Classroom Happenings: Mathematical Identities

Athletic hype videos, mathematics, and innovation: Combine these, add a challenge (and some fun), and you have an equation for learning and ingenuity. 

In Honors Precalculus, students are working on the most difficult topic of the year:  establishing trigonometric identities. As Upper School Mathematics Teacher Scottie O’Neill explained, “Establishing identities is when a statement is proven to be true by making logical jumps using math properties rather than numbers or a calculator.” In mathematics, a property is a characteristic that always remains true. 

But how do teachers convey these complicated concepts? 

“Inspired by the creativity on display in Steward’s athletic hype video and in a highlight reel featuring Curtis Blair ’23 (and created by Charlie Ventura ’23), I had the idea for students to make math highlight reels that focused on establishing mathematical identities … but I had no idea how to bring the assignment to life,” said Ms. O’Neill. She reached out to Middle/Upper School Librarian Crystal Hamlin and the two teamed up to create a lesson plan, plus an example of a math highlight reel for students to use as inspiration.

Working in small groups, Ms. O’Neill’s students filmed in the library after working on four challenging math problems in class. The assignment  —an example of Steward’s commitment to providing a curriculum in which innovative problem-solving is key — tasked students with using technical math vocabulary to explain how they solved the problems.

“These problems involved some of the most difficult-to-prove trigonometric identities I could find,” shared Ms. O’Neill. “I wanted students to explore the math problems together. I believe that if you can talk about something, you can think about it and work through it.” After watching the students’ entertaining highlight reels in class, Ms. Hamlin thought that an Oscars-style awards ceremony was in order, and the QEDtys were born. 

“‘QED,’ Latin for quod erat demonstrandum (‘what was to be demonstrated’), is written at the conclusion of a text to signify that the author’s overall argument has just been proven,” explained Ms. Hamlin. She added, “Students got a lot of satisfaction saying ‘QED!’ whenever they finished one of the math problems in this assignment.” Faculty and staff were invited to vote for their favorite videos. 

Joey Burmeister ’26 said that the project helped him learn how to approach complex trig problems differently. 

“Before starting this assignment, it would take me quite a bit of time and thought to figure out the correct steps to completing them,” he explained. “After practicing and collaborating with my group members, it came more naturally to my mind to look for factoring possibilities, multiplying to get common denominators, and rewriting the functions. I most enjoyed the filming process!”

At the awards ceremony on April 18, the winners were announced in the following categories: Best Video Effects (Joey Burmeister ’26, Justin Fratkin ’25, and Grayson Burke ’25), Best Editing (Nathan Gu ’25 and Jacob Gallagher ’26), Best Mathiness (Jordan Solomon ’26, Dylan Griffin ’26, and Marc-Michel René ’25), Most Cheesy (Charlie Cram ’25, Christian Vanderbeck ’26, and Meira Boyle ’25), Most Funny (Linkin Rose ’26, Ella Grace Saunders ’26, and Caleb Morrison ’26), Overall Most Hype (Linkin, Ella Grace, and Caleb), and Math Reel of the Year (Linkin, Ella Grace, and Caleb). Way to go, Spartans!