#MathArtChallenge 99: Quilts & the Underground Railroad


“My mother was told… that slaves would work out a quilt piece by piece, field by field, until they had an actual map, an escape route. And they used that map to find out how to get off the plantation.” -Mrs. Elizabeth Talford Scott, octogenarian African-American quilt maker

Several years ago, after I’d picked up quilting as a hobby, my mother gave me Hidden in Plain View: A Secret Story of Quilts and the Underground Railroad, which explores the possibility that quilts were used as signaling, planning, or storytelling tools to help with the escape of enslaved people on the Underground Railroad.

The account in the book is based on the the story of Mrs. Ozella McDaniel Williams, an African American quilt maker based in Charleston, South Carolina, who was descended from enslaved people:

“Did you know that quilts were used by slaves to communicate on the Underground Railroad?” – Mrs. Williams

That quote started a years long search by Jacqueline L. Tobin, and her co-author Raymond Dobard, Ph.D., to attempt to track down evidence of just such a code. The authors are clear throughout that what they have is not proof, but rather strong conjecture based on oral history and research. They refer to quilting as a “geometric language”, and their story, while perhaps technically unproven, is incredibly convincing and compelling.

There’s a lot about this book that appeals to me, but I’d like to highlight 3 things in particular:

  • It makes a strong case for the need to rely on histories beyond the written word. I wonder how we can apply this to our student’s lives and experiences in our classrooms. How can we value, oral, artistic, and other types of history? How can we let that guide us into other ways of “knowing”?
  • This story makes for an excellent push back on the very false version of history wherein enslaved people did not resist. In fact, much of the book is dedicated to refuting this, while interweaving the involvement of quilts. There’s a long section dedicated to the various types of rebellions of enslaved people, and another specific to spiritual songs and the need for secrecy among the African American community so as to protect their various rebellions.
  • Because the quilting designs are so geometric, it offers us, math teachers, an easy way to honor a far too often overlooked part of the history of the U.S. All of our students (and teachers) should be better versed in the resistance of enslaved peoples and the ways they were active in attaining their own freedom.

I love the exploration of quilts are a form a language. I’ll let several quotes do the heavy lifting for me here:

“Quilts represent one of the most highly evolved systems of writing in the New World.” (Hidden, p9).

“Patchwork quilts were readable objects in nineteenth-century America.” (28)

“Communicating secrets using ordinary objects is very much a part of African, culture, in which familiarity provides the perfect cover.” (35)

“Did the American quiltmaking tradition, in which geometric patterns were given names and meaning, invite appropriation by black slaves and their descendants seeking ways and means to continue their own encoding traditions?” (31)

A huge part of the book, naturally, is dedicated to the specific code that Mrs. Williams shares with Tobin. It is relatively brief, and alludes to 10 common quilt blocks, all illustrated here.


In case you can’t read that, the code says,

“The monkey wrench turns the wagon wheel toward Canada on a bear’s paw trail to the crossroads. Once they got to the crossroads, they dug a log cabin on the ground. Shoofly told them to dress up in cotton and satin bow ties and go to the cathedral church, get married and exchange double wedding rings. Flying geese stay on the drunkard’s path and follow the stars.”

Each of the bolded phrases represents a quilt block shown in the pictures. (The exception being the double wedding rings, which wasn’t popularized until after the end of the Underground railroad – the authors believe this may have represented the shackles of slavery.) For my contribution to this challenge, I made 6 of the 10 blocks (if you’re keen eyed, you’ll notice they’re the simplest of the 10, but forgive me, my quilting skills are  beginner and a bit rusty.)

Part of the frustration in the book is the inability to prove this code directly. The authors do go through and attempt to explain the significance of each block (I will summarize as best I can, there’s a lot of complexity to each of these as detailed in, you know, a whole book):

  • Monkey Wrench likely refers to a skilled, knowledgable person, perhaps guiding the preparation for escape
  • Wagon Wheel references traveling
  • Bear’s Paw may reference actual bear trails needed to be taken
  • Crossroads likely references Cleveland, Ohio, a major hub of the Underground Railroad
  • Shoofly is thought to reference a person, perhaps a contact, who may assist along the way
  • The bow ties cautioned people to dress formally so as to better blend in
  • The log cabin, specifically mentioned to be “dug” into the ground may refer to drawing symbols in the dirt so as to identify persons to be trusted
  • Flying geese likely meant traveling north…
  • …along a Drunkard’s Path, which winds and turns so as to avoid slave catchers
  • And finally the Stars likely meant ways to navigate north or perhaps simply signaling freedom.

Again, that is really oversimplified from the detail the book goes into. I highly encourage you to get a hold of it. Part of the reason so much of the above is couched in “likely” and “may have” is because we do not have direct records of the code, only Mrs. Williams’ accounting and Tobin and Dobard’s research. Deprived, intentionally, of book literacy, enslaved people relied on oral histories, and the code Mrs. Williams shared with Tobin is one, “passed down orally in her family for generations; Ozella received it from her mother, who received it from Ozella’s grandmother.” The authors also lamented the inability to find quilts made by enslaved people, likely because, in addition to possibly helping with the Underground Railroad, quilts were useful objects, often made from poor cloth, and washed with harsh lye soap which caused them to disintegrate. Part of the publishing of this book (1999) was in hopes that more materials or stories may turn up.

For us, as mathematicians, I think the strength of this story is its beautiful connection between mathematics – the geometric language described by the authors – and such an important aspect of American history. I know I have personally heard complaint from my students that all they learn of African American history is of passive enslavement – and while obviously this is deeply tied to slavery, it highlights the people’s rebellion. It’s unclear exactly how the quilts may have been used – perhaps all 10 were set out sequentially to prepare people for escape – perhaps they were literal maps. There’s a fair bit of evidence for the latter. Not addressed in the book, but it occurred to me that perhaps this quilt code was specific to Mrs. Ozella Williams’s family, which might additionally explain why there is not a wealth of record. That’s just speculation, of course.

“Many times in the discussion of the code, Ozella stated that it was the ‘mathematicians’ who devised the code in the first place and that these mathematicians were similar to what we know of today as fraternities.” (p.103). The authors speculate this references Masonic orders, most likely the Prince Hall Masons, an African-American fraternity. How powerful to help connect our students to such an important use of mathematics and geometric language in the heritage of African Americans. And I don’t just mean for Black students – for all students, this can be a powerful lesson in who does mathematics and how mathematics can be used.

On a practical note, I realize that not everyone wants to take up quilting. I chose to do so because

  1. I have some quilting ability
  2. There is soooooo MUCH mathematics in piecing quilts together.
    1. Precision measurement and cutting
    2. Calculations of angles and fabric allowances
    3. Geometric organization: which pieces sewed first, which next, how do the seams come together?

But I imagine you could easily engage students with any of the following tasks, (and perhaps you’ll suggest others?)

  • Designing their own geometric block with its own meaning to them.
  • Literally constructing, with ruler and compass, the blocks shown above.
  • Coloring or piecing with construction paper or something similar, the blocks above.
  • Exploration of areas of positive and negative spacing in the quilts.
  • Possible arrangements of the blocks: I did a 2×3, if I’d made all 10, how could they be best arranged? Is there a possibility outside of 1×10 or 2×5?

On this, the 99th challenge, my REAL challenge to all of us is to make certain we’re no longer abandoning culture and history in our classes. We may very well screw it up, but I would argue that we’ve already done that by pretending math is neutral for so long. Would love to engage in comments or discussion in the comments or on twitter.

UPDATE: Was reminded by @picaresquity of mathematician Chawne Kimber’s excellent modern quilting. Check out her work at completelycauchy.com. I first heard of her work on this episode of My Favorite Theorem.

#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!)

use tape

Here are mine!

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

3.) Construct viable arguments and critique the reasoning of others. What kinds of interactions between two tori can be made? What can you deduce about the relative radii of tori that “intersect”?

5.) Use appropriate tools strategically. What tools work best for creating these tori? How might you make an image like this best without a compass? Is there a tool that is actually better than a compass? Why or why not?

7.) Look for and make use of structure. Let’s say you start with a circle of radius 5 units. What’s the largest radius you can use for your circles centered on the torus? What’s the minimum?

#MathArtChallenge Day 5: Probability designs!

Day5 MAC

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: Probability, randomness

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.

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

Great example here from Joel Bezaire

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

2.) Reason abstractly and quantitatively. Once you’ve finished a piece, what do you notice about the distribution of values? How does that compare with the relative size of your piece?

5.) Use appropriate tools strategically. What methods make it easiest to explore the probability of values? What are the benefits or drawbacks of using a square grid? Would a 3D model make the chosen values easier or less easy to see?

8.) Look for and express regularity in repeated reasoning When completing with a class, what patterns do you see as you look over all the designs created by the class? How does the distribution of number change?