**ERIC Number:**EJ1053528

**Record Type:**Journal

**Publication Date:**2015-Mar

**Pages:**6

**Abstractor:**ERIC

**Reference Count:**7

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Like Terms: What's in a Name?

de Groot, Cornelis; Boyajian, Meredith

Mathematics Teacher, v108 n7 p506-511 Mar 2015

In introductory algebra and later mathematics courses, students seem to struggle with the concepts of like terms and combining like terms with algebraic expressions. These ideas appear to be unfamiliar to students and do not seem to relate to any mathematics that they have done in the past. In an attempt to link with something that the students do know, teachers may resort to pseudoexplanations or contexts that are not mathematical and that frequently are incorrect concretizations or contextualizations. Although using letters to assign attributes of objects or the objects themselves may, at some point, lead some students to combine like terms in limited circumstances, they will be misunderstanding what they are doing. This approach is not linked with any mathematical structure from their prior knowledge; rather, a pseudomathematical explanation is given (Ma 1999). Proper use of context has been shown to be a fruitful bridge between arithmetic and algebra (Tabach and Friedlander 2008). However, the context must help students develop structure sense (Linchevski and Livneh 1999; Linchevski and Herscovics 1996). Developing structure sense is given an important place in both NCTM's Process Standards (NCTM 2000) and the Common Core Standards for School Mathematics, particularly the Standards for Mathematical Practices (SMPs) (CCSSI 2010). In this article, the authors share the collaborative attempt of a student teacher and her supervisor to support the teaching and learning of the concept of combining like terms in algebra with the structural understanding of arithmetic.

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Algebra, Relevance (Education), Teaching Methods, Context Effect, Student Teachers, Student Teacher Supervisors, Cooperative Planning, Arithmetic, Secondary School Mathematics, State Standards

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:**Higher Education; Postsecondary Education; Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A