Subject Spotlight: Math @ DA
Story by Dylan Howlett | Photography by Kate Auger and Dylan Howlett
If anxiety occupies the narrow divide between fear and desire, then math likely isn’t too far away. Every student who has ever walked into a math class has wanted so desperately to succeed, to recall the correct strategy, to navigate a vexing problem with conviction. What stops a math student from finding that success is both legend and nightmarish. The tangle of word problems, the nerves of sharing a solution in front of the whole class, the challenge of internalizing skills from a previous grade level as new skills come hurtling along at high velocity. The trick, it would seem, would be to do as much math as possible. But how does rote practice help moral, happy and productive students confront real-world issues?
The answer is simple at Durham Academy: For one, prioritize conceptual understanding. “It’s not just, ‘Can I set up the equation or the algorithm to solve the problem?’” said Kristen Klein, associate head of school. “It’s, ‘Why am I doing that? What are the relationships between the numbers that I’m understanding? And let me look at four different ways to solve a problem so I really understand what’s happening conceptually.’”
For another, offer choice. “One of the things that’s really hard about math is that sometimes math struggle turns into, ‘I don’t like math. I’m not a math kid,’” Klein says. “Part of what we’re always trying to look at is how we provide options to students to get to that ‘just right’ level of challenge, but also to make those options malleable.”
The Lower School is now in its sixth year of the Bridges curriculum, which the Preschool has also phased into its instruction. The Middle School remains as unapologetic as ever about preparing students for the rigors of higher-level math. And at those higher levels, soon-to-be graduates in the Upper School aren’t slogging through antiquated textbooks: They are, like Jack Vail ’24 and his classmates in Advanced Mathematical Modeling, preparing for something far more lasting than an assessment.
“A lot more thinking,” Vail said, “and a lot less doing.”
Over the course of a week, the Marketing & Communications team visited four classrooms — one in each of DA’s divisions — to see our math students, teachers and curricula in action.
Welcome to Math at DA. We promise there’s no reason to be anxious.
Kindergarten
Sloan Nuernberger & Ashlee Bailey’s Classroom
There are few better places to see a preview of the Bridges curriculum — or its premium on individualized, hands-on learning — than Sloan Nuernberger’s classroom on a Tuesday afternoon. After overseeing choral counting and a human graph activity, Nuernberger releases her students to choose from one of five “Math Workspaces.” Students select their preferred activity within groups of no more than four, who engage themselves and each other with minimal direction required — and even fewer parameters provided.
Some students use polydron sets to create houses and other small structures, while others snap together Unifix cubes to arrange their own colored patterns. The objective of the lesson, Nuernberger said, is simple: Allow students to explore manipulatives, which serve as a tactile and conceptual staple of Bridges in the Lower School. The impact is far more profound. As they build, rebuild, imagine and reimagine their tiny creations, the Pandas embody the most elemental “Transfer Goal” that all DA math students will reach during any of their 13 levels of math: “recognizing, appreciating and utilizing math as a universal language.” It is just the beginning, Klein says, of lifelong habits.
“We want them to be able to solve problems using math,” she says. “That’s what we want at the end of the day. And to be able to do that, the word ‘transfer’ in education-speak means being able to transfer my skills and understanding to a novel situation, to a new situation that I haven’t seen before. When we design our curricula and approaches, that’s what we’re going for. How do we get to the point where our students can demonstrate that transfer?”
Third Grade
Amanda Dolan & Ana María Enke’s Classroom
Discovery and sense-making begin in Amanda Dolan’s third-grade measurement lesson the moment she hands her students — known as the Dragons — a set of rulers and tape measures. “What do you notice?” Dolan asks. Preliminary answers trend toward the aesthetic: The rulers are transparent, they came from the Lower School’s Math Learning Center and they’re marked “3D” to indicate Dolan’s classroom. But Dolan pushes them further. She implores them to think like a mathematician. One student says he notices 12 inches and 30 centimeters are both denoted on the ruler. “Which is larger?” Dolan asks, and a rousing mathematical discourse ensues.
Within the next five minutes, the Dragons tackle a host of curiosities. Which is larger: 12 inches or 30 centimeters? How can we test whether 12 inches is larger than 30 centimeters? How do we use a symbol to show that one measurement is larger than the other? When would we use a ruler, and when would we use a tape measure? This last question prompts Dolan to remind her students of lasting mathematical mindsets: After one student says he would use a tape measure to determine the width of any round object, Dolan says to always keep precision and accuracy in mind when determining the best tool to use.
It’s the perfect catalyst for the lesson’s culminating activity, a “Length Scavenger Hunt.” Students pair up, collect a handout and try to match six different lengths — measured in centimeters — to items located around the classroom. Before they fan out, Dolan emphasizes students need to find at least six measurements, a nod toward differentiated instruction that allows students to complete work at their own pace. But eagerness and excitement prevail, and the average pairing zips around the room with inventive suggestions for what to measure next.
One student asks Dolan if they can measure the perimeter or circumference of objects. A few pairings bend down on the class carpet — a playful, accurate map of the United States — to measure the lengths of state borders. The activity, which one student would later describe to the whole class as “challenging,” serves as the precursor for the next day’s lesson, when students will add the measured lengths together. As her room fills with the buzz of students thinking like mathematicians and testing the limits of precision, Dolan smiles.
“It’s such a fun way,” Dolan says, “to learn math.”
Pre-Algebra
Kim Aitken’s Classroom
You would be forgiven if you walked into Kim Aitken’s Middle School math classroom and thought you made a wrong turn along the way. During a recent 60-minute lesson, Aitken made no fewer than five references to the Upper School.
“This is the year,” Aitken says to her Pre-Algebra classes, “where I’m transitioning you from lower-level math to higher-level math.”
As the complexity of the content ratchets up, Aitken says she prioritizes reducing the math-based anxiety that Middle Schoolers invariably carry. While she expects every student to solve a problem on her SMART Board by the conclusion of each class period, Aitken never forces a student to do so until it’s necessary. She’ll sometimes privately help a student correct a mistake before they have to share out with the whole group.
On this day, as students toggle seamlessly between direct instruction and group practice, Aitken oversees what she calls a “boot camp lesson” on the order of operations. The mood in the room veers toward anticipation, not dread, as Aitken reinforces the most granular details of simplifying expressions — and does so with an eye toward greater challenges in the Upper School.
Jake Fox ’29 asks whether he could use a dot to represent multiplication while simplifying exponents. “In Upper School, the dots become less and the parentheses become more,” Aitken says. Aitken returns to the SMART Board and points to an expression in the numerator. “Kids in calculus still make this mistake,” she says. Later, she pauses while adding negative numbers. “In the Upper School, they’re going to tell you to write one symbol,” she says.
With three minutes remaining in the class period, Aitken pauses to give students a chance to start their homework. The problem set contains practice from the day’s class — and, of course, at least one accelerated algebra question. Upper School, after all, isn’t that far away.
Advanced Mathematical Modeling
Forrest Hinton & Jarrod Jenzano
Freedom. Imagination. Solving real-world problems. Upper School students used these phrases Tuesday morning — along with “less teacher-guided and more student-driven” — to describe Advanced Mathematical Modeling, which started as an Upper School club and became a semester-long course this fall with support from the Strategic Vision’s Innovation Journey Fund initiative. The charge of the class replicates that of the club: Take a real-world phenomenon and use math to devise a real-world solution. On this day, co-teachers Hinton and Jarrod Jenzano — who co-founded the original club in 2022–2023 — present four groups of students with two of the most intractable conundrums in politics: redistricting and the Electoral College.
Two teams take on redistricting. They are tasked with defining “compactness” for North Carolina’s 14 congressional districts. The teams must abide by basic societal parameters — they can’t, for instance, flout the Constitution — and basic mathematical principles. One team compares the perimeter of a circle to any other given shape in their pursuit of compactness. Another uses ratio work and spreadsheet math to compare their areas of jurisdiction to Supreme Court guidelines. Two computer programs — DistrictBuilder and Districtr — allow the groups to draw their districts and test their assumptions.
The other two teams investigate an alternative to the winner-take-all nature of the Electoral College. Hinton and Jenzano once again provide helpful guardrails: Students can’t forsake the system altogether, and they can’t violate the Constitution. Both groups test systems in which each presidential candidate would receive a proportion of a state’s electoral votes based on their share of the popular vote within a given state. They apply their new formula to the 1992 and 2016 presidential elections to determine whether a different system would have produced a different outcome. One group’s analysis yields a three-way runoff in 1992, and a victory for Hillary Clinton in 2016. The work will culminate at the end of the week in the form of presentations to the rest of the class.
“You have to tackle a huge, complicated problem and use math from different courses, or math that you don’t even know,” Hinton says. “That’s the part that makes it a culminating experience. They have to ask their own questions, do their own research and choose what they can use.”
Mathematical Modeling also offers a peek into the approaching slate of Advanced coursework in 2024–2025, when DA will fully replace Advanced Placement classes with internally designed, rigorous curricula. Within the Upper School, students will still have the opportunity to take traditional math courses, particularly if they need those offerings for careers as physicists or engineers. But the promise of “just right” will prevail in the form of multiple pathways, and abundant choice, for students who want real-world applications.
“We have thought of the pinnacle as Multivariable Calculus,” Jenzano says. “Now that might not be the goal. If somebody is going into engineering, you probably need it — but if you’re not, then you need some other ways of thinking about things. That’s what we’re trying to inculcate.”
This is one of several Subject Spotlights (in-depth looks across all four divisions of DA) published during the 2023–2024 academic year. We hope this series provides a glimpse into the everyday brilliance — no matter how small, fleeting or simple it might seem — that has come to define our kids and teachers. More subject spotlights:
And if you can't get enough, you can walk in the shoes of DA students with our Day in the Life series, which captures the ordinary and extraordinary moments within each of the school's four divisions: