ERIC Number: EJ1269627
Record Type: Journal
Publication Date: 2020-Sep
Pages: 8
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Discovering Radical Simplification through Geometry Connections
Rakes, Christopher R.; Kirvan, Rebecca J.; Witkowski, Ashley
Mathematics Teacher: Learning and Teaching PK-12, v113 n9 p737-744 Sep 2020
Teachers are constantly looking for new ways to make mathematical procedures such as radical simplification meaningful for students. In classes, teachers discovered what researchers have long known, that students who only memorize a set of steps get confused when their steps do not match a new problem or scenario perfectly. The area and side length of squares offer an entry point into understanding radical simplification. In this article, the authors share an activity that helped develop high school students' understanding of the structure of radical expressions. By beginning with a concrete investigation before exploring abstract numerical simplification, students discovered that different radical expressions can represent the same value and why that relationship might exist. This activity addresses content standard 2 of the Common Core State Standards for Mathematics (CCSSM) algebra domain, Seeing Structure in Expressions: "Use the structure of an expression to identify ways to rewrite it" (HSA.SSE.A.2; NGA Center and CCSSO 2010a). The concrete-semiconcrete-abstract framework (Agrawal and Morin 2016; Jordan, Miller, and Mercer 1999) guided the development of this activity by using squares as the foundation for representing lengths with radical expressions before simplifying radicals algorithmically. Although simplifying radical expressions is often presented as a largely procedural endeavor (Hiebert et al. 2005), the authors advocate for a conceptual approach. Skemp (2006) outlined four reasons for approaching such topics from a conceptual perspective: (1) better adaptability to new tasks; (2) less to memorize and remember; (3) improved intrinsic motivation to learn; and (4) a stronger foundation for building on the knowledge. The activity presented in this article helps students develop a conceptual perspective to radical simplification. Students explore equivalent radical expressions using the relationship between area and side lengths of a square.
Descriptors: High School Students, Mathematics Instruction, Common Core State Standards, Algebra, Learning Activities, Student Motivation, Concept Formation, Learning Motivation, Teaching Methods, Mathematical Concepts
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: publicationsdept@nctm.org; Web site: https://pubs.nctm.org/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A