ERIC Number: EJ1201926
Record Type: Journal
Publication Date: 2019-Jan
Finding Meaning in the Quadratic Formula
Edwards, Thomas G.; Chelst, Kenneth R.
Mathematics Teacher, v112 n4 p258-260 Jan 2019
While tutoring his granddaughter in second-year algebra recently, the second author lamented that every textbook he could find expresses the quadratic formula as probably the most common form of the formula. What troubled him is that this form hides the meaning of the various components of the equation. Indeed, the meaning was obscured by the simplification that arose from combining two fractions. When a contextual problem is associated with the mathematics, meaning obscured due to a simplification is often critical. Sometimes, it is critical even in the absence of any context. The authors think this is particularly true in the case of the quadratic formula. In this article, they explain the current approach of quadratic formula and propose a new way of connecting the formula to the graphic representation of quadratic functions that makes the mathematics meaningful to students. They believe the approach we have proposed above is consistent with the visions of mathematics teaching and learning articulated in both "Principles and Standards for School Mathematics" (NCTM 2000) and the Common Core State Standards for Mathematics (CCSSI 2010). When students engage in activities such as those we have described, they will be using algebraic symbols to represent, analyze, and understand a mathematical situation, as suggested in "Principles and Standards." Moreover, they will be reasoning abstractly and quantitatively, making use of structure, attending to precision, and, in particular, using an appropriate tool strategically, as the Common Core State Standards recommend.
Descriptors: Mathematics Instruction, Mathematical Formulas, Algebra, Teaching Methods, Mathematical Concepts, Mathematical Logic, High School Students, Secondary School Mathematics
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Secondary Education
Authoring Institution: N/A