Radical Thoughts on Simplifying Square Roots

Abstract

A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.

Concrete–Representational–Abstract (CRA) Instructional Approach in an Algebra I Inclusion Class: Knowledge Retention Versus Students’ Perception

“…As both concrete and virtual manipulatives have been found to be equally effective [17], the second author in this study used a concrete version of the manipulative; a virtual version is being developed. The manipulative, which was piloted and refined prior to the larger study [52], has since been cited in multiple state standards documents [53][54][55] and has been used…”

“…As both concrete and virtual manipulatives have been found to be equally effective [17], the second author in this study used a concrete version of the manipulative; a virtual version is being developed. The manipulative, which was piloted and refined prior to the larger study [52], has since been cited in multiple state standards documents [53][54][55] and has been used in mathematics professional development grant projects [56]. To initiate the CRA approach, the second author created concrete (i.e., tactile) square manipulatives by printing, laminating, and cutting out squares with whole number areas ranging from 2 cm 2 through 10 cm 2 .…”