Problem Solving and Posing, a mathematics elective for Hewitt seniors, explores the role of math in our culture and how we can change the fixed mindsets people often have about their mathematical abilities. As we think about how we can help move people away from the idea of “You need math!” and toward the concept of “Math needs you!” my classmates and I participate in a variety of activities that are designed to make math feel less daunting, more fun, and more creative than many people in the United States currently understand it to be. We spend a lot of time solving new and challenging problems, and because none of us (not even our teacher, Dr. Benjamin Dickman) knows the answer to many of them, our class becomes less of a pressurized race to find a correct answer and more of a collaborative activity in which everyone works together to come up with solutions. The way we study math in Problem Solving and Posing — as something that can be enjoyable, tangible, and accessible — reflects how we hope the rest of the world might come to see the subject.
One powerful way that we have explored bringing conversations about math to a wider audience is through Sidewalk Math, a movement designed to make math more inviting by taking problems that might look daunting in a textbook and reimagining them using different colors, shapes, and phrases. These more exciting and visually appealing problems are then posed in chalk on the sidewalk so that anyone passing by can stop to solve them. Dr. Dickman was introduced to Sidewalk Math at a math education conference in 2018. “I was struck by the ways in which Sidewalk Math immediately appealed not only to participants at the conference, but also — after we went outside to create sidewalk math of our own — to people walking by who became interested and willing to engage with math problems that, presented in a different context, might have steered folks away. I was eager to bring these ideas back to our class as a way of expanding student understanding of the spaces in which we do mathematics as well as a vehicle through which we could explore both the solving and posing of novel mathematics problems.”
At Hewitt, we started our unit by looking for Twitter posts marked with the hashtag #sidewalkmath, and categorizing the examples we found to create an encyclopedia of sidewalk math problems organized by the type of question being posed. Most of the problems we found had simple setups that invited people to look for patterns or make comparisons as they considered how to find potential solutions. For example, a common type of Sidewalk Math problem involves four boxes filled with numbers or objects and invites passersby to answer the question: “Which one doesn’t belong?” In problems like these, any three of the four numbers or objects can have something in common that will make the fourth item seem like it does not belong. By thinking through how each of the items might “not belong” with the others, we get to consider the possibility of having multiple right answers. Many Sidewalk Math problems do not have obvious right answers that one needs to find, but instead invite participants to think about how deciding on solutions to math problems is a matter of being able to justify and clarify one’s own reasoning.
After getting to know the various types of problems, our next step was to make our own to draw on the concrete in Central Park. We also developed questions to encourage problem solvers to focus on their observations about our problems rather than finding the correct answer. Reflecting on why posing our own problems was a critical element of our Sidewalk Math unit, Dr. Dickman remarks, “Too often students get all the way through their K-12 education, and sometimes even beyond, without ever having the opportunity to create a mathematics problem that feels like their own. Students in other courses — whether they are formulating a thesis for an English paper or deciding how to express their ideas using paint and a canvas — have the chance to feel generative and creative. Yet, math classes all across the United States are leaving children and young adults with the sense that mathematics does not, and cannot, belong to them: that math problems all come from some higher authority, such as textbooks, teachers, or pre-written curricula. Sidewalk Math is an opportunity not only for students to learn more mathematics, but also to feel a sense of ownership over the mathematical ideas that they are generating as a part of this process.”
After a few weeks spent peer reviewing and finalizing our work, our class walked to Central Park with boxes of chalk. We chose different pinks, greens, and blues and started drawing our own unique problems as well questions such as “What patterns do you notice?” and “What did you realize while working on this problem?” to get people thinking about the ideas our problems provoked in their minds.
My own Sidewalk Math problem involved an incomplete Fibonacci sequence and asked people to notice patterns in order to figure out what numbers might come next in the sequence. The way that I posed the problem made it appealing to children, who could make observations about the pattern itself (for example, any set of two consecutive numbers in the sequence can be added to equal the number after) and to adults, who might look beyond the pattern of the sequence to think about its functionality in nature (for example, spirals related to the Golden Ratio). Walking back to school, one of my classmates spotted people trying our problems and we excitedly stopped to watch. It was mostly adults who paused at our drawings, which was nice to see since, at first glance, the colorfully-written problems might have looked like they were only for children. Seeing adults interact with our Sidewalk Math made me feel like we had achieved our goal of designing difficult problems that were inviting to everyone.
The Sidewalk Math project helped me see how creating math problems that are appealing to the eye can attract so many more people than those same math problems might when they are written dryly in textbooks or on blackboards. I think that this concept applies to many realms of mathematics education. We realize that the concepts we study in our Problem Solving and Posing course have the potential to make people feel anxious or overwhelmed with the idea that math is not for them. But, as Sidewalk Math demonstrates, when those same concepts are presented as colorful drawings on the sidewalk without any of the expectations often found in math classrooms, they become more attractive and feel more accessible. Instead of accepting that people must believe math is difficult or boring, my classmates and I are learning that, by highlighting the simple elements that make up complex mathematical structures, we can help change the way people from a variety of backgrounds experience and learn mathematics.
Interested in Learning More?
To learn more about the Sidewalk Math Movement and how to make math feel more accessible to everyone, the author and her class recommend the following resources:
- Sidewalk Math at Lesley University
- Play With Your Math
- Sidewalk Math Blog Post by Brian Palacios
- Math Trails by Mary Margaret Shoaf, Henry Pollak, and Joel Schneider, The Consortium for Mathematics and Its Applications (COMAP)
- Cultivating Mathematics Identities In and Out of School and In Between by Dr. Erica Walker via Journal of Urban Mathematics Education
- On Mathematical Problem Posing by Edward Silver via For the Learning of Mathematics