Radical Thoughts on Simplifying Square Roots

Autor/inn/en	Schultz, Kyle T.; Bismarck, Stephen F.
Titel	Radical Thoughts on Simplifying Square Roots
Quelle	In: Mathematics Teaching in the Middle School, 19 (2013) 4, S.222-228 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1072-0839
Schlagwörter	Mathematics Instruction; Middle Schools; Secondary School Mathematics; Algebra; Visual Stimuli; Cognitive Style; Verbal Communication; Geometric Concepts; Manipulative Materials; Educational Technology; High Schools; Preservice Teacher Education; College Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Middle school; Mittelschule; Mittelstufenschule; Cognitive styles; Kognitiver Stil; Elementare Geometrie; Hilfsmittel; Unterrichtsmedien; High school; Oberschule; Lehramtsstudiengang; Lehrerausbildung
Abstract	A picture is worth a thousand words. This statement is especially true in mathematics teaching and learning. Visual representations such as pictures, diagrams, charts, and tables can illuminate ideas that can be elusive when displayed in symbolic form only. The prevalence of representation as a mathematical process in such documents as "Principles and Standards for School Mathematics" (NCTM 2000), the Common Core State Standards for Mathematics (CCSSI 2010), and the Strands of Mathematical Proficiency (NRC 2001) reinforces the importance of mathematics teachers and their students using multiple representations when exploring mathematical ideas. Simplifying square roots and other radicals is a staple of prealgebra and algebra 1 courses because it is a requisite skill for studying many other topics in the high school curriculum (CCSSI 2010; 8.EE.2). In developing a lesson on simplifying a radical expression for algebra 1 students, the authors sought to address a variety of learning styles. Although they developed verbal and written strategies to supplement teaching the algebraic representation, they struggled initially to determine a way of representing a visual or geometric approach for simplifying radicals. After examining geometric representations of perfect square numbers (1, 4, 9, 16, . . .), they developed a way to think about more complicated examples (e.g., 18, 45, 72), creating tactile and virtual manipulatives that enabled students to explore radical simplification and other concepts. In this article, the authors share their visual representation for simplifying radicals and their initial efforts to use this representation with middle school and high school mathematics students as well as prospective mathematics teachers. (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	2017/4/10