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Mathematics Education Research Journal

, Volume 26, Issue 2, pp 237–255 | Cite as

The identification and validation process of proportional reasoning attributes: an application of a cognitive diagnosis modeling framework

  • Hartono Tjoe
  • Jimmy de la Torre
Article
First Online:

Abstract

In this paper, we discuss the process of identifying and validating students’ abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the deliberation and resolution of differing views by mathematics researchers, mathematics educators, and middle school mathematics teachers of what should be learned theoretically and what can be taught practically in everyday classroom settings. We also present the initial development of proportional reasoning items as part of the two-phase validation process of the previously identified attributes. In particular, we detail in the first phase of the validation process our collaboration with middle school mathematics teachers in the creation of prototype items and the verification of each item-attribute specification in consideration of the most common ways (among many different ways) in which middle school students would have solved these prototype items themselves. In the second phase of the validation process, we elaborate our think-aloud interview procedure in the search for evidence of whether students generally solved the prototype items in the way they were expected to.

Keywords

Ratios Proportions Proportional reasoning Assessment 
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Notes

Acknowledgments

This research was supported by the National Science Foundation CAREER Grant No. DRL-0744486. Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.

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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2013

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityReadingUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

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