X + Y, by Eugenia Cheng

Current Issues, Mathematical, Nonfiction Review, Starred Review 0

X + Y

A Mathematician’s Manifesto for Rethinking Gender

by Eugenia Cheng

Basic Books, 2020. 272 pages.
Review written May 9, 2023, from a library book.
Starred Review

I love this book so very much! And I’m so glad I finally got it read — had meant to ever since it came out. I’m going on vacation this week and decided to finish it before I left — and Wow! — it’s full of transformative concepts.

Now, if you’re not a math-lover like me, please don’t be put off by the fact that this book is written by a mathematician. She works with Category Theory, a branch of mathematics that doesn’t necessarily deal with numbers, but about relationships and how things interact with other things.

In this book, she uses category theory to take on gender. And wow! What a lovely job she does.

Now, she starts with something I related to completely — the lack of women in higher mathematics. I started a PhD program in math at UCLA immediately after college. I was one of only 5 women out of 120 new math graduate students that year. Three of the other women were in master’s programs, not doctoral — and I ended up dropping out a year and a quarter later with my Master’s. So I am very aware that there’s a gender disparity in mathematics.

The first part of the book looks at difficulties with even talking about gender disparities. She looks at problematic arguments about nature or nurture.

And then she takes us to another dimension. She takes the gendered dimension out of the discussion and defines some new terms.

We need new, ungendered language in order to separate character traits from gender and have less divisive conversations in which people don’t have to get defensive about “not all men” or “not all women” being a certain way. Because indeed men are not the same, and neither are women. Not all men are aggressive, competitive, risk-taking, and unempathetic. And even those who do behave in those ways might only do so because of social pressure and the idea, perpetuated by social norms, that this is how to be successful in society. When certain behavior is rewarded by society many people will strive to behave in those ways even if at some deeper level it makes them unhappy.

The ungendered language she comes up with are the terms “ingressive” and “congressive.” Ingressive behavior focuses on the individual, and congressive behavior focuses on the group. Here are her definitions:

ingressive: focusing on oneself over society and community, imposing on people more than taking others into account, emphasizing independence and individualism, more competitive and adversarial than collaborative, tending toward selective or single-track thought processes

congressive: focusing on society and community over self, taking others into account more than imposing on them, emphasizing interdependence and interconnectedness, more collaborative and cooperative than competitive, tending toward circumspect thought processes.

This is not a clean dichotomy even though some aspects sound like exact opposites of each other. It’s not a classification of people into two camps. It’s a way to evaluate behavior in a flexible and dynamic way to reflect the fact that people are flexible and dynamic day by day and also over the course of their lives, not fixed and rigid.

She goes on to talk about spaces that are more ingressive and spaces that are more congressive. Interesting to me, she left her position at a university and began a career teaching math at an art school. Yes, she found many more women at the art school, but she can go beyond gender and talk about how it’s much more set up as an ingressive space. And she’s happier working in that space.

She describes examples of other people, both women and men, who gave up more ingressive careers (after achieving success) for more congressive roles.

And she talks about how math education is set up to reward ingressive behavior, with lots of testing and competition. This was interesting to me, because at first I thought, oh, I must be mostly ingressive because I love competition, and really enjoyed math competitions when I was a student.

But then I think about my happy switch from teaching college math to becoming a librarian. I’ve said many times, “In the library, I still get to help people learn, but now I’m on their side! As an instructor, I had to test them, and I felt like their adversary. Now I get to show kids the fun side of math.” So I have to stand as another example of someone who turned out to be much, much happier in a more ingressive career path.

I was also fascinated by her ideas to make education – yes, even mathematics education — more congressive. She suspects that could attract more people to the field who might be turned off by the current more ingressive way it tends to be taught. I loved when she started elaborating on that idea:

Congressive math is what I have been teaching to art students for several years. I think it’s also what is introduced to children at the very beginning of school, when it’s all about play and exploration with blocks and toys and other things they can touch and feel. It comes back around to being like this at a research level, but by that time I think we’ve already put off far too many congressive people with the phase in between.

I think math should be congressive all the way through. We really don’t need to train people to be human calculators anymore, now that we have actual calculators with us more or less all the time (for example, on our phones). So math could be more congressive by being about exploration and processes. It could be more about ways of thinking than about knowledge.

I would like to see a non-cumulative curriculum so that each stage doesn’t depend on the previous stage. The traditional model is more like a series of hurdles that get higher and higher and are specially designed to weed people out at each level. Not only is this ingressive, it’s also counterproductive, as we are not weeding out the right people.

But I shouldn’t go on so much about math, because that was a side point. The really beautiful thing about this book was how it took gendered language out of discussions about our society. I suspect you could also use these ideas in discussions about race.

I believe that the new dimension of ingressive and congressive traits can help us overcome bias that can’t be addressed on the dimension of gender alone. I think this is how we can deal with implicit bias in the system that comes from our association of character with gender, and how we can deal with indirect bias that comes from favoring ingressive behavior. But I think it will also have an effect on explicit bias, as it is a way for everyone to escape one-dimensional gendered thinking in their heads and think more clearly about what contributions to society we want to see. With every individual who escapes that thinking, the hold of both implicit and explicit gender bias will be lessened.

And the book finishes up with a vision of what things could be like in a society that encourages congressive behavior — and offers tips on ways to be more congressive in your personal life and perhaps in your personal environment (such as her math classrooms in art school). There’s even a helpful appendix at the back that demonstrates how you can respond to personal attacks with congressive statements instead of ingressively attacking back.

Now I’ll admit, I was predisposed to love this book having been a woman working in the field of mathematics, even if it was at a lower level than Dr. Cheng. But I’m also delighted with and impressed by her ideas. May we work together, in our lives and in our communities, to make the world a more congressive place. I highly recommend this book, and would love to discuss it with others who have read it.

eugeniacheng.com
basicbooks.com

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Disclaimer: I am a professional librarian, but the views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

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Review of Too Many Pigs and One Big Bad Wolf, by Davide Cali and Marianna Balducci

Award Winners, Delightfully Silly, Mathematical, Picture Book Review, Stand-outs, Starred Review 0

Too Many Pigs and One Big Bad Wolf

by Davide Cali and Marianna Balducci

Tundra Books, 2022. 32 pages.
Review written January 8, 2023, from my own copy.
Starred Review
2023 Mathical Book Prize Honor Book, Grades K-2
2022 Sonderbooks Standout: #9 Silly Fun Picture Books

This very silly book is a counting book that’s not really a counting book.

Here’s how it begins:

Once upon a time, there were three little pigs.
Then the wolf ate them.
THE END.

This story is too short!
I want a longer one!

In the longer story on the next page, there are four little pigs that get eaten.

And so it progresses, the narrator adding wild things to the story, the “reader” complaining, and the result always the same.

The pigs are drawn from beads on an abacus. There are not more than ten beads on a row, and often they’re grouped by fives, so counting is easy.

The graphics, the silly stories, and the dialogue between the narrator and the objector are simply loads of fun. We never see the pigs get eaten, and there’s a feeling that these are actors that are not really harmed, since the same abacus gets reused. So it keeps things light and silly, despite so very many pigs supposedly getting eaten.

This is another one you’ll enjoy most if you check it out for yourself, as my description can’t do justice to how much fun it is. You can throw in some counting when you read it to your kid, but I don’t think they’ll think of it as a counting book.

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Review of Zero Zebras, by Bruce Goldstone, illustrated by Julien Chung

Delightfully Silly, Mathematical, Picture Book Review, Stand-outs, Starred Review 0

Zero Zebras

A Counting Book about What’s Not There

by Bruce Goldstone
illustrated by Julien Chung

Orchard Books (Scholastic), 2022. 36 pages.
Review written January 8, 2023, from my own copy.
Starred Review
2022 Sonderbooks Stand-out: #6 Silly Fun Picture Books

I love this book in so many ways! In fact, many more than zero ways!

Here’s how the book begins:

I see one wallaby . . .
. . . and zero zebras.

Two tuna splish
and splash
and splosh . . .
. . . with zero zebras.

You get the idea!

As things progress with various jazzy animals, there’s wordplay and visual play:

Ten tigers tiptoe —
that’s how many.

What about zebras?
There aren’t any.

Eleven llamas
like to spit.

It’s zero zebras
that they hit.

But the fun really begins after we pass twelve turtles on the page.

What’s next? What’s here?
What do you see
perching in this tree?
Why, look at that!
By now you’ve guessed.
Zero zebras — obviously.

But that’s not all that isn’t here!
Do you see zero eagles?
You’ll find them next to zero pigs
and zero barking beagles.

Then we’ve got two more spreads with rhymes about all the things pictured that they are zero of.

The finishing thought is this:

So when you want to count a lot,
don’t count what’s there. Count what’s not.

Try counting zeroes with your friends.
The list of zeroes never ends!

The final pages have thoughts from the author about zero and infinity.

So there you have it. A delightfully silly picture book that invites play and imagination and all kinds of fun — while getting kids thinking about the important mathematical concept of zero.

I did quote a lot of this book, but please let that invite you to see it for yourself, because a picture book is always best with the words and pictures together.

brucegoldstone.com
scholastic.com

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Review of Bake Infinite Pie with X + Y, by Eugenia Cheng, illustrated by Amber Ren

Children's Nonfiction Review, Mathematical, Picture Book Review, Starred Review 0

Bake Infinite Pie with X + Y

by Eugenia Cheng
illustrated by Amber Ren

Little, Brown and Company, 2022. 32 pages.
Review written July 13, 2022, from a library book
Starred Review

My readers won’t be surprised that every time mathematician Eugenia Cheng writes a picture book, it delights my heart. I’ll list this under Children’s Nonfiction, because although it is a story, the emphasis is on the ideas.

This one tells of two kids, named X and Y, who are dreaming of infinite pie — X, pie that is infinitely wide, and Y, pie that is infinitely tall. They think of course that such pie isn’t real, but they ask their Aunt Z, who can create amazing things with her brain.

The book that follows explores infinity in many different ways, and all of them involve pie!

There are infinitely different ways you can make pie, and once it’s done, if you keep eating half your pie, it will last until infinity.

You can make a pie with infinite corners, cut pie crust infinite ways, and even make pastry with infinite layers.

I hope that gives you the idea of ways to explore infinity with pie — it’s all presented in a family setting with a fun aunt bending kids’ minds with tasty treats.

And there’s even a recipe for pie at the back! (After a spread that lays out mathematical ideas presented.) The recipe is for Banana Butterscotch Pie — and believe it or not, I couldn’t resist trying it out. (I hadn’t made a pie with crust in decades.) The pie was indeed delicious, but alas – the instructions didn’t specify how big your pie pan should be. I used a 9-inch one, and my pie was more of a tart — the filling only went about halfway up the pie crust. I think an 8-inch pie pan would do nicely. And it still tasted wonderful.

eugeniacheng.com
amber-ren.com
lbyr.com

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Review of Look, Grandma! Ni, Elisi!, by Art Coulson, illustrated by Madelyn Goodnight

Contemporary, Mathematical, Picture Book Review, Starred Review 0

Look, Grandma!
Ni, Elisi!

by Art Coulson
illustrated by Madelyn Goodnight

Storytelling Math (Charlesbridge), 2021. 32 pages.
Review written December 29, 2021, from a library book
Starred Review

Here’s another book from the amazingly good Storytelling Math series. All of them present math concepts in a real-life setting that will appeal to children. All of them also present cultural information, not presented as “other” or “exotic” or “different,” but from the perspective of a child within that culture, excited and proud and enjoying things their family does.

In this book, Bo is working on large colorful stone marbles for the Cherokee National Holiday coming up. The marbles are used in the game Cherokee marbles, digadayosdi, and Bo wants to sell them in his family’s booth at the festival.

Bo has a lot of marbles, and he wants to display them at the booth. But when he finds a nice tray to use to display them, Grandma tells him that the tray is too big. Their booth is small and he can display the marbles in the booth, but whatever he uses needs to fit on a small mat she shows him.

So it’s a volume problem. Bo is trying to find a container with a base as small as the mat that will still display the marbles well. And not so tall that it’s hard to reach inside.

After Bo finds the perfect container (which takes lots of tries), they show him happily displaying them in his family’s booth — and then playing Cherokee marbles together to get a break.

The book weaves in some Cherokee words, and there’s a glossary at the back along with the feature at the back of every Storytelling Math book called “Exploring the Math.” In this book, that section gives ideas of activities to help kids explore volume and area. I love the way these stories are jumping-off places for more learning.

artcoulson.com
madelyngoodnight.com
terc.edu
charlesbridge.com

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Review of Much Ado About Baseball, by Rajani LaRocca

Children's Fiction Review, Contemporary, Fantasy, Mathematical, Paranormal 0

Much Ado About Baseball

by Rajani LaRocca

Yellow Jacket (Little Bee), 2021. 312 pages.
Review written January 4, 2022, from a library book
2022 Mathical Honor Book, grades 6-8

12-year-old Trish is new in town. She’s used to being the only girl on the baseball team and the only girl and sixth grader on the Math Puzzler team – but just when her old teammates had gotten used to her, now she has to win over a new team. Her brother Sanjay has encouraged her to win them over by being good at baseball.

Ben is back on the baseball team this summer after two years off. And he’s upset when he sees Trish – the girl who beat him for the Individual Math Puzzler championship. Now she’s going to do better than him at baseball? But they both love math and baseball, so shouldn’t they be friends?

There are hints of something magical happening this summer, some amazing treats, and then two magical books of math puzzles show up at Trish’s house and at Ben’s house. Ben right away figures out it’s magic, but Trish thinks it’s probably some special formula invisible ink. But either way, there are some fun and challenging math puzzles to solve, woven into this story of baseball, rivalry, and friendship.

Perhaps if I knew the Shakespeare play Much Ado About Nothing better, the plot wouldn’t have seemed quite as random. The magic didn’t really seem to operate with rules, but perhaps chaotic fairy magic, as in A Midsummer Night’s Dream doesn’t need to. Anyway, it was a fun story, and for me the math puzzles woven in made it even more fun. There’s material at the back taking some of the concepts further.

RajaniLaRocca.com
yellowjacketreads.com

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Review of It’s a Numbers Game! Baseball, by James Buckley, Jr.

Children's Nonfiction Review, Mathematical, Starred Review 0

It’s a Numbers Game!

Baseball

by James Buckley, Jr.

National Geographic Kids, 2021. 128 pages.
Review written January 6, 2022, from my own copy, purchased for the Mathical awards.
Starred Review
2022 Mathical Honor Book, Grades 6-8

Math and baseball! It’s a natural pairing, and this book explores all the connections, inviting readers in with plenty of action shots on every page.

Did you know that Major League Baseball teams now hire mathematicians? There’s a spread titled “Averages Your Grandparents Know” about Pitching stats of ERA, WPCT, and WHIP. Then comes a spread called “Averages Your Grandparents (Probably) Don’t Know,” and I was a little chagrined that I fit a reader’s grandparents. But that second spread had some interesting information:

There are a lot of stats you can calculate on your own. But for some of these stats, it’s as if you need an advanced math degree to understand them! In fact, many MLB teams now employ professional mathematicians. Every MLB team has a special department that does nothing but crunch numbers. Called sports analytics, these calculations and stats are changing how players are selected and sometimes even how the game is played.

On another page I learned about a new tool used since 2015:

In recent seasons, MLB started using a new way of tracking and measuring home runs. Cameras track every movement of the ball, and computers quickly calculate information using a system called Statcast. As players and coaches study the Statcast data, they develop new ways to go after the long ball.

With statcast, they can find and report the launch angle, the speed, and the actual distance a home run ball will travel. For pitchers, they now have a much more accurate measure of the speed of a pitch and can even tell you the spin rate.

That’s some of the interesting information found in this book packed with information about baseball and every kind of statistic you can imagine. My older brother was a big Angels fan and very interested in the statistics, so I thought I would know most of what’s in this book, but it turned out to be only the part your grandparents would know!

The book does say a little bit about women’s softball, about Little League, and about baseball in other countries, but this is mostly a book about Major League Baseball. I do like, though, that each chapter has something for the reader to try. It’s usually related to statistics, but also pertaining to what the chapter discussed. Kids will learn to keep score and to read a box score, for example.

This book is packed with the numbers of baseball, including stats and records, and even numbers on jerseys that have been retired. It’s all done in an inviting format, with colors and pictures and charts. The text is in small chunks, and each page is visually interesting. I was much more engaged than I had expected to be, since I haven’t watched baseball in years.

This book will intrigue both kids who love sports and kids who love numbers, and perhaps help build overlap between those groups!

natgeokids.com

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Disclaimer: I am a professional librarian, but the views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

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Review of What Will Fit? by Grace Lin

Good for the Very Young, Mathematical, Picture Book Review, Starred Review 0

What Will Fit?

by Grace Lin

Charlesbridge, 2020. 16 pages.
Review written September 30, 2021, from my own copy ordered via Amazon.com
Starred Review

What Will Fit? is a board book in Charlesbridge’s wonderful “Storytelling Math” series.

This one is perfect – exploring spatial relationships in a way that is vitally interesting to the toddlers it’s written for.

The story is board-book simple. We’ve got a little girl going to the farmer’s market with a basket. She wants to find something that fits just right in her basket. She looks at a beet, an apple, a zucchini (turned both ways), and an eggplant.

Finally, she finds a pumpkin just the right size and celebrates.

On the back spread are notes to parents with playful ways you can build your child’s spatial sense.

The package all adds up to a sweet little story for short attention spans that will springboard into conversations that will help children learn an important concept fundamental to mathematical understanding. And all in a way that is interesting to them.

gracelin.com
charlesbridge.com/storytellingmath

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Review of Molly and the Mathematical Mysteries, by Eugenia Cheng, illustrated by Aleksandra Artymowska

Children's Nonfiction Review, Mathematical, Starred Review 0

Molly and the Mathematical Mysteries

Ten Interactive Adventures in Mathematical Wonderland

by Eugenia Cheng
illustrated by Aleksandra Artymowska

Big Picture Press (Candlewick), 2021. First published in 2020 in the United Kingdom. 30 pages.
Review written January 4, 2022, from my own copy
Starred Review
2022 Mathical Book Prize Honor Book, Grades 3-5

Oh, this book is delightful! It’s a lift-the-flap adventure that demonstrates intriguing mathematical oddities. I know – that doesn’t sound amazing and inviting, but this book is both of those things.

A girl named Molly gets a series of mysterious notes. We get to lift flaps and read these notes. The notes tell her what to do to get past that page. The first note, for example, tells her to open her window and turn her room inside out – at least in her imagination. Flaps open the window. Then on the next page, we’ve got an inside-out world, explaining the mathematical concept of inverses.

Some of the pages have puzzles in the flaps. An impossible staircase Molly can only escape by lifting the flaps. A maze Molly can only traverse if you lift the correct flaps. Figuring out which flaps can be folded into a cube. Weaving strips so that pink squares are hidden. Turning paper dials to reveal the correct answer. Each page has something different to figure out or uncover, and it leads you through the book along with Molly.

And the mathematical concepts are fun ones. This book helps kids think about dimensions, tiling, self-similarity, symmetry, combinations, fractals, and more. After completing Molly’s adventure, five colorful pages give the reader more mathematical information.

I had a lot of fun going through this book – and I’m an adult who already knows all the concepts. I would love to watch a kid go through it. Of course, the one drawback is that with all the flaps, this is not a good choice for a library collection. But I think a kid who had it at home would find themselves returning to it again and again.

Note: Even though this is presented as a story about Molly and is thus technically Fiction, the focus is on the mathematical concepts, so I think it fits better with Children’s Nonfiction, which is where I’ll file it.

eugeniacheng.com
candlewick.com

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Review of 1 Smile 10 Toes, by Nelleke Verhoeff

Animal Characters, Award Winners, Good for the Very Young, Mathematical, Picture Book Review 0

1 Smile 10 Toes

by Nelleke Verhoeff

Barefoot Books, 2021. 24 pages.
Review written December 10, 2021, from my own copy, purchased via amazon.com
Starred Review
2022 Mathical Book Prize Winner, PreK

1 Smile 10 Toes is now one of my favorite board books. As with many board books, this one is part toy. All the pages except the last one are split in two, featuring a friendly imaginary animal all the same width in the middle. So you can turn parts of pages to mix and match the tops and bottoms and create many different kinds of creatures.

But the learning part is that each half-page has something to count. The only text is a numeral with the body part being featured. Some examples on top are 8 Feathers, 7 Curls, 3 Beaks, 5 Eyelashes, 4 Ears, 10 Spikes. Some examples on the bottom are 8 Toes, 9 Claws, 4 Feathers, 10 Hooves, 2 Thighs, 9 Fingers.

You can tell from the examples, the author didn’t worry about being conventional. I imagine that adults will get tired of counting things for kids long before a child will get tired of looking at these pages. I remember as a small child being fascinated with mix-and-match books, and this one has the additional bonus of teaching counting.

There’s no order to the number of things featured – all the numbers between 1 and 10 are featured, but in random order, which works well with the mix-and-match theme. You might want to wait to use it with a kid who knows that having 4 ears is silly.

No matter what, it’s a lovely way to give a small child endless things to count.

barefootbooks.com

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