Part of the series Advances in Mathematics Education pp 259276
Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable
 Eric J. KnuthAffiliated withDepartment of Curriculum & Instruction, University of WisconsinMadison Email author
 , Martha W. AlibaliAffiliated withDepartment of Psychology, University of WisconsinMadison
 , Nicole M. McNeilAffiliated withDepartment of Psychology, University of Notre Dame
 , Aaron WeinbergAffiliated withDepartment of Mathematics, Ithaca College
 , Ana C. StephensAffiliated withWisconsin Center for Education Research, University of WisconsinMadison
Abstract
Algebra is a focal point of reform efforts in mathematics education, with many mathematics educators advocating that algebraic reasoning should be integrated at all grade levels K12. Recent research has begun to investigate algebra reform in the context of elementary school (grades K5) mathematics, focusing in particular on the development of algebraic reasoning. Yet, to date, little research has focused on the development of algebraic reasoning in middle school (grades 6–8). This article focuses on middle school students’ understanding of two core algebraic ideas—equivalence and variable—and the relationship of their understanding to performance on problems that require use of these two ideas. The data suggest that students’ understanding of these core ideas influences their success in solving problems, the strategies they use in their solution processes, and the justifications they provide for their solutions. Implications for instruction and curricular design are discussed.
 Title
 Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable
 Book Title
 Early Algebraization
 Book Subtitle
 A Global Dialogue from Multiple Perspectives
 Pages
 pp 259276
 Copyright
 2011
 DOI
 10.1007/9783642177354_15
 Print ISBN
 9783642177347
 Online ISBN
 9783642177354
 Series Title
 Advances in Mathematics Education
 Series ISSN
 18694918
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 Editors

 Jinfa Cai ^{(ID1)}
 Eric Knuth ^{(ID2)}
 Editor Affiliations

 ID1. Dept. Mathematical Sciences, University of Delaware
 ID2. University of WisconsinMadison
 Authors

 Eric J. Knuth ^{(1)}
 Martha W. Alibali ^{(2)}
 Nicole M. McNeil ^{(3)}
 Aaron Weinberg ^{(4)}
 Ana C. Stephens ^{(5)}
 Author Affiliations

 1. Department of Curriculum & Instruction, University of WisconsinMadison, Madison, USA
 2. Department of Psychology, University of WisconsinMadison, Madison, USA
 3. Department of Psychology, University of Notre Dame, Notre Dame, USA
 4. Department of Mathematics, Ithaca College, Ithaca, USA
 5. Wisconsin Center for Education Research, University of WisconsinMadison, Madison, USA
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