ERIC Number: EJ1044175
Record Type: Journal
Publication Date: 2013-Nov
Teaching Structure in Algebra
Merlin, Ethan M.
Mathematics Teacher, v107 n4 p292-297 Nov 2013
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using "Trees," and describing "subexpression addresses"--all help students avoid these longstanding mistakes and, more significant, cultivate true fluency in algebra. Herein, he discusses the "glue" concept, diagramming expressions as "trees," where the subexpression "lives," and tackling "strange mistakes" in simplifying fractions. All the exercises discussed force students to engage with the structure of algebraic expressions and with how that structure permits subsequent transformations. The author concludes that once his students have mastered these skills, they are delighted to have become technically proficient enough to truly understand the structure of the algebraic expressions with which they are working.
Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Visual Aids, Error Patterns, Mathematical Concepts, Concept Formation, Misconceptions, Secondary School 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: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Authoring Institution: N/A
Grant or Contract Numbers: N/A