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

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