**ERIC Number:**EJ1029390

**Record Type:**Journal

**Publication Date:**2013-Nov

**Pages:**7

**Abstractor:**ERIC

**Reference Count:**4

**ISBN:**N/A

**ISSN:**ISSN-1072-0839

Radical Thoughts on Simplifying Square Roots

Schultz, Kyle T.; Bismarck, Stephen F.

Mathematics Teaching in the Middle School, v19 n4 p222-228 Nov 2013

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.

Descriptors: 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

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/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Middle Schools; High Schools; Secondary Education; Higher Education; Postsecondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A