#MathArtChallenge Day 6: Circle Toruses!

The Challenge: Find a smaller circle you can trace. Then trace large circle to use as a guide. Finally, trace a bunch of smaller circles in a ring to create a torus (more commonly known as a donut).

Materials Needed: Paper, writing utensil(s), circles/compass. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!)
Math concepts you could explore with this challenge: circles, geometric construction, proportions/ratios (to get interlocking tori, there are restrictions on the possible ratios between the circles)

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#MathArtChallenge Day 5: Probability designs!

Day5 MAC
Square pattern of designs randomly assigned by a die.

The Challenge: Use something like a die or a coin to get random outputs. The probabilities don’t need to be equally spread! Assign a design to each output, and then get to designing. I have two examples for you below.

Materials Needed: Honestly, whatever you want. There are endless possibilities on this one. Some examples: paper & pencil (like above and in the video below), yarn (friend ship bracelets or crochet), legos… See the examples of other people’s work below!
Math concepts you could explore with this challenge:  Probability, probability distributions, randomness

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#MathArtChallenge Day 4: Hyperbolic Geometry

Day4 MAC hyperbolic planes
5 differently colored origami hyperbolic planes

The Challenge: Fold your very own Hyperbolic Plane from a simple piece of paper!

Materials Needed: A square piece of paper. Youtube instructional video below!
Math concepts you could explore with this challenge:  Algebra (how many folds per stage?), angles, counting, exponents, functions, geometry, Hyperbolic planes, proportions/ratios, sequences, symmetry, topology, vertices/intersections

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#MathArtChallenge Day 3: Isometric Cube Cutouts

Day3 MAC
Purple 3D looking cube with instructions for how to draw

The Challenge: Draw a cube by connecting 3 rhombi (see below). Then use lines parallel to those of the rhombi to embellish the cube.

Materials Needed: writing surface, writing utensil, straight edge, colors
Math concepts you could explore with this challenge: geometric construction, isometric grids, lines, perspective, polygons, polyhedra, topology, vertices/intersections

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#MathArtChallenge: Day 2 Looping Colors

Day2 MAC
A looping line, with created spaces alternating blue and red in color.

The Challenge: Draw a long, looping, self-intersecting line that meets back with itself at the start. Avoid having any 3 lines cross at the same intersection (although after a bit it may be fun to play with this). Then, select a color, and start coloring in the spaces created by your line’s intersections.
Can you color it such that you end with every section alternating colors?

Materials Needed: writing utensil, writing surface
Math concepts you could explore with this challenge: counting, functions, geometry, knot theory, vertices/intersections

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#MathArtChallenge Day 1: Tons of triangles

Day1 MAC
A sketch of many connected triangles, 7 per vertex. The triangles radiate out from the center, and begin bunching together at the edges as they’re no more space for the growing number of triangles.

The Challenge: Draw as many connected triangles as you can. Goal is to have as many vertices with 7 triangles as possible.

Materials Required: Writing surface, writing utensil
Math concepts you could explore with this challenge: angles, counting, exponents, fractals, functions (exponential), triangles, geometry, graph theory, hyperbolic geometry, lines, polygons, sequences, intersections/vertices

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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.

Lybrya

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:

3D40A747-B53A-48B3-874B-F1B165EB08C0

https://twitter.com/valeriabrownedu/status/1029907613264302080?s=21

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!