A Novel Method for Completing the Square

Abstract

SummaryIn this paper, the authors present a new approach for teaching completing the square that does not rely on geometrical or algebraic models. Instead the authors’ novel approach relies on purely numerical reasoning. Additional informationNotes on contributorsEllen LehetEllen Lehet (elehet@alumni.nd.edu) works in mathematics curriculum and is interested in the intersection of mathematical practice, philosophy, and education. She earned her Ph.D. in philosophy from the University of Notre Dame in 2020 with a focus in philosophy of mathematics. Her research interests are focused in mathematical explanation and understanding from both a philosophical and a pedagogical perspective.Kuo-Liang Chang Kuo-Liang Chang (kchang@uvu.edu) is currently a professor in the department of Mathematical and Quantitative Reasoning at Utah Valley University. He earned his Ph.D. degree in mathematics education (2010) and master’s degree in applied mathematics (2003) from Michigan State University. His research interests center on the originality and flexibility of mathematical reasoning, and mathematical problem solving. He believes offering students alternative perspectives in problem solving and helping students complete their own reasoning attempts (for obtaining their perspectives) could be a way of enhancing students’ learning experience.