Chapter

Early Algebraization

Part of the series Advances in Mathematics Education pp 259-276

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

  • Eric J. KnuthAffiliated withDepartment of Curriculum & Instruction, University of Wisconsin-Madison Email author 
  • , Martha W. AlibaliAffiliated withDepartment of Psychology, University of Wisconsin-Madison
  • , 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 Wisconsin-Madison

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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 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.