Educational Studies in Mathematics

, Volume 79, Issue 1, pp 61–83 | Cite as

Levels of students’ “conception” of fractions

  • Marilena PantziaraEmail author
  • George Philippou


In this paper, we examine sixth grade students’ degree of conceptualization of fractions. A specially developed test aimed to measure students’ understanding of fractions along the three stages proposed by Sfard (1991) was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test across the sample and cluster analysis to locate groups by facility level. The analysis revealed six such levels. The characteristics of each level were specified according to Sfard’s framework and the results of the fraction test. Based on our findings, we draw implications for the learning and teaching of fractions and provide suggestions for future research.


Procedural and conceptual understanding Fraction Part–whole subconstruct Measurement Equivalence Comparison Rasch model 



We wish to thank Dr. Leonidas Kyriakides and Dr. Demetra Pitta-Pantazi of the University of Cyprus for their constructive comments during the research of this study.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Cyprus Pedagogical InstituteNicosiaCyprus
  2. 2.University of NicosiaNicosiaCyprus

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