
The Challenge: Inspired by this tweet (below), the goal here is to make a knot surface*.
Materials Needed: Can be done with tape and paper, also through crochet.
Math concepts you could explore with this challenge: Knot theory, topology
The Challenge: Inspired by this tweet (below), the goal here is to make a knot surface*.
Materials Needed: Can be done with tape and paper, also through crochet.
Math concepts you could explore with this challenge: Knot theory, topology
The Challenge: Create this design, and then once you have the basic underlying grid, play around with the possible interpretations of how to color and “finalize” it.
Materials Needed: compass, straight edge, colors; could use graphing software.
Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, tessellations
The Challenge: Today’s math art challenge is to play the chaos game, and was inspired while I was perusing the excellent Power in Numbers by Talithia Williams. Her chapter on Fern Hunt indicated one of her research interests as Chaos Theory – something that always grabs kids attention, and leads to one of the more fascinating probability related math-art creations.
Materials Needed: randomizer (die, coin, etc.), paper, pencil, possibly graphing software.
Math concepts you could explore with this challenge: fractals, probability, randomness
The Challenge: Create this decagon using the symmetries visible in the piece. The central images are rhombi.
Materials Needed: compass or ruler, could also use graphing software (see below!)
Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, polygons, symmetry, vertices/intersetions.
The Math Art Challenge has been on hiatus for about a week now. Mostly because it’s jarring to see folk happily engaging in math art while protestors are getting arrested. I couldn’t conscionably post things about the Hilbert curve, knowing it would divert time and energy that we need focused elsewhere.
I am keenly aware that a lot of white educators are doing more harm than good right now. Often because we’re moving too fast in an attempt to assuage guilty feelings that are hard to sit with. I am trying to let myself sit with and consider those feelings while also making sure that I am taking thoughtful, productive action and planning to be in this for the long haul. Because we need to be here beyond this week. Especially white folk. Especially white educators.
I’m just now starting “summer”, and I want my time this summer to be spent thoughtfully planning for how I can do better, and how I can help support other educators to do better this fall. As I’m considering what I can contribute to the dismantling of white supremacy, specifically that within schools, right now, I’m trying to hold these things in my mind:
The whole impetus for the #MathArtChallenge was a desperate need to stay in touch with students after we left the school building. I knew worksheets and traditional lessons would not engage them, but that math art could, and it could do so in a meaningful way. Like pretty much everything else that happened this spring, the MathArtChallenge was put together haphazardly, without a lot of deep thought going into the specific outcomes nor goals beyond getting students to engage somehow in mathematical thinking from afar.
I know many teachers are doing great work in their classes, and some people may really have broken out of the factory model of education, but too many math classes (including mine) are still primarily focused on getting through a list of standards rather than championing our student’s brilliance and giving them space to direct more of their own learning.
Considering it now, had I thoughtfully planned from the beginning, here are the goals I’d like to see accomplished by the #mathartchallenge, all of which are aimed at disrupting the factory model of education.
I want to be clear that I understand that planning to disrupt a factory model of education is not going to happen overnight, nor am I the first to encourage or work toward it, nor does this work absolve me from doing work elsewhere: supporting protests, engaging politically, being intentional with how and where I spend money.
I am teaching two new-to-me classes next year, and I already hear voices in my head:
“You still have to prep them for the test”
“How will your co-workers react?”
“What will the parents say?”
“You need to hit all the chapters.”
I want to be clear. Those voices are the ingrained white supremacy that pervades education. I firmly believe that slow, deep mathematical thinking, as opposed to a factory model, will benefit students. So I need to research and prepare to teach this way, and to address these voices, focusing primarily on my student’s brilliance and humanity.
This summer, I do plan to finish out the 100 Math Art Challenges. They are not likely to come out one per day, because I hope to actually take the time that summer affords me to do more intentional research. I hope to have each of the coming challenges rooted in some sort of larger context, whether that is through connection to a non-white mathematician working in a related field or through historical connections.
As with anything, collaborative work is stronger than individual work. If you are interested in helping me with this, I would love to collaborate. I am also keenly aware that my plans may need to change as I progress through this. Push back on any and all of this is welcome, especially if it centers student learning and making math class more equitable for students.
I live in Minneapolis. Today, on May 31st, 2020, things are challenging. People keep asking how they can help. So here are some ways you can help.
3. If you are white, talk with your people: your family, your co-workers, your neighbors. It may get uncomfortable, but it is not as uncomfortable as being Black in America. And again, in those spaces, do not put the weight of the work on the people of color. If you hear something along the lines of, “but the protests are so destructive”, point them to the many examples of peaceful protests. Then remind them that peaceful protests have been tried. Colin Kaepernick’s kneel was peaceful. Then, point them to this thread and article which documents many, many, many instances of the police escalating and inciting violence.
4. You can donate to help out at these organizations:
5. And here is an EXCELLENT list of resources to help support the Minneapolis Protests.
6. You can call Mike Freeman, the DA responsible for bringing charges to the police officers. (612) 348-5550
This is a partial and small list. But if you do any #mathartchallenge do this one. I’d love for you to add any additional suggestions in the comments.
Black Lives Matter.
And don’t think that this means we can’t talk the 8 mathematical practices! We sure can.
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
1.) Make sense of problems and persevere in solving them. How will American society , which is still predominatly white, address the problems of systemic racism? What structural changes can be advocated for so Black Americans live freely and safely in our communities?
2.) Reason abstractly and quantitatively. Why are Black Americans proportionally overrepresented in interactions with police?
3.) Construct viable arguments and critique the reasoning of others. In the book, Weapons of Math Destruction, Cathy O’Neil examines the way in which some police departments use algorithms to determine where to send their officers. Study that phenomena and form an opinion as to the merits of those systems.
4.) Model with mathematics. How can you help those who may not yet see the disproportionate experiences Black Americans have with the police see that? What data is useful to collect? What is not? How is your data skewed or representative?
5.) Use appropriate tools strategically. What methods are available to you to help deconstruct systemic racism?
6.) Attend to precision. Avoid speaking in generalities. How is systemic racism present in your life? What can you do about it?
7.) Look for and make use of structure. In what ways is our society constructed in unfair ways? In what ways is it fair? What structures exist that you may or may not have yet noticed?
8.) Look for and express regularity in repeated reasoning. There have been way too many names. The problem is not something we can ignore. How will you help?
The Challenge: Create the above tessellation using compass and straight edge or isometric grid paper.
Materials Needed: compass, straight edge, grid paper, possibly isometric paper. Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, vertices/intersections.
The Challenge: Create the tessellation above using a compass and straight edge.
Materials Needed: Compass, straight edge, possibly grid paper
Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, vertices/intersections.
The Challenge: Create all of the possible “stars” given a certain number of vertices.
Materials Needed: Pencil/paper
Math concepts you could explore with this challenge: angles, arithmetic, circles, combinations & permutations, lines, proportions/ratios, symmetry, vertices/intersections
Given what’s happening in my community right now, I felt it was necessary to highlight some Black brilliance today.
The Challenge: (Re)create a Sona drawing. I did a couple hours of research yesterday (which is totally insufficient to fully understand it), but what I can tell you is that these drawings originate with the Chokwe people in southwestern Africa, specifically Angola and the southern part of the Democratic Republic of the Congo. The drawings are told in conjunction with a story, and the goal of most is to draw them in as unbroken a line. Please check out some of the resources below, and if you have others to add, I’d love to see them and link them here.
Materials Needed: grid, pencil, paper, perhaps graphing software.
Math concepts you could explore with this challenge: angles, counting, geometry, graph theory, proportions/ratios, slope, symmetry, vertices/intersections