Tessalation! is a new children’s book about a little girl who discovers tessellations in the outdoor world. I backed the project when it was on Kickstarter earlier this year, and my book just arrived. Both the drawings and the writing is beautiful, and it is, to my knowledge, the only book for kids about tessellations.

Emily Grosvenor, the author of Tessalation!, and I have been interviewing each other about tessellations, the mathematical projects that stick with us from elementary school, and big words for little kids. A lightly edited version of this conversation is below.

The website for the book is here.
Tessalation! is also on Kindle here.

Dan: Why did you choose to write a book about tessellations?

Emily: I’d say tessellations chose me. I’m a magazine writer and memoirist, but one day I got it in my head that I was going to write a children’s book and sat down to do it. I think most parents have this compulsion — when you’re reading a dozen every night you start to see the world in picture book ideas. From there, I thought about what I loved as a child and what I love now. I had discovered tessellations in a 4th grade gifted class and remembered having a blast making them. But I also love tessellated pattern as an adult. All I had to do was look around my home and its patterned curtains and pillows and floors to see I had an obsession. All that remained was the challenge of creating a book where tessellations were organic to the story. Patterns are soothing to look at.

D: Your description of the love of patterns cuts close to my own feelings. I used to imagine the imaginary ball that would ricochet around the room just right to hit some chosen spot, like a trick pool shot. Tessellations are similar—the shapes that align perfectly so foreground and background flip back and forth. There’s a visual beauty there that’s easy to fall in love with. For me, mathematical love is like that: the recognition that ideas fit together with the same sort of elegance and precision as shapes, so that everything meshes perfectly. There’s a deep satisfaction and also a sense of awe that can arise when all the pieces fit. Elation, you might say.

I’m curious about your original encounter with tessellations in fourth grade. Do you actually remember the lessons you did with tessellations? What about that experience grabbed you?

E: Yes, I do remember. Fourth grade was a seminal year for me. Nearly everything I’m passionate about had its seeds in fourth grade: tessellations, Germany (our country of study, I later majored in German and worked for the German Embassy in Washington, D.C.), poetry (our teacher made us memorize a poem a month and I still know three of them and write my own), novels (I specifically remember a book report I did on Mischievous Meg) and Oregon (I think Emily’s Runaway Imagination is the real reason I moved across the country as an adult). All I remember about the tessellation lesson was being shown how to make my own using a square. I made some seals leaping out of waves which, admittedly, was not a very compelling tessellation. But I think it stuck most because of the setting. I was shy and gifted class gave me a small group setting where we could do creative projects and where I felt comfortable enough to participate. It was also distinctly hands-on. Nearly every lesson I remember from elementary school had that quality. And it involved art. Dreamy, imaginative kids absolutely need to make art. I did not connect tessellations to math at all.

What do you think determines whether or not lessons “stick?”

D: That’s a great question, and one I’m often preoccupied with. I remember certain lessons and experiences from elementary school too, and I do think there are some hallmarks that distinguish the memorable ones from those we forget.

I think having control over the experience is critical to making an experience memorable. This is why art can be so compelling: we get to be the actor, the doer. We choose where the line goes, what the colors are, and even if we can’t always make it look like what we imagined, we’re still in charge. Mathematical experiences can involve the same kind of creative ownership, and when they do, they stand out.

Looping this back to tessellations, I taught a class for 2nd and 3rd graders on tessellations a little while ago. It eventually centered on the question of whether you can create a polygon with any number of sides that still tessellates. Can you make a 17-gon that tessellates? A 31-gon? A 99-gon? The problem is really fascinating. It starts with the more artistic project of just finding examples that do tessellate, and there’s a fair amount of coloring and decorating polygons to make cool looking designs. Eventually, we start discovering certain “moves” that change the number of sides of our polygon in a predictable way, and still produce something that tessellates: joining two polygons together, for example, or adding a bump to an existing tessellating shape. Suddenly we have families of tessellating polygons with 4, 8, 12, 16, 20, etc. sides, for example. And then there’s a very clear goal: how do we get those missing ones?

I don’t know for sure, but I suspect this problem, and problems like it, are memorable. There’s a clear answer, but constructing the argument (and all the tessellations) calls for a tremendous amount of choice and autonomy from the students. The fact that the products are so pretty is nice. And the arguments are just as beautiful, even though they’re harder to draw pictures of.

But back to the book! Do you have a vision of how it will be used? A good book for bedtime reading, or for classroom use, or to launch a rainy Sunday craft project at home, or for a walk in the woods? Or is it for all of the above?

E: Tessalation! definitely works best in the classroom or as an introduction to an afternoon activity at home. I am already getting emails from teachers who are using the book as a jumping off point to a discussion of patterns, tessellations and pattern-making. One of my backers hasn’t got the book yet in her hands but printed out her digital PDF for just that.

I specifically designed the book to have entry points for several age groups. For younger kids, such as preschoolers, just finding Tessa within the tessellations is excitement enough. My three-year-old, Griffin, points out tessellations wherever we go.

Older kids will want to make their own and may respond to some of the other, more complicated ideas in the text. For example, on one page I write about bees dancing where to imbibe. What does imbibe mean? Why are they dancing?

Children 3-8 have a natural obsession with animal life and the outdoors and love learning about how nature works. Conventional wisdom in children’s books holds that you use the simplest words possible, but if I want my children to know that the back of a turtle is called a carapace, and it works with the rhyme, I’m going for it!

As for getting kids outside, I have a strong fondness for the international nonprofit Hike It Baby and have been developing a Tessa Hike to do at Hike It Baby meetups. Basically, you read the book, gather objects on your hike, and then make patterns with them in the parking lot. Fun!

D: One more question for you. Tessalation! include lots of long words. Why use advanced words in a children’s book? And are there implications for math learning here?

E: I’ve long bristled at the thought that young people can’t handle big words. The publishing market is designed within evermore defined reading age groups, and understandably so. A teacher or parent who goes looking for a story or book kids can connect with will inevitably search out one that has the themes, language and subject matter appropriate for that age.

I will always be a fan of the simple story well told in simple language — the Llama Llama books are still big in our house — but I also know that children will take ownership of words that they hear. So when my 3-year-old tells me he just found a tessellation on the bottom of his new shoe, it is because he has been exposed to the word and the visual of a tessellation.

Here’s another 4th grade story for you. I remember doing a book report on Mischievous Meg by Astrid Lindgren and using the word “fabricate” to describe the main character’s penchant for storytelling. The teacher marked it with a little note that said: “Your word?”
I was highly insulted — was she asking if my mom had helped or suggesting that that couldn’t be my word?
One of my all-time favorite children’s books is Bubble Trouble by Margaret Mahy. Here’s an example, from the climax of the book’s action:

“But Abel, though a treble, was a rascal and a rebel,
fond of getting into trouble when he didn’t have to sing.
Pushing quickly through the people, Abel clambered up the steeple,
With nefarious intentions and a pebble in his sling!”

When my older son was young, he simply basked in the rhythms of the language, but as he got older he started asking what the words meant. With language, exposure is important. How would you rather learn a word — spoken by your parents, in your favorite book, or on a worksheet in Middle School?

As for Tessalation!, the reason it sat in a drawer for a year and a half was because I got some early feedback that it was a book for highly literate children, and I might think about making it more accessible to all readers. I sat on that for a while. It’s valid criticism. But in the end, I plowed ahead with my original goal, which was to make the cleverest book I could. Kickstarter was a good way to connect with people who respond to that.

Thanks, Emily Grosvenor, for a wonderful conversation, and best of luck with the book!