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

Watanabe, Tad; Lo, Jane-Jane; Son, Ji-Won

doi:10.1007/978-3-319-51187-0_2

Cited by 8 publications

(8 citation statements)

References 23 publications

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“…Earlier comparative studies focusing on various mathematical subjects have shown that countries succeeding in international examinations start the teaching of mathematics subjects earlier than other countries (Ding & Li, 2010;Hong & Choi, 2014). For instance, the multiplication of fractions in Taiwanese textbooks begins in the 4th grade; and in Japanese and Korean textbooks, it begins in the 5th grade (Watanabe et al, 2017). On the other hand, Grade-5 textbook coded TM covers the subject of "multiplication of fractions" on 5.42% of all its pages whereas the Turkish mathematics textbook coded TR covers the subject on 2.08 of all its pages.…”

Section: Discussionmentioning

confidence: 99%

“…Similarly, Gagatsis and Shiakalli (2004) underlined that a single representation in the learning context reveals only certain aspects of the concept, and that multiple forms of representation have the potential to complement each other. Similarly, Japanese textbooks teach fractions by combining the area model and the number line model to provide students with the opportunity to apply proportional reasoning in multiplying fractions (Watanabe et al, 2017). In fact, a number line indicates that a fraction is both a number and possesses relative greatness compared to other numbers.…”

Section: Discussionmentioning

confidence: 99%

“…The extant literature comprises studies that compared textbooks in terms of their multiplying fractions content (Kar et al, 2018;Son, 2005;Son & Senk, 2010;Watanabe, Lo, & Son, 2017). For instance, Son and Senk (2010) compared Korean and American mathematics textbooks; Kar et al (2018) compared Turkish and American mathematics textbooks; and Watanabe et al (2017) compared Japanese, Korean, and Taiwanese mathematics textbooks in terms of their multiplying fractions content. Son and Senk (2010) compared Korean and American mathematics textbooks in terms of their content on multiplying and dividing fractions and the subject-relevant problems the textbooks covered.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…However, Korean textbooks were richer than American textbooks in terms of multi-step problems. Similarly, Watanabe et al (2017) compared Japanese, Korean, and Taiwanese mathematics textbooks in terms of multiplying fractions. In Japanese textbooks, unlike in Korean and Taiwanese textbooks, the multiplication of fractions was presented after teaching the division of a proper fraction by a positive whole number.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions

Bütüner

2021

REDIMAT

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In this study, Turkish and Singaporean textbooks were compared in terms of teaching content for multiplying fractions, a subject that most students have difficulty in understanding. The study analyzed the 6th-grade mathematics textbook published by the Turkish Ministry of National Education and its Singaporean counterpart. While the Singaporean textbook covered all meanings of multiplying fractions, the Turkish textbook did not include the operator meaning of multiplying fractions. Compared to the Turkish textbook, the Singaporean textbook included more solution strategies. The number line model was not used in the textbooks of either country, and only one representation format was used to model a fraction multiplication problem. The Singaporean textbook included more fraction multiplication problems than did the Turkish textbook. Many problems in both textbooks were of a one-step fashion and required numerical answers.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

Section: Theoretical Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions

Bütüner

2021

REDIMAT

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“…They are primary resources for teachers to plan and teach their lessons (Beaton et al, 1997;Schmidt et al, 1997;Escolano & Gairín, 2005;Reys et al, 2007;Alajmi, 2009Alajmi, , 2012. At the same time, textbooks are often the only material students access to learn about mathematical objects and their operations (Watanabe et al, 2017). In parallel assessments, Chingos and Whitehurst (2012), Fan, Zhu, and Miao (2013) note that "researchers generally agree that textbooks are important means of conveying curriculum and play a dominant role in modern education scenes in different school disciplines" (p. 635).…”

Section: Introductionmentioning

confidence: 99%

How do textbooks from Brazil, the United States, and Japan deal with fractions?

Souza

Powell

2021

Acta Sci.

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Background: Researchers recognise the importance of textbooks for teachers’ lesson planning and the importance of fraction knowledge for shaping students’ future mathematics performance. Objectives: The finding of discrepant achievement by Brazilian, American, and Japanese students in the last three editions of PISA led us to investigate how textbook authors from these countries approach fraction content in elementary education relating to magnitude, flexibility, reasonableness, as well as conceptual and procedural knowledge from both symbolic and nonsymbolic perspectives. Design: The quantitative performances in mathematics of Brazilian, American, and Japanese students in the last three PISA editions lack qualitative and exploratory research to understand some reasons presented by the numerical results. Data collection and analysis: To achieve the objectives, we selected three textbook series, one each from Brazil, the United States of America, and Japan, that schools in those countries widely use. Results: The main results revealed that all textbook series practised flexibility and reasonableness with different emphases, but not the sense of magnitude. Brazilian and U.S. textbooks were based primarily on part-whole interpretation and on a procedural approach. In contrast, Japanese textbooks emphasised the understanding of measurement as the iteration of unit fractions and more conceptual development. Conclusions: The fraction knowledge approach in the Japanese textbook series seems to be close to what the mathematics education researchers recommend, which can be an essential differential to explain the Japanese results in PISA.

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