Going off the beaten path…

I find myself always pressed for time in class. Doing inquiry-based work, and going at the pace of the kids’ understanding, means that inevitably there are stretches of time when I’m feeling like “ARGH! We need to go faster! We have to be further along to cover the content!” Every teacher I know feels this, and in my office we talk about this, so that makes me feel better. I’m not alone. I also know in the back of my mind that somehow, each year, we manage to get things done. That helps.

That being said, this past week I had one of the very few times that one class was about half a day in front of the other and I didn’t feel the need to forge forward as acutely as I usually do. And in that short exciting window, I saw a student’s shirt which I thought was mathematically beautiful…


… which of course I told to the student. “Math?” He didn’t see it, nor did others in the class. It was an 90 minute class, and when having kids work on some problems together, my mind started thinking… I want to show kids how I see this shirt. The glasses I use to see the world are different from theirs. We take a break in the middle of class for kids to get water or quickly grab a snack, and so 5 minutes before the break I stop everyone. I have them look up. And I say something like: “I know many of you don’t see math in [Stu]’s shirt, but I think if you start looking at the world with math in mind, something like that shirt will pop out as beautiful mathematics. So grant me 5 minutes where I’m on stage, you’re the audience, and I live give you my thought process for creating a version of that shirt on desmos. It may not work, but I think it will be neat to try.”

So they are sitting watching me sit at a laptop. I start by graphing f(x)=e^{-x^2}. They ooh. Maybe they don’t. But in my mind’s recreation of the event, I hear them ooh. I explain that this isn’t a random thing I created. I ask who is taking statistics. I mention the “normal distribution.” A few nod knowingly, and for those who don’t, I say “this isn’t genius, this is me seeing [Stu]’s shirt and recognizing one of the most famous equation shapes in the world.” Then I graph the reflection over the x-axis. They understood that. But then I said I need more lines.


So I say: “I am now going to try to make the same curve with a higher peak. I think I should do a slight vertical stretch.”


But then I note that it isn’t just that each curve gets slightly stretched, but also the width of the bump gets slightly widened too. I go to the board and explain how I’m going to do a horizontal stretch too, and write up how I’m going to alter the x-variable in the equation to do that.


I flipped that over the x-axis and then manually entered a bunch more equations that did the same thing — slightly higher peaks, slightly wider bumps. Kids asked me to add in the two circles in the middle, so I did. It looked meh because I only had 6 or 8 curves. I sent them on break and promised them I’d get it to look a bit better when they returned. And that I would do this with just one equation.

During break, I whipped this up using lists.


When they returned, I explained how the list worked in Desmos — so one equation actually plotted a bunch of equations.

I didn’t know what to make of doing this. I wanted them to see how I saw things, how I thought about things. That math is in lots of places if you just look for it. That playing with math can be fun and what they already know mathematically are quite powerful tools. If for just a second one of the kids was like “Oh, yeah, wait, math is pretty neat,” I’d be happy. It might have happened because the next day I was talking with a science teacher who was telling me that my kids who she also taught were talking about it in her class.

Also, you know, I always find that when I deviate from my plans for something I’m excited about, I always feel so good about doing what I’m doing with my life. I have to keep this in mind and try to go off the beaten path more…

PS. Of course when I saw the shirt, I didn’t initially “see” the normal distribution. I saw fluid flow around a cylinder:


But I forgot everything mathematical I know about that. :) So normal distribution it is!



On stepping aside.

Note: I debated whether to #pushend or not. Hopefully this helps anyone curious about why I’m stepping aside from TMC.

I posted this tweet yesterday:


I’ve been on the organizing committee for Twitter Math Camp for the last three TMCs and also for this upcoming one in Berkeley, CA. It was initially a surprise — and also upon reflection not as much of a surprise — to me that board member Marian D. stepped down from the board of TMC a few days ago. When I called Tina C., also a board member, to talk about possible next steps, she told me she was ready to step down also.

I will let Marian and Tina talk about their reasons themselves if they wish. But without much information out there, I figure people in the TMC community are confused and filling in the empty space with their own conclusions. I mean three people leaving organizing TMC in the span of a few days? That is a message encoded in an action, right?

Here’s what I want to share about that, from my perspective. I love TMC. I love the people who put on TMC. If I had to point to one thing in my teaching career that has grown me the most as an educator, it would be MTBoS generally and TMC specifically. I don’t have adequate words for my love and appreciation for it.

And mostly, I worry that because of these departures, people are going to vilify TMC. I don’t want TMC to be vilified. And in my opinion, it doesn’t deserve to be vilified.

It was born out of desire and necessity, to have math teachers who knew each other on twitter to meet in person. It provided a space for teacher voice to have value, and a place of emotional support for many who didn’t have any locally. It created one pathway for classroom teachers to become teacher leaders. I can’t say it enough. I love TMC, I love TMC, I love TMC, I love TMC, I love TMC, I love TMC. And for many, many, many people who have attended and have had amazing experiences, they too have a special place in their hearts for TMC.

So know that although I am not going to be a committee member, I am not anti-TMC.

So why, then, would I leave? Before that, I need to say it was a terrifying decision to make. I had committed to helping out, and shirking on something I committed to is a huge sin in my book. The good news is that the work that I commit to doing every year is quite simple logistically and not a huge time suck (organize a new-attendee/supporter mentorship, plan a new-attendee dinner, design some buttons, organize a homespun photobooth). And we’re five months before the conference and I told the committee that I’d work with someone on helping them learn to do these things with all my documentation. I wanted to leave as responsibly as I could.

But yes, why did I leave? As much as I love TMC, I didn’t enjoy the process of planning TMC. I’ve been in so many awesome collaborations where we have the opportunity to plan something awesome (whether it be a lesson or a workshop or whatever). And TMC is one of those. I mean, imagine you got a bunch of dedicated, passionate, awesome, thoughtful math teacher friends together (the committee/board is full of people I call friends!) and you get to put on this awesome event. I mean can you even imagine how fun and exciting that would be? Brainstorming, debating, revising, throwing things out, having a genius moment, outlining, revising? Simultaneously intellectually draining and intellectually invigorating. All the good! But the reality is that the process of planning TMC was broken, and over the years, it has remained so. It shouldn’t be so, and I tried to help change things, but without going into specifics, it never became unbroken. TMC, for me, was amazing. But planning TMC is a different story.

I was on the phone talking with Tina about Marian’s sudden departure, and Tina told me she was thinking of stepping down too. For the past few years, but more so in the last year, I’ve been working alongside Tina on a number of projects. We worked on creating a TMC mission statement with core values (engaging with the community in multiple ways to do this), we worked on improving communication and defining roles in the TMC leadership (beforehand, everything was haphazard and no one knew what everyone else was doing), we worked on figuring out where TMC needed to improve (diversity) and putting together a plan to address that, we worked on spearheading the first TMC fundraiser, and we were working on implementing ideas from the diversity proposal that the TMC committee and board had approved. My earlier work — things like calling a few restaurants and sending out emails pairing up new attendees and supporters — started to feel less important to me. I was excited about working alongside Tina with professionalizing TMC and addressing our deficits. That was the work that felt difficult and juicy but so much more important. Working with Tina on all this was that exhilarating collaboration that I had talked about above. So when Tina told me she was leaving, I sat down and wrote and wrote and wrote nonstop 40 minutes just trying to figure where my head was at with all of this.

What I realized I was losing my mentor-leader who brought meaning to my work. And she was my rock when trying to navigate our dysfunctional planning process. I tried to imagine doing our work without her and thinking about the frustration level of planning with the committee. I couldn’t imagine it. And that’s when I realized I had to leave with her. I thought: better all at once, a little less than half a year before the conference, so the committee/board can regroup.

I was excited about the directions we were taking this year in terms of diversity and equity. Marian reached out to educators of color to present and attend. In the program, a strand of sessions throughout the conference was focused on equity. Affinity spaces for educators of color and LGBTQ+ folk were built into the schedule. Marian kept the idea of “safety” for educators of color on our minds and we were explicitly thinking about people with mobility problems, deafness, etc. In other words, we as a conference knew we were generally inviting, but we were working on being specifically inviting.

The people organizing TMC are friends. They might not create a synergistic working group, but they are doing selfless work which has helped so many. There are still people organizing TMC who are hoping to try to make these things listed above a reality. Any one of these things — well-crafted affinity spaces, a strand of strong equity sessions, thinking deeply on small and big ways to put on a conference where marginalized groups are valued and welcome and feel safe — would have pushed TMC forward leaps and bounds. It is a fair statement to say the committee is not strong at thinking about equity and diversity as a whole yet (I’m honestly very far below where I know I need to be at this point, but I’m learning from every conversation I have and pushback I am given). There is a steep learning curve and it’s not always easy to see through these lenses. Mistakes are par for the course. (We’re math teachers, we know this!) But there are those who are invested in this work and they are going to continue pushing TMC forward. They deserve all our gratitude and thanks. And support. If they ask for help, I hope many of you who want to see TMC do better on these fronts charge in and give them an assist. Help make TMC the place you want it to be. This is what TMC has always been to me: a space for passionate people to do good things together.



A simple question

I know I haven’t posted a lot this year. I actually have tons to post on because I’m writing a lot of Algebra 2 material, but because I’m doing that work, I haven’t been able to carve out the time to post about it. Blerg.

But today I wanted to write a short but sweet post. Every so often, I ask for feedback from my classes. I’ll create a google form and ask how things are going, if kids’ pronouns have changed, how long their nightly work takes, and other thing I’m curious about. Sometimes I have kids reflect about their own work or their groupwork.

But last year, I started occasionally including this question:


I love that it gives kids a chance to think about who has helped them out. I don’t make it a required question. Only about 1/2 or 1/3 of my kids filled that question out this time. But I really loved the short bits I did get to see. I learned who might have been studying together for tests, or who worked super patiently with another person who might have been struggling, or whatever. And kids got to have a moment where they got to be grateful for someone else.

What was nice is that I actually asked for this survey a week before parent-teacher conferences, so I was able to share with parents who came some shoutouts about their kids (if they got any). Parents really appreciated hearing that their kid received praise from another kid (and why).

And today, I sent short emails to any kid who got a shoutout…

Hi Stu,

In our last check-in survey, I asked students to give a shoutout to someone who was an important part of their learning experience. I wanted to privately share these with students…

Stu2 wrote:

Stu! We work great together because we have different strengths and weaknesses, so when we do a problem together I’m able to understand the whole problem, not just the aspects I’m especially strong at.
Stu3 wrote:
Stu! He is always great at explaining things to me!
Hope this brightens your day!
Mr. Shah

And… that’s it! A little sweet thing that I came up with that I really like. Short, simple, but for the right kid at the right time, it can be meaningful. (A few kids emailed me back saying that reading the email did make them smile or brought some light in a dark day…)

PS. Once, I had a bulletin board in my room that I had reserved for “shoutouts” or “notices of gratitude.” Where kids could post index cards with shoutouts for other students. I wanted it to be public and for it to “grow.” I would occasionally build in time for students to reflect and add to the bulletin board. That was years ago. It didn’t really take off, which means I didn’t roll it out and implement it well. But what I’m doing with this google form is really nice because it isn’t intensive or involve much planning!

PPS. If you’re at my school and want advice on how to do something like this, feel free to ask. I’m happy to brainstorm with you. I just don’t want everyone doing this which then will take away the “specialness” of when I do it!

End of Year Donations

Throughout the year, I tend to donate to causes that my good friends are spearheading. If they’re going to take the time to spearhead a cause, the least I can do is show my support by throwing a few bucks here and there.

However at the end of each year, around November and December, I think about what I truly value and I find an organization or two that fit a good number of things that I care about. This year, I have two organizations that I am donating to. I’m writing this short post in case any of y’all out there are thinking about places to make end-of-year donations to, and these organizations speak to you in some way.

(1) BEAM: Bridge to Enter Advanced Mathematics.


This is an organization that I started volunteering for last year. It was created by a friend of mine. The idea is that there are a lot of underserved kids in New York City who like and can do mathematical thinking, but aren’t getting what they need to excel. BEAM is a summer mathcamp for underserved middle school kids. The organization goes out and finds these kids, and then creates a summer program that’s free for them.

The reason the organization focuses on middle school kids is that’s where the most good can happen from an intervention. And these kids who go through the program get support for many years afterwards. It isn’t a “one and done” experience. Often times, kid return to the camp a second year. But more importantly, the organization helps kids navigate the high school admissions process (which is super complicated in NYC), helps them succeed with open office hours where kids can drop by to ask for help with any subject (this is how I help out… I staff the office hours!), and helps to with the college application and financial aid process. It’s a long-term program that has a huge impact on kids.  (If you want to learn more about it, this New York Times profile is amazing.)

So yeah. A thoughtful, wonderful, amazing program. I’ve worked with these kids and they rock. Right now donating $1 will bring in $3.14 dollars through a matching campaign. If this organization sounds like it fits your values, and you have some bucks to spare at the end of the year, consider donating!


(2) Twitter Math Camp (TMC/TMathC)


This organization hits close to home for me. This is a math conference that started up in 2012. It was literally the most grassroots thing ever. A bunch of us math teachers who had been communicating online decided we wanted to all meet and do math together… and that morphed into an embryonic conference. A school donated space, people offered to present on things they were doing in their classrooms, and a small conference was born. It has been running every year since, and has been entirely run through volunteer efforts. Schools or colleges donate space. We have people volunteer to present. Organizers (disclosure: I’m an organizer) work out the logistics, while they’re also working/teaching/coaching/etc-ing full time. It’s pretty awesome. And because of the goodwill of all these people, synergy happens. It is an incredible space for math teachers to grow their own practice and forge life-long relationships with other math teachers.

So as an organization, financially, it’s pretty efficient. We only charge a $20 registration fee because we want to keep costs low. But there are costs associated with the conference (e.g. buses from the hotel to the school/university where the conference is held, custodial charges from the school/university, renting a conference room in the hotel for registration and game night, providing supplies for speakers, etc.). Amazingly, with the few thousand we get from the registration fee, we’ve been able to pay for everything.

But for the first time ever, TMC is hosting its first fundraiser (read more about it here) and is asking for donations. And like with BEAM, TMC has a matching donors program, so every $1 donated will actually be worth $2! Now here’s the thing. When deciding to donate my own money to TMC, I had to take a beat. I thought: “Wait, I’m giving my money to a conference. Which I go to and pay hotel fees and transportation fees for. And I’m asking my friends to give money to a conference. A conference they likely are not even going attend. Does this make sense?”

But here’s what I realized… The conference encapsulates things I value. It gives classroom teachers a voice. It creates a space for teachers to share their thoughts, and maybe realize for the first time that their thoughts are useful to others. By having a powerful conference experience (which often lasts far beyond the conference itself through the relationships forged and communication that happens on social media), TMC is having a positive impact on math education for so many students. My donation is going to go to help increase access to educators of colors and seed a scholarship fund to help provide access to the conference for teachers whose schools might not be able to afford it.

I want to help the conference become financially stable and not have to rely on only the the small $20 registration fees it collects. I want to help increase access to the conference for teachers of color and teachers who can’t pay out of pocket and whose schools won’t help them out financially. It isn’t about me and the conference. I’m giving because I want to make sure that this conference can exist for others, and provide for them the same sort of experiences that helped shaped me as a teacher. [1]

So there you go. I wanted to share these in case you were wanting to donate to some causes, but hadn’t quite hit on the ones that made your heart pitter-patter yet. (Both are non-profits so donations are tax-deductable.) These are the ones that do it for me. And I’d encourage you to give a few bucks if you happen to have them at the end of the year. (You’re probably a teacher if you’re reading this, so you probably don’t have a few bucks to spare, so in that case forget everything you just read!) And if you have any organizations you think I’d be interested in, please throw them in the comments!


[1] That’s precisely why I give to the mathcamp I attended when I was in high school, and which made such a large impact on me. Or occasionally why I’ll give to my college (even though I don’t usually give a lot because they are pretty darn flush and already have a lot of wealthy donors… I like to give to smaller organizations where I know a small amount of money will help a lot.).

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: https://sites.google.com/site/desmosbank/


@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.)



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@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!]


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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: