Geometry

Math is one of the foundational subjects in school that many students either hate or love. Here at TEEN DAY, teachers like Amanda Gray are pushing boundaries and encouraging students to see the subject in a new, refreshing light. One that isn’t so scary.

In her class, students are learning proofs and puzzle-solving. They’re doing parallel line proofs, congruent triangles, properties of triangles, and coordinate geometry. While there is still a good amount of calculator usage in geometry, it can be a big shift for students because it’s no longer about getting an answer, but rather knowing and explaining how that answer is true.

“She’s a good teacher— she explains things well and is very helpful with classwork and also makes it fun.” – Eloise L.

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Classes are structured so that students get a mix of lecture, group work, class discussion, individual practice, and sharing. The mix of formats leads to various conversations of approaches to a problem or proof. Students can see things from multiple perspectives and can benefit from hearing how other people approach or see the same problem. Students are sharpening their individual critical thinking skills as well as building their confidence when asked to share aloud.

Additionally, students are applying what they’re learning in the classroom to real-world things. Over winter break, the students were asked to complete a “construction art project,” a collection of geometric shapes that were turned into artwork. Geometry doesn’t have to solely be about theorems and proofs, and instead can be used for various, fun designs. (See picture to the left and more pictures below.)

“…Amanda always makes math fun to learn. As someone who isn’t super math oriented, I’ve found that throughout algebra and geometry, Amanda has made the learning process quite a lot better than other experiences I’ve had.” – Addi F-W

Amanda Gray really enjoys math and science and works at Tompkins Cortland Community College (TC3) as a tutor in those subjects. In her free time, she works with TEEN DAY to provide excellent instruction on a wide range of subjects within the math and science fields. She wants to share her love of math with her students and help them to see the joy in the subject.

Overall, students are thriving in this collaborative setting and enjoying what they’re learning. Amanda’s instruction goes beyond that of the traditional classroom, with students sitting quietly in their seats, memorizing steps. But rather, her teaching style engages the students critically in the various stages of a problem, creating a unique and welcoming environment.

“It’s a classroom where students aren’t just doing geometry, they’re talking it through, questioning it, and starting to think like real mathematicians.” – Amanda Gray

Geometry is a part of a three-year rotation for lower-level math. First, Algebra I is offered, then Geometry, and finally Algebra II (which has a dual enrollment option). In 2026-2027, Algebra II will be offered, and the year after that, the cycle will reset, starting with Algebra I.

Calculus (Dual Enrollment Offered Through TC3)

Calculus is commonly known as the entry point for upper-level mathematics used in college and various jobs. It lays the foundational concepts used in many more advanced practices.

“I am a visual learner and Nick makes good use of the three (!!) whiteboards we have at Teen Day to show everything either written out or as a picture; I think that helps everyone in the class understand the material better.” – Juliet A.

At TEEN DAY, Calculus is offered as a dual enrollment course, meaning students may opt into earning college-level credits while simultaneously earning high school credits. If students choose this option, they may save time and money in the future, in addition to increasing their college readiness.

Regardless of a student’s decision to earn college-level credits, they’re receiving the same education as all other students in the class. In the first half of the course, students focused their efforts on derivatives— the rate of change of a function in relation to a variable. Currently, students are learning about integrals— a tool used to determine volumes, areas, and other quantities. The core principle of calculus is the connection between those two concepts.

Nick LaVigne, the instructor for this class, has a background in applied mathematics and currently works as a machine learning engineer at Ursa Space Systems. His work primarily focuses on Synthetic Aperture Radar satellite imagery. He is more than qualified to teach this course and get students interested in calculus.

“I’m trying to frame the course in a way that points to the wonder and beauty of mathematics rather than just a handful of problems to solve.” – Nick L.

“One fun thing is that during some classes we watched videos showing some interesting applications of what we’ve learned, and we also got to pick one math themed novel to read and write a book report about to present by the end of classes.” – Asher V.

He structures his classes so that students can work on interactive lectures, homework, quizzes, and various other workshops while at TEEN DAY. At home, he encourages students to explore and play around with online resources to understand complex subjects better, but doesn’t allow students to use these resources or a calculator on graded work, such as tests and quizzes. This also increases the accessibility of his class. Calculators (specifically, the TI-84) are expensive, and with access to more powerful tools online, there is no need to purchase one.

Lastly, it is important to note the math schedule at TEEN DAY. There are two distinct levels of math offered at a time. Each has a three-year rotation cycle. Calculus is part of the Upper-Level Math rotation and consists of Precalculus, Calculus, and Statistics (the latter two are offered for dual enrollment through Tompkins Cortland Community College). This year, Calculus is being offered, which means next year Statistics will be offered, and Precalculus the year after that.

Courses are offered in this way so that students have more academic options available to them. They’re not confined to a specific mathematical advancement, and can take the courses that make the most sense for them. Having a three-year cycle allows for more flexible scheduling. It also allows students to take two separate math classes at a time (an Upper- and Lower-level course), if they choose.