#MathArtChallenge Day 6: Circle Toruses!

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

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. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!)

Here are mine!

#MathArtChallenge Day 5: Probability designs!

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

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.

Huge thanks to Emily Lynch Victory for the inspiration for this challenge. She’s a fantastic mathematical artist that I met a few years ago at a math teacher conference, who had a piece like (but far superior!) to my first one below.

MATERIALS NEEDED: Honestly, whatever you want. There are endless possibilities on this one.

Example 1: Roll a die, design a grid!

I assigned a design to each of the 6 outputs of a regular die, and then rolled the die to figure out how I should color in a 6×6 grid.

Example 2: Crochet!

Here I flipped 2 coins and assigned each of the permutations a type of crochet stitch. I made each row 10 stitches long, and switched stitches each row. In the end, I made it into a möbius strip, because that’s just cooler.

HH: single crochet

HT: half double rochet

TH: double crochet

TT: Triple crochet

#MathArtChallenge Day 4: Hyperbolic Geometry

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

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!

#MathArtChallenge Day 3: Isometric Cube Cutouts

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

THE CHALLENGE: Draw a cube by connecting 3 rhombi (see below). Then use only parallel lines to those in the rhombi to embellish the cube.

MATERIALS NEEDED: writing surface, writing utensil, colors?

Video:

#MathArtChallenge: Day 2 Looping Colors

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

THE CHALLENGE: Draw a looping, intersecting line that meets itself where it started, then color in alternating sections!

MATERIALS NEEDED: writing surface, writing utensil, colors

Video:

#MathArtChallenge Day 1: Tons of triangles

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

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

MATERIALS NEEDED: writing utensil, writing surface (paper, whiteboard, whatever!)

UPDATE (4/3) Here’s a quick video tutorial after lots of requests for help in the comments: http://www.youtube.com/watch?v=1ObGkAqoN-Q

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.