High School Senior, Gilee Hershco recognized a numerical pattern in one of the rules for finding the derivative of a function. She spent several weeks exploring this pattern and applying it to various other functions and derivative rules studied in Calculus class. She recognized that a pattern existed within the exponents and coefficients of a function and its derivative in regards to the quotient and product rules.

According to Math Teacher, Michael Gentile, “Gilee not only recognized and questioned her findings, she independently explored her findings and has come up with a set of rules that clearly explain the patterns she recognized. She then came up with an alternative way to find the derivative involving rational expressions and polynomials. This pattern recognition was sparked by her own interest and curiosity. She enjoys analyzing situations and finding new ways to solve. Her interest in analyzing and critical and abstract thinking will quench her thirst for knowledge and bring her great success in the future.”

Lee Stemkoski, Professor of Mathematics and Computer Science at Adelphi University, says, “Kudos…[Gilee] has noticed a pattern for the case f(x) = Ax^2, g(x) = Bx^2 + C, and goes on to derive formulas for more complex cases, ultimately looking at functions of the form f(x) = Ax^m + Bx^n, g(x) = Cx^p + Dx^q, presumably in the search for more patterns. An exploratory question like this would typically be seen in a “transition to higher mathematics” or “bridge-style” sophomore-level college mathematics course, where students learn to shift focus from computational to more theoretical and abstract questions.”

Congratulations Gilee and may your love of learning only grow stronger as time goes on!