5 minute read
The Classroom
BY MELISSIA MASON
Brett LaFave Thinking Mathematically
Statistics with Discrete Math. The course title alone may seem daunting, but Math Instructor Brett LaFave is on a mission to guide students toward the true goal: thinking about the world in a way that is informed by a deep understanding of mathematics.
When he first prepared to teach Statistics with Discrete Math at Emma Willard School, Brett considered discrete math to be a fairly advanced category of mathematics for high school. What he discovered in the textbook was a series of skills that are vital in interpreting the plethora of information that bombards us.
Not every student has a positive feeling about math, sometimes presuming they’re simply not good at it. Brett has found that a focus on thinking mathematically can change that perception. “A field like logic or set theory looks different—no plus signs, multiplication symbols, or even that many numbers—but you’re still using the same critical reasoning skills,” he explains. “It’s a different language that students can learn, and it’s amazing how it allows kids to shine in the classroom.”
In the curriculum, students still build on the rules of algebra, look into probability, and delve into statistics, but Brett’s class allows students to get there from a different path. “I really love how taking the back door into traditional math curriculum allows more kids to thrive and show their critical thinking skills,” he enthuses.
In addition to traditional math skills, Brett’s focus on thinking mathematically has pushed Emma’s young mathematicians out of the classroom to see the real-world implications of what they’re learning. Through a connection with Emma Willard parent Kevin Lanahan P’20 ’23—a senior leader in corporate affairs and communications at New York Independent System Operator, Inc.—students have been thinking critically about decision-making, risk, and reward as it pertains to environmentalism.
Anne McEntee P’24—CEO of digital services at GE Renewables— also welcomed Brett’s class. Brett says of the visit, “We talked to several female engineers about their work to not only produce wind turbines, but also to handle data from wind and solar assets around the world.”
These conversations—like learning what happens when it’s not sunny in a certain part of the world, and what happens when it’s not windy, and what different perspectives on nuclear energy may reveal—are not necessarily subjects that are addressed in a typical math class. They can be eyeopening and challenge one’s world view. “Some of the things students think are true they should think deeper about and look at available solutions,” Brett notes. His students are faced with the question, “What’s the best way to balance conflicting challenges in the world?”
Brett’s perspective on the impact that math can have on our understanding of the world is backed by unique insight into math throughout history. “Math is a pure discipline that doesn’t necessarily evolve with time in the same way that other disciplines do. One plus one is always going to be two. But the discipline does grow,” he shares. Brett notes the evolution of an unsolvable mathematical problem: calculating the square root of a negative number. Mathematicians devised imaginary numbers to solve for the square root of negative numbers. A number of years later, engineers took the invention of those mathematicians and used imaginary numbers to describe how electrical fields and magnetic fields interacted. “I think that’s something that’s really amazing—math is a pretty static field, but it’s a leading
indicator of what’s possible in other fields.” Brett adds, “There’s so much that mathematicians have already produced that has the capacity to change the world.”
This capacity to change the world and our view of it is one thing that inextricably links Brett’s classroom with the Emma Willard School mission to educate future leaders who will serve and shape their worlds.
Although some find math to be unrelated to their personal real-world experience, Brett contends that wrestling with mathematics is a uniquely human experience. “For an aseptic discipline that often has almost nothing to do with humanity in the actual material, mathematics becomes all about how I relate to students and how they relate to me,” Brett notes. “It becomes about emotions and wellbeing. Our strongest positive or negative emotions can often be elicited from math.”
He goes on to explain that whatever a student is feeling any given day—whether anxiety or joy or frustration or hopefulness—is often amplified in the solving of a mathematical problem. A correct answer intensifies positive emotions just as missing the mark can heighten previously existing negative ones. “You go to more advanced levels of abstract thinking because you’re free of the complexity of the real world,” Brett says. “It pushes the intellect—to be purely in your mind—which can feel good when you figure things out, but horrible when you can’t.”
Brett finds that working through those moments of perceived failure can develop a skill set that has more far-reaching implications. “Many times, the only way that you can find a good approach when you’re struggling with a math problem is talking through it with a classmate or asking a question in class,” Brett explains. “I have gratitude for the students being brave enough to grapple with these abstract, complicated concepts.”
Brett reflects, “Really no human being in the world could do what we do in a precalculus class until relatively recent history. So it’s really amazing how much progress we’ve made as humans.” Brett tries to put this history in perspective for students, showing them that they are really tackling something that is extraordinary in the greater scheme of human history. “It’s really important to me that students feel recognized when they are willing to venture a guess even when they might be wrong. That takes some amount of courage, and it is the only thing that moves the classroom forward.”
In moving his own classroom forward, Brett is adding a new dimension of real-world application to the math curriculum by offering a class on financial literacy, a personal passion of his. “I feel very lucky that my parents talked about money,” Brett shares. “I understood how compound interest works and that you can’t wait until you’re 55 to start saving for retirement. How you are with money is as important as how much money you make.” He hopes to pass this knowledge on to his students, from teaching how college loans and taxes work to how jobs compensate you in different ways. “The more students can be free to make their own financial decisions, the better.”
In all ways—from solving challenges like environmental change to more personal concerns like wellness and finances—Brett hopes to encourage students who come through his Emma classroom to think, not just mathematically, but also critically.
