Origami Quilt Squares at Math-on-a-Stick

I sure did not. But now I do.

I learned this particular mathy art from @RosieL52 during a math art club arranged over the summer by Siddhi Desai, Shraddha Shirude & Jenn White. She learned it from the book Extreme Origami by Kunihiro Kasahara.

To make these, you start with the pinwheel base. You can look up many, many tutorials for “origami pinwheel base” and I’ve made a quick video below (no sound). Then… just start folding. It helps if you keep your folds working in 4-fold symmetry (do the same to all 4 squares made by the pinwheel base), but I sure won’t discourage you from trying other things.

Lots of examples below that you can create through experimenting. One of the things I liked today about the kids who stopped by the Math-on-a-Stick booth was that a lot of them would immediately know what they wanted to try after they got the pinwheel base done. Mostly, you figure these out with experiments. Try folding up. Try folding down. Can you make squares? How about a kite? Fold forward. Fold backward… Everything goes, and if you mess it up, well, I bet you can get a hold of more paper. By all means, try recreating some of the images below.

A #MathArtChallenge Update. Goal: Day 100

Welcome to Day 50.

This thing has brought ME so much joy, and I hope it’s brought some to you, too. I am just tickled at how this silly thing I started has grown. I love seeing that other folk (some I’ve never interacted with at all) have posted their own #mathartchallenge-s, and it is a highlight of my day when, each night, I search the hashtag. There has yet to be a day when there isn’t something new you have created.

And, of course, it’s not accidental that this is happening when so many things in the world are overwhelming. That’s why this started. I wanted a way to connect with my students when I felt I was getting pulled apart from them. I figured they’d check an instagram page more quickly than they’d check google classroom. I hope it’s understood that I don’t bring math art to everyone to downplay or ignore the pandemic or to distract from the deep inequities we’re seeing it expose. I’m bringing it because I deeply believe that we have to have joy around to help, even in a tiny way, counteract the horrible things in the world, even as we work to fix them. 

The only downside (to the Math Art Challenge) from my end is that I don’t personally have the time to linger over the challenges that I’d like to, but the trade-off, for now, is worth it to me. It has long been obvious to me that math is beautiful and deeply intertwined with art, but I get regular posts from folk saying it had never occurred to them. I’m ever so glad to be spreading that obvious-to-me truth, especially if it’s not so obvious to everyone else.

By no means do I want this thing to “stop” at any point. I’m hoping that long after I cease posting daily challenges, folk circle back to any of the ones I have posted and find something new. Or that y’all just post your own whenever they come up. (Thanks, Squidge!) That said, I think I will have to stop at some point. So I am setting the admittedly arbitrary, but still quite satisfying goal of reaching day 100. We’re half-way there. It may turn out that days 70-100 are just different versions of origami, knots or islamic geometry (I’d be fine with that), but I’m confident I can seek out enough new things to fill those days. You can, of course, offer suggestions here.

Some folk have posted their own challenges and I absolutely LOVE that. Some I fully  intend to use in later days (Mark Kaercher posted George Hart’s Card construction on Tuesday, and that, along with several more George Hart creations, are in my list somewhere in the day 60-70 range). But the beauty of this thing is that almost no one can keep up doing every challenge every day, so just play when you can. Almost everything has been posted somewhere else sometime before, so I hope no one feels any time pressure to engage. I love that folk post their versions of a challenge from years ago (several of you had this with the origami firework). The whole point of the thing is to play. It brings me great joy that there are #mathartchallenge conversations and tangents I find that have no connection to me. Feels like I’ve let this thing loose in the world and it’s taking its own shape.

But my goal is to post a total of 100 math art creations for you all. Many are still low-tech, but some are (and are going to be) a little more specialized. I hope that if those tickle you, you can tuck them away for a time when you have the energy, materials, and enthusiasm to tackle them. When I’m all done, I’ll circle back to those I want to linger on, and will return to some projects I’ve semi-abandoned (my knots! I’m coming back to you, I swear!). Then you go wherever you want with it.

Musing on the #MathArtChallenge

Hey folk. If you’re here, you’ve probably seen the #MathArtChallenge(s) that I’ve been putting on Twitter and Instagram. I just wanted to share some musing I’ve had as this has progressed, and I would love to hear any that you have as well.

The most prominent is easily that this is bringing me so much joy. Like most of you, I expect, I have moments in my day when I am overcome with dread and grief at what the world is facing in this pandemic, and I’m trying to condition myself to not wallow in that too long (if I can avoid it). One of the best ways I’ve found is to just search through the hashtag #mathartchallenge and I find so much joy that I am temporarily relieved of my existential dread.

For that reason, I’m not too bummed if there are days when only 1 or 2 people post their thinking/creations. Many of you have said that just seeing the math art challenges is a bright point in your day (and perhaps more importantly to me, many of my students have said that). My favorite challenge from the past week was almost definitely the Brunnian links and very few of you seem to have taken that up, but who cares as long as the ideas get spread and maybe someone can engage, even if thats days, weeks, months or years later. One of my actual students engaged in that one and just sent me a private video of her solution and I gotta say, I nearly burst into tears I was so happy.

Another joyful thing about it is the friendships I’m building with enthusiastic participants. Due to Katherine Seaton’s excellent challenge I’ve been introduced to her and even if it’s just a message here or there, it’s one more person I’m connected to. There are probably a dozen more people out there now who I hadn’t been as connected to as I am now, and much as I feel confident that many of you feel existential dread right now, I trust that just as many of you also crave human connection.

Back to the challenges themselves, I’m just delighted in the variety that has come up through your brilliant suggestions, and even more so that when I post one I happen to think is too simple or not interesting enough, figuring “I’m going to be doing this for a while, so I can’t be too picky”, that you all make it absolutely wonderful. Truly. I am floored that I can throw just any old thing out there, and your brilliant creativity and artistry makes it shine.

As for the ideas themselves, I’ve been operating under a few parameters as to what I will actually share:

  • If I’m using something that is decidedly a specific person’s creation, I’ve tried to ask first and if they say yes, to of course, credit them. I don’t know a single human who can lay claim to the connection between golden spirals and icosahedrons, so I didn’t worry too much about crediting that. But I do know that I was first introduced to the overlapping circles because of my brother and he through numberphile so I tried to link and thereby credit that creation. There have been a couple of requests that I haven’t yet used because I’m trying to get permission from their creators.
  • I have a list through about day 50 right now (we’re on day 28 now, as soon as I get my cat off my lap and go make it), and I have a lot of other ideas that I’ve hesitated to put out there because I want them to be accessible to as many people as possible. I guess I’d love some feedback on that. I would love to use hyperbolic crochet (crediting Daina Taimina, naturally), but I know not many people are going to have crochet needles and yarn, nor the enthusiasm to learn a whole new skill in a day. But maybe it’s worth putting out there for the few who would and for those who don’t to just play with the idea? Or Penrose tiles – I’d love to show those off and spread the idea, but it’ll be harder for everyone to play. What do you all think? 
  • I’m mostly trying to spread ideas that you all can take and share in your classes. I certainly won’t lay claim to anything except my own creations – I don’t own these ideas and you shouldn’t feel it necessary to credit me when you share them unless you’re sharing a specific image of one of my creations.

I dunno. These are just some of my musings right now. I’ll probably write again later, but for any who are following along, I guess I’d be curious as to what you’re thinking. And of course, feel free to add suggestions to the list.

TMC & Water

I’m writing this as a member of the MTBoS community, I’m writing it to own my part in the harm done, and I’m writing to help continue the conversation. I’ve intentionally waited a few days to post this – I wanted to really sit with what has been shared by the teachers of color (ToC) – letting their words sink in. I want to make sure that after a few days, when people start going back to their lives outside this community, that I help the conversation to continue, and I wanted to give myself time to try to synthesize all of the things in my own head.

Especially to any white educators reading this, I want to be a source spreading some of the wisdom below that I’ve had access to, and because these have all been meaningful for me, I hope they may be for you, as well. There are many more, but here are some  things that have helped me find my feet in this conversation.

  1. Whiteness as water: I think I first ran into this at TMC 17(??). The idea is that just like fish don’t notice water, white people don’t notice their privilege. It takes effort and conscious work to make sure you’re seeing it. I am aware of it, and I have tried and tried and tried to notice it, but I still find myself regularly getting surprised. (For example, it didn’t occur to me until embarrassingly recently just how dehumanizing the term “slave” is. “A person who is/was enslaved” packs so much more punch. Acknowledges their humanity.)
  2. Marian Dingle’s blog post. If you haven’t read it, what are you still doing here?   Marian has been asking me (and many many others) what I mean by wanting “diversity”, and I haven’t had a good answer. Her framing in this post, that is it insufficient to welcome others to your space, what’s needed is that collectively, without having to pull and demand, each space is built together, collaboratively. TMC, a classroom, a community of math educators like the MTBoS needs to organically require that everyone is involved and anything short of that feels wrong.  Her push for collective construction is huge. The need to not just to be welcomed, but to build together something that belongs to everyone. I can that while TMC and MTBoS has tried to welcome everyone, it has not belonged to everyone. We (the original constructors, overwhelmingly white) welcome folk to join us and play by our rules, but it is painful that when we built it, they were not considered and their absence unnoticed.
  3. Shana White’s question from back in September.

I think about this question all the time. And it relates to Anne’s contribution just below here. I know that I have needed time to start seeing water. I have needed processing time to “see” the privilege I swim in. And I can’t imagine how maddening it must be for ToC who must see it so clearly to wait for me to catch up. And then for ToC to see all the folk who aren’t even trying. I imagine there have been times when someone has wanted to shake me, absolutely baffled at how long its taking. I wish I had a solution to that, I do not, but I will promise to continue working at noticing the water & pointing it out to others.

4. Anne Schwartz’s significant receipts on how long this work has been happening, and how often (white) folk say they’re “beginning” the work:

This is serious. Really. I get so many passes. So many freebies. I acknowledge the most basic of things (see “slave” vs. “enslaved person”) and sometimes it feels like I get a congratulatory pat on the back when really, the reaction should be, “good god, what took you so long?” Our society allots a seemingly unending quantity of forgiveness for white people who can say nice words and claim that they’re trying, without really doing the work. It’s time that we stop that. No one should get accolades or praise or told how powerful it is that they’ve just finally noticed there is injustice. I will absolutely, of course, continue to have these revelations myself – I’m too deep in the water – but please, let’s have our reactions acknowledge the actual “accomplishment”. “What took you so long? Now go convince some others,” seems a better reaction than commending someone for noticing an injustice that’s been there all along. To be sure, these commendations don’t happen all the time, and there are good people out there who do roll their eyes and give me a pity clap for taking noticing something they’ve known for years or their whole lives, but there is still too much patience and praise for people committing to the absolute minimum of noticing someone else’s humanity.

5. And lastly, this incredibly powerful whack for me regarding TMC (shared with permission) from Lybrya Kebreab.


This gets to the heart of the TMC thing. It’s one thing for TMC to have started as an exclusive group by happenstance. The problem isn’t that friends wanted to get together and that happened to be a select group. The problem is that these friends weren’t getting together to play games or watch a TV show, they were getting together with a focus on improving math education. That anyone should create a formal gathering to improve education and not have equity at the center of their work, is inexcusable.

I have loved TMC. There’s no denying it. But I didn’t see the water, and for that I deeply apologize. I wrote a whole post titled, “A Love Letter to TMC“, and going back to re-read it now, I see the need for me to acknowledge my complicity in making TMC a place I thought was “welcoming” for everyone, without considering that everyone isn’t me. I can’t deny it, TMC has been a wonderful place for me. I am so absolutely, totally, and wonderfully comfortable there. But I am not everyone. And when you have a gathering of dedicated teachers trying to improve their craft and influencing math education all across the country, but do not yet have a serious commitment to equity, that’s a problem. I’d like to address the following passage in my TMC post:

There is NEVER a question as to whether you or your friend or that person on the other side of the room has something to contribute. It’s assumed. And sought. I had a friend ask me if TMC is clique-y at all, and after a second of thought I said that sure, there are definitely groups of people who tend to hang out more. BUT BUT BUT… There is absolutely NO EXCLUSION. If you walk up to any group of people at TMC, you will be welcomed with open arms, a hug and a compliment.

Reading it now, I cringe. But I genuinely felt that at the time. I believe there are people who’ve attended TMC who believe this at their core. The thing I need to acknowledge is that I felt this. The ToC who wrote the extraordinary letter below do not feel that. And I didn’t stop to consider that while I felt this welcoming, and I felt I belonged, folk who are not me did not. I made some pretty sweeping assumptions about how everyone felt because I was in the water, and my own bubbling joy over this place that felt so wonderful to me could not see the water or consider that anyone else felt differently in that. For that I apologize.

In closing, please read and try to genuinely let in the letter Lauren Baucom shared below. Let the overwhelmingly white MTBoS community step back to really consider what it means to build this community together. Let us actually hear that no matter how often we say that MTBoS belongs to everyone, everyone does not feel it is theirs. (If you’re looking for an action step, start by joining the #cleartheair talks. It’s the best PD I’ve ever experienced, and it’s helping me to see the water.) I don’t intend for this to be my last contribution to the conversation – I think we need to talk a lot more. For right now, though, I don’t want my silence to be ringing in the ears of the ToC that have already given so much. I am listening, I am working on seeing the water, and I firmly believe that equity must be at the core, not peripheral, to everything we do to improve math education.


Reading “White Rage” & Grappling with Past-Present on MLK Day

I really cannot recommend White Rage: The Unspoken Truth or Our Racial Divide enough. I have learned so much (the lengths southern states went through to keep Black people from leaving, the extreme violence of disenfranchisement, states shutting down public education systems to avoid integration, Reagan and Nixon’s direct control of drugs entering the US), and have a much better view to what I have yet to learn as a result of reading it. Having finished, the feeling that’s sticking most with me is the one I had when reading,

…centuries of oppression and brutality suddenly reduced to the harmless symbolism of a bus seat and a water fountain. p.99

When I think of the Civil Rights movement, the images that flood my mind are “White Only” signs, busses, and MLK giving his “I Have a Dream” speech. The clothing is old fashioned, and everything’s got a tinge of past to it. It’s history. Intellectually, I know it wasn’t that long ago, but I have to remind myself of that every time. And still, I tell myself it is past. Not present.

Obviously, I know of inequity today, and intellectually, I know its roots are the history of the country, but I haven’t really let in the unbroken connection between then and now. It’s as though I’ve puts pauses in history. Like when you reach the end of the history book chapter on Civil Rights and start in on the next one. The labeling of movements and moments gives me a shield allowing me to think there’s a clear divide between then and now. White Rage has disabused me of that. Dr. Anderson does a powerful job of seamlessly connecting each history book chapter to the next, right up until today. I feel the connections to history so strongly after reading the book. And it’s left me feeling helpless, sad, angry, embarrassed and mournful for the country we should be living in.

All of this is particularly striking today as my twitter feed is actively reminding me how whitewashed Dr. King’s legacy is. Not having done the homework before, I spent my morning today following Shana White’s instructions.

I printed out and read Letter from a Birmingham Jail, and found it jarring (and telling) to see the publicly praised quotes, like, “Injustice anywhere is a threat to justice everywhere,” next to the ones new to me:

“Shallow understanding from people of good will is more frustrating that absolute misunderstanding from people of ill will. Lukewarm acceptance is much more bewildering that outright rejection.”

“In the midst of blatant injustices inflicted upon the Negro, I have watched white churchmen stand on the sideline and mouth pious irrelevancies and sanctimonious trivialities.”

“I suppose I should have realized that few members of the oppressor race can understand the deep groans and passionate yearnings of the oppressed race, and still fewer have the vision to see that injustice must be rooted out by strong, persistent and determined action.”

I certainly wasn’t surprised to see these sentiments, but I bet a lot of white America would be.

In continuing the homework Shana blessed me with, I will say I was surprised to see  both Ijeoma Oluo and Michael Harriot talk about how MLK is used as a tool by white people to chastise Black people into compliance.

Dr. King wouldn’t have been that demanding, people say. MLK wouldn’t have been so angryHe was a nonviolent man, remember? -Ijeoma Oluo

Even now, if you ask any black person whose name do white people bring up whenever black anger gives them the heebie-jeebies, “Is that what MLK would have wanted?” is second only to “What would Jesus do?” – Michael Harriot

I haven’t come across this explicitly – but of course I haven’t, I’m white. If I get upset or angry, people are likely to listen to me, and they sure won’t use the diluted version of a Black icon to get me to “calm down”.

Last thought: The most emotional part of Dr. King’s Letter from a Birmingham Jail was the following on white people telling him now was not the time to press Civil Rights:

Perhaps it is easy for those who have never felt the stinging darts of segregation to say, “Wait.” But when you have seen vicious mobs lynch your mothers and fathers at will and drown your sisters and brothers at whim; when you have seen hate filled policemen curse, kick and even kill your black brothers and sisters; when you see the vast majority of your twenty million Negro brothers smothering in an airtight cage of poverty in the midst of an affluent society; when you suddenly find your tongue twisted and your speech stammering as you seek to explain to your six year old daughter why she can’t go to the public amusement park that has just been advertised on television, and see tears welling up in her eyes when she is told that Funtown is closed to colored children, and see ominous clouds of inferiority beginning to form in her little mental sky, and see her beginning to distort her personality by developing an unconscious bitterness toward white people; when you have to concoct an answer for a five year old son who is asking: “Daddy, why do white people treat colored people so mean?”; when you take a cross county drive and find it necessary to sleep night after night in the uncomfortable corners of your automobile because no motel will accept you; when you are humiliated day in and day out by nagging signs reading “white” and “colored”; when your first name becomes “n*****,” your middle name becomes “boy” (however old you are) and your last name becomes “John,” and your wife and mother are never given the respected title “Mrs.”; when you are harried by day and haunted by night by the fact that you are a Negro, living constantly at tiptoe stance, never quite knowing what to expect next, and are plagued with inner fears and outer resentments; when you are forever fighting a degenerating sense of “nobodiness”–then you will understand why we find it difficult to wait. There comes a time when the cup of endurance runs over, and men are no longer willing to be plunged into the abyss of despair. I hope, sirs, you can understand our legitimate and unavoidable impatience.

I read this about an hour after reading this excerpt from White Rage:

p158-159 white rage

Well, that drove home the past-present connection pretty darn well.

Some Thoughts on Teaching, the Internet vs. Real World, and “the Work”

I’ve been comparatively muted online recently. Mostly this is because I am swamped by school – I have new classes and I have a student teacher for the first time ever. My student teacher is fantastic – I’m a huge fan – but I will admit that it takes SO much more work & time than I’d anticipated. As a result, I’ve had much less time available to interact and converse with my online community (#mtbos and #iteachmath). This means that more of my energy has gone into to the “real world” community of math teachers that surrounds me. I must say, this is a very different picture than the online community I’ve built for myself.

I’ll get into that in a bit, but  I want to make sure that I acknowledge a series of tweets I’m seeing this weekend.

Here is the tweet that I first saw about this conversation on Friday:

It is a wonderful thread, and you should click through to read it. I also saw Christopher Danielson‘s thread here:

Another good thread. Please click and read.

For my part, I would like to comment on some things I’ve noticed as my lack of time has turned me into a bit of twitter lurker rather than conversationalist as of recently.

My time on twitter talking with & reading from brilliant educators like Marian Dingle, Jose Vilson, Lybrya Kebreab, Val Brown and Shana White has made me more conscious of what’s happening in my day to day life. Because of those conversations and now that more of my time actively interacting with the math community is off line, I’m more aware of how I move in the world, the white spaces I inhabit, and how those contrast with the school community I’m a part of. While I am currently less active online, I put time in when I had more available and that’s helping to keep me aware of how race & privilege affect my work now. I’m so grateful for having spent that time, and know that when my load lightens a bit, I intend to be more engaged online again.

Part of not being as involved online has been noticing just how less engaged the “real” communities I’m a part of are in “the Work”. Issues of inequity come up regularly, and they’re frequently brushed to the side. Or they’re seen, the comment, “yeah, this isn’t how it should be,” is made, and then they’re brushed to the side. I’ve been pondering why this is and I’ve come up with a couple reasons why this may be. The first is that teachers are so insanely overworked that we can’t find the time or energy to fight the really big fights unless a platform is created for us to do so. The second is that we have so much curriculum to get through that we have neither the time nor the resources to explore social justice through our lessons as often as we should unless something is pushing us to do so. I think I’ve been pushed to do more of this because of the school I’m in that is genuinely diverse. My students demand it of me. I wonder if the teachers who work in predominantly white schools don’t have that extra push, so they don’t end up addressing it. And that’s a genuine wonder. I don’t know enough or have enough contact with teachers outside my district to know if that’s the case. I’d love to hear from you if you have insight there.

To the first reason of not having enough time, I’ll use an example from my own experience. Tracking in schools tends to be wildly inequitable. Students of mine regularly make note of who is in advanced classes (white students) and who is not (students of color). When my department is tasked with and given time to revamp the structure of classes at school, we can, and do, have conversations about tracking and how to reduce/address it. We make actionable plans. But it’s not that often that we’re asked to revamp classes, given time to make a plan of attack, and then we’re off to teaching again. Teaching hits and we’re all so swamped with grading and parent meetings and checking in on kids that bad habits creep back in that undo most of the good work intended to create change. We shift kids to less challenging classes, and the only ones that get truly challenged and moved up are the ones who have the support structures to demand it. Often times, those are the white students and families.

I’ve made a conscious decision to work in a public school in Minneapolis. My reasons are/were 3-fold: 1) I love Minneapolis, and want to live here, so obviously, I’d like to work here, too. 2) I believe in public education, and I do not want to work for a private or charter school. 3) I totally started out choosing this with some white savior nonsense in my head. This 3rd one is a problem, but I need to still acknowledge it, because I’d like for it to now turn into “I need to address some white savior nonsense with my colleagues, as well as making sure that we’re continually acknowledging and addressing race as we do our jobs and live in this world.

I struggle regularly with whether or not I should be a public teacher in Minneapolis. I see how few TOC (teacher of color) there are, I hear, directly and regularly from my students that they want more TOC and that it matters SO MUCH to them when they get a TOC. Does that mean I should step aside? Should I go work in a predominantly white school district? I don’t think so, but I’m not sure. Right now, I’m actively choosing to stay where I am because I, unfortunately, don’t see a huge flood of TOC being turned away, and as both Anne and Christopher noted, I want to make sure that I’m not isolating myself. I do know that I am so much better for working in a public school with many SOC (students of color), but, as a result, I have a responsibility to make sure that I’m acknowledging my place in this space and that I’m creating spaces in my classroom for students to talk about race, their community, and what’s affecting their lives right now. I’m trying really hard to make sure that my role here is not to fix anything (except for the lack of conversations around race in schools), but rather to give my students a space to talk, and push to make sure my colleagues are doing something similar. I have a student teacher right now, and you better believe that I talk to him explicitly and regularly about how I am trying to dig out my own biases and give kids spaces that work for them.

For example, I notice and name if I’ve called out only students of color, and I’ve talked to my student teacher about when I saw that, how I saw it, and what I plan to do about it. When we talk seating charts, I’m constantly offering suggestions and asking questions about why we’re choosing to put certain students together or not. I explicitly address race when we do this. I have asked him to start doing the Mathematician’s Project. I am trying to model noticing things like who are in advanced classes right now, and which parents we’ve called or not, and how our grading system affects students with different backgrounds.

I’ve actively tried to name and notice more often when we have false binaries – for example I used this graph (from fivethirtyeight.com) and made note, with students that this assumes a gender binary, and then we talked about why that may or may not be appropriate in this graph. I talked to my student teacher about that decision.

I do this because of the online community that has pushed me to do better for students of color. I also do it because once students have a taste of it, they demand it of me.

In closing these long rambling thoughts, I guess what I’m wondering is how we get more people to take the extra time and effort (and believe me, I know that it’s that) to work social justice into the curriculum. Again, from my own experience, I’ll share just how challenging that can be. On Friday, I taught my seniors about optimization problems. I saw this tweet:

and thought what a great opportunity it would be to incorporate that! But time ran out, I couldn’t create a problem fast enough, couldn’t find one in the curriculum I have, and thus I ended up skipping it on Friday. Just taught straight up optimization. (Don’t worry, I plan to do it on tomorrow.) It’s hard to get this stuff in. And it takes a lot of work. And we’re already all so gosh darn tired and overworked already. But those are excuses, and we can do a lot better, we just need to drink more coffee? I don’t know. I’m going to close this out, not with something profound, but just because I need to post it and get to planning lessons for tomorrow. I’d really appreciate any thoughts any of you reading have on it. It seems like an intractable problem, but I also firmly believe it’s one that we have to address as a community. If we don’t, we’re failing a lot of our students.


Fall #mtbosBook Club: #ClearTheAir

Hey friends! My apologies for leaving this so long. I freely admit I’ve been soaking up every last minute of summer.

I fully intend to continue with the #mtbos book club this year, although the format of it may change slightly. For example, it’s been suggested that we do a “book club” using the Netflix documentary The 13th, which I fully intend to make happen. I also have not yet finished the summer book The Brilliance of a Black Children in Mathematics, and that book deserves to be properly finished. I intend to do so and get all those blog posts up over the next months.

For right now, though, I need to accept that I have little to no extra time outside school (new course and 1st student teacher!). I’d also like to spend time learning from the pros. So I am going to participate in the already established #ClearTheAir talk, on White Fragility. Please join me!

Val Brown does extraordinary work, and I’ve been lurking on these chats. They’ll be worth your while. Here’s the schedule:



Not sure if you want to dip your toes in? I just listened to an extraordinary podcast that might whet your appetite on the book.

And a final note, I’ll be posting late this week, as I have a Math on a Stick shift during the chat, but I’ll still read and post!

Christina Lincoln-Moore “Talk Number to Me: Mathematics and Mindfulness” A Guest Post for the Virtual Conference of Mathematical Flavors

Christina MooreThis is a guest post written by Christina Lincoln-Moore Assistant Principal, Los Angeles Unified School District. Her twitter handle is @virtuouscm and she can be reached by email at: christina.moore@lausd.net

Christina Lincoln-Moore: Chairperson of the California Mathematics Council – South (CMC-S) Equity, Access and Empowerment Committee, West Regional Director of the Benjamin Banneker Association (BBA); affiliate of NCTM. Co-chartered the National Society of Black Engineers NSBE Jr. Chapter. Students build and compete in STEM projects/competitions. NSBE Jr SoCal provides STEM enrichment to 50 4th-8th graders twice a month. I present nationally, statewide, and locally focusing on equity and access of African-Americans to algebra.

Learn more about the Virtual Conference of Mathematical Flavors.

Talk Number to Me: Mathematics and Mindfulness

“Mathematics is about Social Justice-Period!” One of my opening lines as an Ignite speaker at the 2017 California Mathematics Council-Southern Section Conference in Palm Springs. I call myself a Lieutenant in our Mathematics Revolution. I am compelled to fight against mediocrity and complacency for our children. I passionately believe mathematics and social emotional intelligence are the key components to engendering formidable joyful life-long learning. A focus on social emotional learning develops authentic positive mathematical identities as sense-makers, problem solvers, and creators of ideas.

Continue reading “Christina Lincoln-Moore “Talk Number to Me: Mathematics and Mindfulness” A Guest Post for the Virtual Conference of Mathematical Flavors”

Embrace Detours: The Virtual Conference of Mathematical Flavors

In the first, let me thank the extraordinary Sam Shah for organizing this. Please join in the fun and write your own post. The prompt 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?

I’m so excited to see what everyone has to say.

In the longer version of Sam’s prompt for this virtual conference, he asks us to examine these wordles (courtesy of Tracy Zager). Please do so for a moment. I’ll wait.

Tracys word cloudsDone? Lovely.

I feel this divide in my bones. I hated math until I was 24. My whole experience of math was the wordle on the left. I won’t relive my entire story here (you can read it if you like), but the short version is I was tracked, decided the math community didn’t want me, and quit taking math classes as soon as I could to escape the drudgery of staring mindlessly at textbook examples while I did all the odd numbered homework problems. Math had nothing to do with me or my life, it made no sense, and it was boring to boot. 

When, at last, I was shown the beauty of math, my reaction was first surprise and joy, but it was quickly followed by a cold-burning fury. How the hell had I gotten all the way through college without knowing these formulas had meaning? That math was supposed to make sense? How is it possible that no one took my hand and showed me the awesome majesty of prime numbers?!

I concede it’s possible someone tried to show me, but that I was so turned off to math that I refused to see it. I am, however, absolutely certain that no one ever tried to talk about me about the platonics being duals of each other. Which, frankly, borders on  criminal educational negligence.

I realize this is a long prelude to answering Sam’s question, but it’s vital background to me, because it’s at the core of who I am (or at least who I want to be) as a math teacher.  I don’t want any of my students to get to the ripe old age of 25, find out there are multiple sizes of infinity and become inconsolably enraged that such an amazing fact existed and no one had bothered to tell me about it. (You can ask my boyfriend. I refused to calm down for at least a week.) Nor do I want my students deprived of experiencing how math can help them make sense of and strengthen their place in the world.

To be clear, my answer to Sam’s question is a single thing, although there are two halves to it. I believe strongly in detouring from the lesson whenever possible if it allows me to (1) expose students to awesome math or (2) if students have something they want or need to talk about. And to hell with the pacing guide.

To do this, I talk, early and often, about the point of math class. While conceding that linear equations have some value, I tell students that’s not really what we care about.

We care about the patterns and hidden structures that support linear functions.

We care that thinking about a visual pattern going backwards might lead somewhere crazy fun.

We care that statistics gives us a way to quantify the messy world we live in. Maybe it doesn’t explain the problems of the world, but it can be a place to rest our emotions while we sort out our feelings, then we can use mathematics to build a stronger argument for acting on what we believe.

We care that how I see something might be totally different than how you see it. And we’ll both learn things by teaching our vision to the other person.

We do not actually care about mx+b.

I state, as clearly and frequently as I can, that if there is any compelling reason to detour from the lesson I had planned, we should do that. These “compelling reasons” normally fall into the two categories I outlined above. Either students have some awesome question about some math topic outside the scope of my planned lesson (for example, we’re talking place value, and they question the base 10 system), or there’s something important happening in their lives and they need some space to process it.

“But Annie,” you gently prod. “Don’t you get distracted and off topic a lot? Do you get through all the standards?”

Of course we’re distracted! Of course we have to rush some things! Of course I don’t always want to do it, but students remind me that I was the one that told them to interrupt and of course, I’m forced to concede that yes, I did say that, but we still have to learn absolute value inequalities or I’ll get fired, and they respond, “that’s stupid,” and I say, “you’re right,” and then we make space for whatever it is they need space for.

Encouraging them, right off the bat, to interrupt me with things they’re interested in or that affect their lives is absolutely not a recipe for calm, compliant students, but I don’t want that. I want them to fight back and make me expose them to good stuff, make me create space for their lives. They keep me honest. They keep me from complacently looking at what’s next in the book and making sure they know exactly what they need to know to pass the test as if that were the most important thing in their lives. It makes me eager to find new ways to engage them in mathematics.

You see, I am petrified that I will do to some of my students what was done to me. That because I am tired or lazy or behind on the pacing guide, I will cut them off from the mathematical community through some thoughtless act of drudgery or dismissal. Big aside: It’s also the reason the Mathematicians Project is a staple of my classroom. Just like I want them to question what we’re learning, I also want them to question the context we learn it in. Most textbooks pay lip service to at least one female mathematician, but rarely, if ever, do they include black and brown men (much less a black or brown woman, heaven forbid). I’ve written and presented about it a lot already, so I will summarize it here for you by asking: if you want to convince ALL your students they are mathematicians but the only Mathematicians you ever show them are old, dead, white men, why should they believe you? 

I have a LOT of respect for teachers who can look at a unit, then go find something in their community that fits perfectly into that unit. Someday I’ll be able to do that. I’ll seamlessly weave my students lives into the content according to the timing as it appears on the calendar at the beginning of the year. But right now, I’m not there. It always feels forced when I try to fit the “real world” onto the pacing guide my team uses. I know my students don’t care about two fictional brothers racing each other on a graph taken from the textbook, and it would be so great if I could always find a relevant connection to their lives that fits the math I’m supposed to teach, but it doesn’t often work out that way. So right now, I detour.

School shootings were a frequent topic at school this year, and when my students wanted to talk about it, I found a way to talk about it. I connected it to math, although it rarely (if ever) had anything to do with our unit at the time. I frequently fell behind on the pacing guide, but my students are more engaged in class because they know if they need to derail me because it’s important, I’ll derail.

At the end of every year, I give my students an anonymous survey and one of the questions I ask is if anything was particularly memorable from the year. Again and again, students mention when we did things outside the book, the standards, the *curriculum*. Some quotes:

  • In the beginning of the year when I thought the hurricanes in America stood for Verizon [referenced this which I stole from Sara VDW]
  • The school shooting maps
  • i liked our conversations that included real world events
  • Ms. Perkins always relating math to things going on in the outside world
  • Discussing topics outside of math
  • The mathmetician [sic]  was always fun and so was the stats about world disasters (hurricanes, shootings, etc.) it was nice to apply math to real, current events.
  • 5 dimensional shapes are really just bubbles

I also ask them how they currently feel about math, and while the responses are not always 100% positive, they have (thus far) always been an improvement on the beginning of the year.

So that’s my bit. Derail for math or for life, whenever your students need you to. I would love to hear how any of you are doing this or some version of it in your classroom. I would REALLY love to hear if you have ideas on how I can improve on it.

Also, (especially since you made it all the way to the end!) if you don’t have a blog of your own and want to participate in these Mathematical Flavors, shoot me a message, and I would be happy to host your guest post on this blog.

Supply List – Islamic Art

This is primarily for the sake of my TMC session attendees, but if anyone else likes, here you are.

supply image

  1. Pencil case – I made my own from this pattern. Most people are probably not as picky as me but I love mine.
  2. Erasers – I use the Mono erasers for fine work. There’s a rectangle and a circle tip it’s way more useful than I thought originally. Great for erasing mistake lines & prepping weave work.
  3. Pencils – Pencils with “H” in them are harder, stay sharp longer, and draw lightly. 3H is lighter and harder than H. Pencils with “B” in them are softer and draw darker. They need sharpening more often. Pick whatever you want. I use tombow and  staedler pencils a lot and a range is nice so you can use darker pencils to highlight things you’re working on.
  4. Mechanical Pencils – this is new for me, but these are way more precise than sharpener pencils. I currently have a 0.3 and a 0.5 with a couple different lead hardnesses. My current ones are Alvin’s, but I can’t say that’s more or less wonderful than others because they’re so new to me.
  5. Markers – I love prismacolor markers, but they’re expensive. This set is nice though and is less than $20. I also use a lot of grey markers – this set is reasonable.
  6. Pen Sketcher’s Book/Hot Press watercolor paper – My personal favorite type of paper is the Pen Sketcher’s pad, but that’s because I like markers. If you also like markers, that’s great and I suggest this. If you don’t, you’re on your own. I also use watercolor paper, and try to use hot press paper because it’s less textured and is nicer to my markers.
  7. Pens – I like prismacolor pens. Specfically this set. Mostly use them for outlining and hard edges.
  8. White pens – This is strictly used by me to fix really dumb mistakes. Occasionally helpful, never ideal.
  9. rulers – I love these rulers. 12×2 inch  6×1 inch I have multiple of each. (Just because I lose them a lot.)


10. If you have sharpening pencils, get a decent pencil sharpener. Many options are great.

11. Compass – I like this one.

12. Regular erasers. There are lots of good choices, but my experience is that anything red is terrible.

Here’s Megan’s list:


Megan’s go to page by Joumana Medlej

Annie’s go to page by Samira Mian (You can also get links to her online courses there.)

The Ferzokah Jaali on desmos geometry

Two articles on coloring in Islamic Art (found by Stephen)

This book is an EXCELLENT resource. I got it from my library, but will likely end up purchasing it myself.