The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School

  • Susan B. EmpsonEmail author
  • Linda Levi
  • Thomas P. Carpenter
Part of the Advances in Mathematics Education book series (AME)


The authors present a new view of the relationship between learning fractions and learning algebra that (1) emphasizes the conceptual continuities between whole-number arithmetic and fractions; and (2) shows how the fundamental properties of operations and equality that form the foundations of algebra are used naturally by children in their strategies for problems involving operating on and with fractions. This view is grounded in empirical research on how algebraic structure emerges in young children’s reasoning. Specifically, the authors argue that there is a broad class of children’s strategies for fraction problems motivated by the same mathematical relationships that are essential to understanding high-school algebra and that these relationships cannot be presented to children as discrete skills or learned as isolated rules. The authors refer to the thinking that guides such strategies as Relational thinking.


Elementary School Fundamental Property Concrete Material Goal Structure Algebraic Thinking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Susan B. Empson
    • 1
    Email author
  • Linda Levi
    • 2
  • Thomas P. Carpenter
    • 3
  1. 1.College of EducationUniversity of Texas at AustinAustinUSA
  2. 2.Cognitively Guided Instruction (CGI) Professional Development InitiativesTeachers Development GroupMadisonUSA
  3. 3.Department of Curriculum and InstructionUniversity of Wisconsin-MadisonMadisonUSA

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