BRATTLEBORO — Many people, when they hear the word “calculus,” immediately make excuses about how they never understood math to begin with.
Not so the 18 students in Kevan O'Donnell's Advanced Placement Calculus class at Brattleboro Union High School.
On May 28, these students participated in “Theorems Out Loud,” an event during which each one recited from memory a calculus theorem to an assembly of their peers in the BUHS auditorium. A theorem is a general proposition not self-evident but proved by a chain of reasoning, or a truth established by means of accepted truths.
In a recent interview, the three top winners of the contest and their teacher reflected on the experience.
Atreyu H. Singleton-Spencer, who came in third, recited “Limits at Infinity.”
He became interested in math in sixth grade at Newfane Elementary, after his teacher Gary Keiser pointed out that he was good at it.
“This was a very different type of assignment,” Singleton-Spencer said. “I listen to a lot of music, so I looked at the theorems available and picked one that naturally fell into some sort of rhythm.”
Jonah Goldenbird, who has taken an accelerated schedule of math classes since eighth grade, recited “The First Derivative Test.” He earned second place.
“I looked at a four-stanza theorem,” he said. “I added some words to it to beef it up and make it even more confusing. Memorizing wasn't too hard because of the parallel phrasing of the stanzas. It was fun. We got to dress up, and we were in a room with air conditioning on a hot day.”
At this point, O'Donnell interjected that the theorems this year were accurately worded and recited with their integrity intact.
Naina Tejani, an exchange student from Pakistan, won first place. She recited “Derivative of Inverse Functions,” not only in English, but also in Urdu, her native language.
“Mr. O'Donnell gave us a list of theorems to choose from,” she said. “The popular ones were taken quickly, so I remained with the one he gave me. [This contest] was a concept I never heard before. I wanted to do my best.”
Tejani, who has always enjoyed math, thought about how to make the theorem interesting to the audience.
“I've grown up with stories that begin 'Once upon a time,' taking you into another world, so I told the story of function f and function g. I also wanted to make rhymes in it to make it fun.”
O'Donnell, who has taught AP Calculus for the past several years, said serving as score keeper for the BUHS Poetry Out Loud contest, which began five years ago, inspired him to think about how to do something similar in math.
Poetry Out Loud is a national recitation competition which encourages students to memorize and recite great poems. In Vermont, schools organize local competitions. School winners then compete in regional semi-finals and the state finals. The Vermont winner competes with other state winners at the national level in April in Washington, D.C.
“I was jealous of Poetry Out Loud,” O'Donnell said. “It was such a full spectrum of participants, from those students who clearly enjoy poetry and performing to those who don't really, but for reasons of their own, go through with it anyway.
“I look for every excuse I can find to bring poetry and math together,” he continued, “so last year after the AP exam in early May, when I was looking for a project for the class, kind of spur-of-the-moment, I put 'Theorems Out Loud' on the course calendar. I'd had those students for three years in a row, and they were very willing to go along with the idea.”
The students that first year “really got into it,” O'Donnell said. “A talented group of performers and athletes, they were ambassadors for the love of math, and they set the bar very high for this year's group.”
O'Donnell used the same performance evaluation criteria as Poetry Out Loud: physical presence, voice and articulation, dramatic appropriateness, level of complexity, evidence of understanding, and overall performance.
“I talked with the Poetry Out Loud people at the state about using their materials, and they were very encouraging,” he said.
O'Donnell said he has searched online to see if anyone else anywhere is doing something like this, and as far as he could find, his idea is unique to BUHS.
Reciting theorems has a certain amount of humor in it, O'Donnell pointed out.
“Take 'Jabberwocky' by Lewis Carroll, for example,” he said. “There was a mathematician using voice and language patterns to communicate something.”
The students said they learned more than their theorems.
“This was a different medium for learning math,” Singleton-Spencer said. “I learned stage presence.”
“We learned how to share,” Tejani said. “We were supportive of each other, and it was a more interactive manner of working. Everyone was nervous.”
“It was a lot of pressure,” Goldenbird said. “I play trumpet in band and sing in chorus, and I was in this year's musical, Grease, but I learned more about how to quell stage fright. Going up to the mike, I was hiding the leg shakes, thinking let's not make this visible.”
Having all 18 students reciting up on stage was a major victory, O'Donnell said.
“And what a wonderful display of support from peers,” he added. “I've always been impressed by how appreciative assembled audiences are at BUHS. Imagine everyone whooping and hollering after you've just recited the 'Second Fundamental Theorem of Calculus.'”
The greatest value of this project has talented mathematicians contradicting the bookish stereotype, O'Donnell said.
“This whole event shows the awesome brevity of mathematical symbols,” he said. “It's uplifting to the field of mathematics at BUHS. Math becomes more of an avenue that people might choose. They see that all you have to do is enjoy it.”