will never consider myself a master teacher. That’s probably due to my own psychological makeup. But in the #MTBoS we have this idea that “everyone has valuable things to share.” And I truly believe that. But I also wonder if — now that I’m seeing so many ways people teach —  I don’t believe in the idea of a master teacher anymore? As opposed to my first few years of teaching,  I now don’t really think about it at all. Because over the years in the MTBoS I’ve see so many different ways people reach their kids, I recently realized that I don’t have a single ideal/standard to live up to. There are so many ways to be an awesome teacher. (Hence, my virtual conference of mathematical flavors was born. I wanted to showcase this diversity!) I just have to figure out who I am as a teacher as best as I can and just keep on trucking.


Senior Letter 2017-2018

Every year that I’ve been teaching, And at the end of each year, when I start growing wistful (but also a little bit glad to get them out of school because their second semester-ness starts to take over), I write them a letter which I give to them on the last day of classes. The letter usually always says the same thing, hits on similar themes, but I write it from the heart.

Sometimes I remember to post it on my blog, sometimes I don’t. This year (obvs) I remembered!

Even though they got to be a bit punchy at the end of the year, I’m kinda missing my seniors right now.