Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable

  • Eric J. KnuthEmail author
  • Martha W. Alibali
  • Nicole M. McNeil
  • Aaron Weinberg
  • Ana C. Stephens
Part of the Advances in Mathematics Education book series (AME)


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 K-12. Recent research has begun to investigate algebra reform in the context of elementary school (grades K-5) 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.


Middle School Grade Level Large Problem Grade Student Middle School Student 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Eric J. Knuth
    • 1
    Email author
  • Martha W. Alibali
    • 2
  • Nicole M. McNeil
    • 3
  • Aaron Weinberg
    • 4
  • Ana C. Stephens
    • 5
  1. 1.Department of Curriculum & InstructionUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of PsychologyUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.Department of PsychologyUniversity of Notre DameNotre DameUSA
  4. 4.Department of MathematicsIthaca CollegeIthacaUSA
  5. 5.Wisconsin Center for Education ResearchUniversity of Wisconsin-MadisonMadisonUSA

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