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Intended Treatment of Fractions and Fraction Operations in Mathematics Curricula from Japan, Korea, and Taiwan

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What Matters? Research Trends in International Comparative Studies in Mathematics Education

Part of the book series: Research in Mathematics Education ((RME))

Abstract

In spite of extensive research efforts, teaching and learning fractions remain challenging throughout the world. Although students’ mathematics learning is influenced by many factors, one important factor is the learning opportunities afforded by their textbooks. Therefore, we examined how textbooks from Japan, Korea, and Taiwan—three high-achieving countries prominent in comparative studies—introduced and developed fraction concepts and fraction arithmetic. We used the content analysis method (National Research Council, On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations, 2004) to analyze the problems presented in the textbooks. Our analysis revealed that there were many similarities among the textbooks from these three countries, including the overall flow of the topics related to fraction concepts and fraction arithmetic. However, significant differences included how various fraction subconstructs were integrated in the textbooks and how fraction multiplication and division were discussed. These similarities and differences among high-achieving countries suggest fruitful directions for future research in the area of fraction teaching and learning.

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Notes

  1. 1.

    In all three Asian textbook series, a multiplication equation is written in the form (multiplicand) × (multiplier) = (product), or (group size) × (number of groups) = (product). In this chapter, we adopt the convention that seems to be more common in English-speaking countries, (multiplier) × (multiplicand) = (product). However, we keep the Asian notation in figures or quotes taken directly from the textbooks.

  2. 2.

    In order to match the verbal description, this expression should really be written as a × (q ÷ b).

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Authors and Affiliations

  1. Department of Mathematics, Kennesaw State University, Kennesaw, GA, USA

    Tad Watanabe

  2. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Jane-Jane Lo

  3. Department of Learning and Instruction, University at Buffalo—The State University of New York, Buffalo, NY, USA

    Ji-Won Son

Authors
  1. Tad Watanabe
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  2. Jane-Jane Lo
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  3. Ji-Won Son
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Correspondence to Tad Watanabe .

Editor information

Editors and Affiliations

  1. Department of Learning and Instruction, University at Buffalo–The State University of New York, Buffalo, New York, USA

    Ji-Won Son

  2. Department of Mathematics, Kennesaw State University, Kennesaw, Georgia, USA

    Tad Watanabe

  3. Department of Mathematics, Western Michigan University, Kalamazoo, Michigan, USA

    Jane-Jane Lo

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Watanabe, T., Lo, JJ., Son, JW. (2017). Intended Treatment of Fractions and Fraction Operations in Mathematics Curricula from Japan, Korea, and Taiwan. In: Son, JW., Watanabe, T., Lo, JJ. (eds) What Matters? Research Trends in International Comparative Studies in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-51187-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-51187-0_2

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