Mathematical Play

I have recently fallen in love with the book Mathematics for Human Flourishing by Francis Su (2020). If you haven’t read it, go get it now. You won’t regret it. The premise of the book is that mathematics is core to our humanity, and that engaging in the world through a mathematical lens can help us experience the world with our full humanity, as well as develop ways of being that will support us in all areas of our lives. 

Each chapter of the book is focused on a specific human desire, desires which Su argues should be central to the way we approach the teaching and learning of math. The desire I keep returning to is that of play. Su points out that from the very beginning of each human’s life, we make sense of the world through play, that, “Play is a deep human desire, and it is a mark of human flourishing” (p. 49). Why then are so many of us taught to see math as a “serious” subject, one devoid of play and exploration, focused on memorization, reproduction, and efficiency? Why do we limit math play to routinized games or one day of the week for “math centers”? How might we find opportunities for mathematical play in daily lessons, or better yet in daily life, both within the confines of the classroom and beyond?

Math play is deeply connected to patterns and questions - when we approach the world through the lens of expecting and looking for patterns all around us, and we are willing to ask questions about those patterns, we generate ideas and problems that we can play with. A few months ago I joined a third grade class on some math fieldwork they participated in during their unit on area. The target, or objective, of the fieldwork was simply beautiful: I can explore and wonder about math in the world! What a way to set students up for engaging in math through the lens of play. 

Students visited a local community garden and explored with the goal of thinking about and directly experiencing how a gardener might use the concept of area in planning for, planting, and maintaining their garden. The excursion involved very little direct teaching - a basic overview of the garden, setting some ground rules around where to walk and what to touch/eat/leave alone - but other than that students were given some guiding questions and the freedom to explore, observe, and generate questions of their own. 

Students began by taking a lap around the garden and reflecting on the questions “Where do YOU see math in the garden? What do you notice? What do you wonder?” These students were supported both in observing patterns and asking questions about what they observed. Su writes, “Mathematics makes the mind its playground. Doing math properly is engaging in a kind of play: having fun with ideas that emerge when you explore patterns, and cultivating wonder about how things work” (p. 50). This teacher opened the door for students to play with the math around them! 

From there, students were given the opportunity to select something from the garden to measure the area of, and the tools to do so (rulers). As a teacher of young children might expect, this yielded a wide range of area measurements, from the pragmatic students who measured the area of a small plot and began thinking about how many plants of different types that plot could hold, to those who wondered about the area of a single flower, or the wasps nest all were advised against getting close to that was flourishing in the corner of the garden shed. As teachers, we might consider what students were learning based on what they chose to measure. The students finding the area of rectangular plots had the opportunity to directly practice the 3rd grade standards under the bundle 3.MD.C, but what about students attempting to measure the area of a cosmo flower? What were they learning? What were they practicing?

You might be unsurprised to hear that these students did not successfully find the area of a flower, and the questions generated by these students, while intriguing, were difficult for a third grade student to answer. However, these students were supported in, and exemplifying the spirit of, mathematical play. As Su encourages, “Build a community around you –  in your home, classroom, or friendship circle – that values asking interesting questions (p. 63).” He then goes on to warn, “As a parent or as a teacher, you may find this scary because the activities may generate questions that you can’t answer. But that is part of modeling who an explorer is: you won’t always know the answer, but you will know how to highlight and cultivate the virtues, built through math play, that will help others find the answers they are looking for” (p. 64). 

Although these students may not have successfully found the area of something in the garden, they undoubtedly met that day’s target, I can explore and wonder about math in the world! Through mathematical play, they are building the virtues that will support them and others in answering intriguing and difficult questions in the future, mathematically and otherwise. 

Interested in trying out math fieldwork with your students? Check out this folder with some awesome resources! Thank you to Claire Adams, 3rd grade crew leader at Downtown Denver Expeditionary School, for creating and sharing these resources with us!

Much of this math fieldwork was inspired by the book “Math Trails” by Mary Margaret Shoaf, Henry Pollack, and Joel Schneider (2004). If you’re interested, check out this excerpt from the book

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