Developing the Vertex Formula Meaningfully

Autor/inn/en	Nebesniak, Amy L.; Burgoa, A. Aaron
Titel	Developing the Vertex Formula Meaningfully
Quelle	In: Mathematics Teacher, 108 (2015) 6, S.429-433 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Mathematics Instruction; Algebra; Equations (Mathematics); Mathematical Formulas; Textbooks; Mathematical Concepts; Concept Formation; Prior Learning; Graphs; Teaching Methods; Secondary School Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Equations; Mathematics; Gleichungslehre; Mathematische Formel; Textbook; Text book; Schulbuch; Lehrbuch; Concept learning; Begriffsbildung; Vorkenntnisse; Grafische Darstellung; Teaching method; Lehrmethode; Unterrichtsmethode
Abstract	As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students to graph quadratic equations. The algebra textbook in their school district introduced the concept by giving students a formula for the x-coordinate of the vertex as x = -b/(2a). (Note: The vertex form y = a(x - h)[superscript 2] + k is not introduced in the textbook and district standards until advanced algebra.) For a number of years, they provided students with the vertex formula, and the students successfully graphed by substituting values into the formula. Yet when asked where the formula came from or how it connected to the defining characteristics of quadratics, students did not know. They were performing procedures using this "magical" formula but did not understand how the formula developed. In this article, Nebesniak and Burgoa present a method for graphing quadratic equations that connects students' prior knowledge of graphing linear equations with intercepts and calculating mean. This atypical approach is effective only for a quadratic that has real roots. However, they use this method because the goal is to help students reason how to graph a quadratic with understanding rather than memorize the vertex formula. They believe that this initial approach to graphing is beneficial, despite the limitations, because students are making sense of the concept by connecting it to prior knowledge (NCTM 2009). A brief bibliography is included. (ERIC).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01