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Mathematics Education Research Journal

, Volume 26, Issue 1, pp 79–99 | Cite as

Unit fractions in the context of proportionality: supporting students' reasoning about the inverse order relationship

  • Jose Luis Cortina
  • Jana Visnovska
  • Claudia Zuniga
Original Article
First Online:

Abstract

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as equal-sized parts of a whole, but as entities that are always separate from a reference unit. We argue that such a path is crucial for helping students develop deep quantitative understandings of fractions, where fraction quantities are, from the very start, linked to the reciprocal and multiplicative relations that their use implies. We focus on the first part of the design experiment in which we helped the students make sense of a concept that is important for initial fraction learning and proportional reasoning, the inverse order relationship among unit fractions.

Keywords

Design experiment Fractions Proportional reasoning Primary education 
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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  • Jose Luis Cortina
    • 1
  • Jana Visnovska
    • 2
  • Claudia Zuniga
    • 3
  1. 1.Universidad Pedagógica Nacional, MéxicoMéxico CityMexico
  2. 2.School of EducationThe University of QueenslandSt LuciaAustralia
  3. 3.Universidad IberoamericanaMéxico CityMexico

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