Playing with Integer Concepts: A Quest for Structure

  • Laura BofferdingEmail author
  • Mahtob Aqazade
  • Sherri Farmer
Part of the Research in Mathematics Education book series (RME)


How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve integer arithmetic problems (encouraging them to play around with the concepts of addition and subtraction involving negative integers). When playing around with the number paths, students made patterns, continued the number sequence in interesting ways, and used invented notation. When playing around with the operations, they interpreted negative signs as subtraction signs or added negative signs to their answers. Their play with the number path often connected to their play with operations, revealing that although some students were attuned to the pattern in the order of numbers and operations as movement in a particular direction, others focused more on numerical values and operations as changes in amount. The various ways in which children played with integers provide insight into their conceptual change process and can provide guidance for ways teachers could help students build on their logic.



This research was supported by NSF CAREER award DRL-1350281.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Laura Bofferding
    • 1
    Email author
  • Mahtob Aqazade
    • 1
  • Sherri Farmer
    • 1
    • 2
  1. 1.Department of Curriculum and Instruction, Beering Hall of Liberal Arts and EducationPurdue UniversityWest LafayetteUSA
  2. 2.BloomfieldUSA

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