The following is an extended excerpt of a cover letter for Is It a Vehicle?, a book I have play-tested many hundreds of times in a wide range of situations over the last five-plus years and not yet found a publishing home for.
I hope you enjoy the writing, and I invite you to share widely. Maybe we’ll find it a home together?
We are having a cultural moment—one which requires the wisdom of children to advance our common understanding.
Is a hot dog a sandwich? Is an elevator a vehicle? Is an emoji a word?
These are questions that start conversations, and that prompt insight, delight, and empathy. Thoughtful and joyful discussion is my purpose for the trio of books Is It a Vehicle?, Is It a Sandwich?, and Is It a Word? Like my published books (Which One Doesn’t Belong?, How Many? and How Did You Count?), these books assume that children are intelligent and creative, that they are brimming with ideas, and that they enjoy using their minds.
These new books have a history. My niece (now graduated with honors from Harvard and writing professionally) asked me the hot dog/sandwich question on a beach vacation when she was 8 years old. This simple question supported laughter and joyful argumentation for days, drawing in several other family members but never quite reaching resolution.
The question resurfaced in my online math teacher community on Twitter a couple years ago, where we began to catalog discussion and references under the #sandwichchat hashtag (which remains 100% searchable and delightful, although the medium itself does not). But in summer 2018, a friend and her 6-year-old daughter blew things wide open when Kassia (the mom) reported that they disagreed about whether an elevator is a vehicle.
Lulu (6) and I have an ongoing debate about “What makes a vehicle a vehicle.” She says, “Moves people and stuff from place to place.” She’s arguing hard for elevator and escalator as vehicles. She loudly announces “All aboard the vehicle!” as we get on elevators.
[This is] followed by a snicker because she knows I don’t think elevators are vehicles but I don’t have a good argument as to why!
The ensuing online discussion led me to write (with Lulu’s endorsement) Is It a Vehicle? and its cousins. Each book uses simple language and bold photographs, and has a common structure. We begin with an easy yes. (Is a dump truck a vehicle? Is a PBJ a sandwich? Is “hello” a word?), followed by an easy no (salad, flower, and the Mona Lisa, respectively). We return to an easy yes (airplane, turkey on wheat, palabra), and then to increasingly controversial edge cases (e.g. horse, smore, kapow) that probe the many corners of these concepts, of which we are usually unaware. In any case, we certainly don’t all agree, and the text makes this clear. “What do you think someone who disagrees with you might say about whether a tricycle is a vehicle?”
These books—and the conversations they foster—are less obviously mathematical than Which One Doesn’t Belong?, How Many?, and How Did You Count? but that doesn’t much matter for supporting children’s math learning. The ideas and practices are important, not what we label them. Mathematics is a discipline that depends on logic and definitions, but most of the time our minds work with images and gut instincts. As Daniel Kahneman demonstrated in Thinking Fast and Slow, it takes intentional provocation to engage the slow-thinking logical mind. These books are that provocation. We think we know what a vehicle, or sandwich, or word is, but we find our reasoning shifting as problematic cases arise. As a result, our implicit definitions become explicit and more clearly, well, defined.
Here is an example to apply these ideas to learning math. Young children will routinely state that “a triangle has three sides,” but then rule out a tall skinny triangle because it doesn’t “look right”. Here the tension between image and definition arises in children’s interactions with math in school, and the examples extend far beyond triangles to a wide range of mathematical objects—fractions, parabolas, functions, and limits are some well-studied examples. These books support parents, teachers, and children in moving back and forth across the line between image and definition without the anxiety that math in school (or math that looks like school) too often triggers.
Two triangles. Only one of them matches the image children develop in response to most geometry resources they encounter.
I have extensively play-tested these books. We had copies of Is It a Vehicle? at Math On-A-Stick at the Minnesota State Fair in 2019, where we had hundreds of vehicle conversations. In 2020, Is It a Vehicle? was the center of two invited (virtual) presentations at the National Museum of Mathematics. I have conducted joyous conversations about vehicles in classrooms, homes, and business meetings.
That my 8 year-old niece was delighted 15 years ago by the question of a hot dog’s nature, and that this same question remains a lively topic of discourse (e.g. on social media), speaks to the lasting power of these ideas. These questions are simple yet deep. They can inform our current conversations in which we seek to regain our understanding of truth, meaning, and empathy.
I look forward to an opportunity to share current drafts of these books with you, and to working together to bring joyful and liberating mathematical conversation to parents and children everywhere.
Sincerely,
Christopher