Teaching interrelated concepts of fraction for understanding and teacher’s pedagogical content knowledge

A Correction to this article was published on 27 July 2019

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Fractions are perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity are fractions having five interrelated constructs (part-whole, ratio, operator, quotient and measure) and teachers’ pedagogical approaches to address these constructs. The present study used the five interrelated constructs of fraction and the Knowledge Quartet Framework to investigate a teacher’s teaching of fraction in a New Zealand Year 7 classroom. Video recordings and transcribed audio-recordings were analysed through the lenses of the five integrated constructs of fraction and the Knowledge Quartet Framework. The findings showed that students often initiated uses of fractions as quotient and as operator, drawing on part-whole understanding when solving fraction problems. The study showed that the teacher’s focus in connecting the constructs and procedures of the lesson as well as shaping the classroom discussion when the lesson unfolded supported students’ learning of the fraction constructs.

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The involvement and contributions of Professor Kim Beswick, Associate Professor Helen Chick, and Professor Tom Nicholson are acknowledged, as is the support of Professor Roberta Hunter.


This project was funded by the Australian Research Council Grant No. DP130103144.

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Correspondence to Seyum Getenet.

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The original version of this article unfortunately contained a mistake. The figures in Fig. 2 and Fig. 3 are misplaced. The figure in Fig. 3 is “An example of representing the measure construct of fraction (Siemon et al. 2015)” and should be placed in Fig.2, whereas, the figure in Fig. 2 represents “The operator construct of fraction (Getenet and Callingham 2017)” and should be placed in Fig. 3.

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Getenet, S., Callingham, R. Teaching interrelated concepts of fraction for understanding and teacher’s pedagogical content knowledge. Math Ed Res J 33, 201–221 (2021). https://doi.org/10.1007/s13394-019-00275-0

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  • Teaching fractions
  • Pedagogy and content knowledge
  • Knowledge Quartet
  • Mathematics