Changing the Way Students Think About Math

By Page Stites, Upper School Director & Math Teacher

When students go beyond learning rote computational procedures and learn math in these ways, they understand themselves as mathematical thinkers, and math becomes “curiously different and surprisingly engaging.”

“There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today’s students, get them excited about math, and prepare them for the future.”

-Jo Boaler 

I have a printed copy of this quote from Stanford University Education Professor Jo Boaler taped to the wall next to my desk. Although I’m now Field’s Upper School Director, I have been a math teacher for most of my career in independent schools, and I still have the pleasure of teaching a class at Field called “Mathematics & Modern Society.” My course is organized around a central question: “How do we use math to make decisions?” Behind this question lies the logic of Dr. Boaler’s quote - my students are exploring the “math of the world” and, in doing so, preparing for the future. 

Designed for 11th and 12th graders, the class explores its central question by studying a range of math topics that aren’t typically found in high school math programs. Drawing from data science, operations research, management science, and economics, students learn modern mathematical techniques such as K-means clustering, graph theory, linear programming, transportation problems, and even machine learning. Along the way, I challenge them to be reflective and think critically about the tools they are learning to use. In a recent assignment, students had to reflect on the data analysis technique they were employing—answering questions about its strengths and weaknesses—and consider what insights they were able to gain from the technique. 

Our current project, inspired by and supported with materials from Dr. Boaler’s amazing “YouCubed” curriculum, asks the students to collect and analyze both qualitative and quantitative data and then draw conclusions and communicate their findings in writing. The context for this work is another central question: “How do popular magazines represent a range of human skin tones across advertisements and articles?” To begin the project, students read articles and watched videos about the importance of skin tone representation in a number of fields: media, health care, the arts, technology, and AI programming. They also learned about the history of “colorism” and looked at the issue across multiple cultural settings from around the world. At the end of the unit, when they’ve collected and analyzed their data drawn from contemporary magazines, they will write an article to lay out their findings and make recommendations about skin tone representation, supporting their conclusions with their data analysis. I believe, like Dr. Boaler, that using math to explore and understand the world and important issues in our society like skin-tone representation and colorism gives students access to the “interesting set of ideas” and helps them understand math as a relevant and useful discipline to study. 

My math-teaching colleagues share these beliefs. In Advanced Algebra II, teachers Liz Chausse and Jake Hirsch are excited to launch a project where students will employ their mathematical modeling skills to understand the rising costs of college tuition. Students research four different colleges of various sizes and types and perform regression analyses to determine whether they think a linear, quadratic, or exponential function best represents the data and would best predict the cost of them attending college. Beyond the technical math learning, Jake and Liz have designed the project so that students also interview a family member, friend, or teacher about their own college experience and will also spend time with Field’s college counselors to discuss how college tuition, financial aid, loans, and scholarships work. Finally, students will communicate and justify their findings—an important and real-world last step. Liz and Jake have thoughtfully made the context of learning just as relevant as the content—engaging students with the “math of the world” and helping prepare them for the future in meaningful ways.  

In Gil Gallagher’s 6th grade “Integers, Operations, and Number Sense” (IONS) class, students learned all about how to calculate the area of different shapes earlier this year. Rather than simply memorizing formulas for regular shapes, Gil leaned on the work of Dr. Boaler and engaged students to understand area as a concept. They spent time discussing and debating how to find the area of irregular shapes, learned how to think about decomposing and composing shapes, and developed and shared multiple mathematical strategies for computing area. To create a real-world connection that would both help them understand the relevance of the math and engage them in solving an actual real-world problem, Gil then challenged his students to help with the planning for ordering new classroom furniture. The goal was to identify the shapes and configurations of chairs and desks that maximize space and collaborative learning. Impressively, this context for learning was not artificial as the work of the 6th graders actually informed discussions among the school’s leadership team about the ideal configurations of different-shaped desks for our classrooms. 

Dr. Boaler’s work inspires me as a math teacher and an academic leader. I’ve used her materials and read her research. I have also seen the incredible benefits to students that come from the work my colleagues and I have done to unlock the world of interesting and engaging mathematical ideas she refers to in her quote. Beyond math learning, which is, of course, important, I have seen students change the way they think about math and, even more powerfully, start to think about themselves differently. When students go beyond learning rote computational procedures and learn math in these ways, they understand themselves as mathematical thinkers, and math becomes “curiously different and surprisingly engaging.” I’m grateful for Dr. Boaler’s work and especially to my math colleagues at Field for embracing this approach, and I know that it benefits our students most of all.