#MathArtChallenge 78: Ferozkoh Jaali & perspectives

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

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#MathArtChallenge Day 77: Chaos Game and Fern Hunt

A triangle shape with multiple points distributed throughout it.

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

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#MathArtChallenge 76: Decagon & Pride Flag

MAC 75 Decagon pride flag

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.

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Current & Future Plans re: Math Art Challenge

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: 

  • I am not an expert in community organizing, nor in the dismantling of police brutality. I can listen to, support, and lift up the voices of those who are. 
  • I am growing my expertise in math education, and how math art can be used in math class to refocus education on patience, deep thinking, and connection making. 
  • Whiteness pervades math curricula and the structure of math classes in America, and it must be dismantled. 
  • Math classrooms are deeply segregated. Both the students that comprise them, and the way curriculum is presented. If we are to change that, I believe the fundamental structure of math classes has to change. 
  • Many of the followers of the #mathartchallenge are white educators. It is not lost on me that when I post pretty math art, it gets many likes, while posts about #BlackTransLivesMatter gets crickets. I can marry the two better so that when you come to me for math art, you also are challenged to consider how you are upholding or dismantling white supremacy. 
  • Given COVID-19, there has never been an easier time for us to change what math class looks like. We already know that the fall will be different. Let’s seize on that. 

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.

  1. Create a bank of resources, that anyone, but teachers specifically, can draw on, to inspire creative mathematical thought. Aware that teachers commonly only use resources directly connected to their curriculum, I will do my best to go back and tag each of the Math Art Challenges with content standards. I understand that ease of use will make the resource more likely to be used. I also know that simply by virtue of being art, math art opens possibilities for students to creatively explore mathematically. That is simply less true (if at all) of traditional standards-based learning. 
  2. Research and share the historical context for as many #mathartchallenge-s that I can. If we’re to decolonize the curriculum, we have to stop pretending that all math comes from Europe and that the only mathematical thinkers worthy of celebrating are old white dead men. That takes active, intentional work and planning. To that end, I’m committing to also spending much of my summer updating, revising and adding to the Mathematicians Project. With respect to the #mathartchallenge, that will also mean doing things like connecting the Islamic geometry challenges to actual mosques where the original designs were found. Highlighting mathematicians, specifically non-white mathematicians, who do work related to each challenge. We need to connect math to history. And specifically to the history that has so long been denied Black and Brown students. The history that centers the brilliance of their ancestry. 
  3. Encourage patient, slow thinking in classrooms. Art takes a while. That’s a huge benefit. The factory model of education has not worked for way too many students, and it doesn’t take much thinking to know why. When I seek to learn a new math concept, I mentally prepare to take enormous amounts of time to deeply engage. I give myself room to explore paths that may very well take lots of time and lead to dead ends. I don’t place a schedule on when I must have reached mastery. Though I get why people create and use pacing guides, if we’re to center math class on actual mathematical thinking and on our student’s humanity, we need to throw those in the trash heap. Yes, definitely, some standards will have to go. Tough. We should be focused on teaching students how to learn, not making sure they know every math concept we can cram in. If they know how to learn, they can teach themselves whatever concept they didn’t get in school when it becomes necessary for them. I truly believe this shift makes math class more welcoming and reflective of what math actually is. 
  4. Plan for necessary reflection and connection making. I have, thus far, utterly failed at this, trusting that in the process of creation, we end up naturally reflecting and making connections. But if we’re to effectively use math art not just as a healing source (though that is a wonderful and necessary thing that art can provide), we need to be intentional in the ways we’ll ask students to process their creations. To this end, I plan to spend time this summer going back to formulate reflection questions that can be used broadly, for any #mathartchallenge-s, and specifically, to be used for individual ones. 

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. 

 

 

#MathArtChallenge Day 75: Black Lives Matter

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.

  1. First, please say out loud with me right now, “Black Lives Matter.” Don’t just tweet it, say it out loud where ever you are. Believe it.
  2. Please do not ask any person of color to do the work for you. That includes putting the onus on them to figure out how 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?

#MathArtChallenge Day 74

IMG_1463

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.

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#MathArtChallenge Day 73: More Islamic Design

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.

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#MathArtChallenge Day 72: Stars

A number of hand drawn stars.

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

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#MathArtChallenge Day 71: Sona Drawings

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

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#MathArtChallenge Day 70: Spinning Heptagon

gif of a spinning heptagon

The Challenge: This is a modular origami (7 squares) spinning top.

Materials needed: 7 squares of paper. Any paper will do, it doesn’t need to be origami paper.
Math concepts you could explore with this challenge: angles, geometry, origami, polygons, symmetry, vertices/intersections

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