Gun control. COVID-19. Incarceration rates by race. Degrees earned by gender. Are these topics you'd expect from a typical precalculus assignment? Mr. Andrew Otero's Upper School precalculus class is anything but typical. He has a passion for challenging his students to think independently, to form data-based arguments about topics that matter, and to develop habits of mind that reach beyond math. As data literacy becomes an increasingly valuable skill, Mr. Otero's precalculus classroom is a practice ground for translating big mathematical ideas into real-world solutions.
Putting Theory Into Practice
Math is more than theory. In application, it's necessary to our daily lives. To ensure that his students make the connection between theory and practice, Mr. Otero structures his classes with project-based assignments that explore fundamental concepts within meaningful context. This fall, he presented his precalculus students a quarter-long assignment to develop a topical argument based on mathematical modeling. Taking the place of many quizzes and tests, this bigger project inspired students to ask insightful questions, challenge the validity of their ideas, and vigorously tackle unfamiliar problems.
Clear Goals for Deep Discovery
Before collecting and manipulating the data, precalculus students had to choose a topic of personal interest, defend their choice, and articulate a clear hypothesis of what they hoped to prove. Every step of this project challenges them to be curious about their topic, view it from multiple perspectives, test their assumptions, and systematically evaluate data toward a logical, well-researched conclusion. A selection of student topics includes:
The Effect of Driving Distances on Top Ten Placements in the PGA
Incarceration Rates and Race in the U.S.
Modeling the Number of COVID-19 Cases Surrounding the 2020 Sturgis Motorcycle Rally
The Relationship Between Social Media and Depression
A Call for Gun Reform in the U.S.
Marijuana Convictions and Race
The Electoral College System: Useful or Antiquated?
Georgia Elections Results Affected by Urbanization
Exponential Growth of Home Prices in Maryland
Increase of High Tide Height and Sea Level Rise Caused by Climate Change
Population Growth in the U.S. and Overcrowding in Schools
Modeling the Data
Applied calculus is a way of solving real problems with math. It includes mathematical modeling techniques used by professionals in an array of industries from engineering to economics. Using data from the past, models can represent just about anything in the tangible world, allowing us to make reasonably accurate predictions about future outcomes.
“Mathematical models are ubiquitous, providing a quantitative framework for understanding, prediction, and decision making in nearly every aspect of life, ranging from the timing of traffic lights, to the control of the spread of disease, resource management, and sports. They also play a fundamental role in all natural sciences and increasingly in the social sciences as well.” — Harvard University, 2007
For this project, students used log-linear regression, linear regression, and exponential regression models to represent data collected from vetted, reliable sources of their choosing, with approval from Mr. Otero. They assessed whether the data could be represented with each model to either support or debunk their hypothesis. Rather than making assumptions based on anecdotal evidence or popular beliefs, our students are learning precise methods to understand our world and develop data-based arguments for future change.
Communication Is Key
The best analytical problem-solving has little value without the ability to communicate it to others; aptitude for writing clear, concise, and accurate reports is as important as the analysis itself. For the final phase of the project, students compiled their data, regression model formulas and charts, and analytic work into a formal written report to either assert or disprove their hypothesis. Much more than "showing the work" of math, the formal report helps students synthesize every step of the process, consider the larger implication of their findings, and prepare for the type of work expected in higher education and the professional realm.
More Relevant Than Ever
Research-based mathematical modeling is a powerful way to teach students how to use data — it has far-reaching applications and can be used to solve high-stakes problems. We are currently in a global health crisis in which mathematical modeling is used to make critical decisions that affect us every day. Projects like these teach our students to think critically and use their academic mastery to envision a better future.