References
- Brown, G. & Quinn, R. (2006). Algebra students' difficulty with fractions: An error analysis. AMT 62(4), 28-40.
- Bruner, J. (1966). Toward a theory of instruction. Cambridge, MA: Belknap Press.
- Chang, B. L., Cromley, J. G., & Tran, N. (2016). Coordinating multiple representations in a reform calculus textbook. International Journal of Science and Mathematics Education, 14(8), 1475 - 1497. https://doi.org/10.1007/s10763-015-9652-3
- Charalambous, C. Y., Delaney, S., Hsu, H.-Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117-151. https://doi.org/10.1080/10986060903460070
- Choy, B. H., Lee, M. Y., & Mizzi, A. (2015). Textbook signatures: An exploratory study of the notion of gradient in Germany, Singapore and South Korea. In Beswick, K., Muir, T., & Wells, J. (Eds.), Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 201-208. Hobart, Australia: PME.
- Choy, B. H., Lee, M. Y., & Mizzi, A. (2020). Insights into the teaching of gradient from an exploratory study of mathematics textbooks from Germany, Singapore, and South Korea. International Electronic Journal of Mathematics Education, 15(3). https://doi.org/10.29333/iejme/8273
- Clarke, D. M., Roche, A., & Mitchell, A. (2008). Ten practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(7), 373-380.
- Cramer, K. A., Post, T. R., & del Mas, R. C. (2002) Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricular with the effects of using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33(2), 111-144. https://doi.org/10.2307/749646
- Cramer, K., & Whitney, S. (2010). Learning rational number concepts and skills in elementary classrooms. In D. V. Lambdin & F. K. Lester (Eds.), Teaching and learning mathematics: Translating research to the elementary classroom (pp. 15-22). Reston, VA: NCTM.
- Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM, 45(5), 633-646. https://doi.org/10.1007/s11858-013-0539-x
- Getenet, S., & Callingham, R. (2019). Teaching interrelated concepts of fraction for understanding and teacher's pedagogical content knowledge. Mathematics Education Research Journal, 33, 201-221. https://doi.org/10.1007/s13394-019-00275-0
- Hackenberg, A. J., & Lee, M. Y. (2015). Relationships between students' fractional knowledge and equation writing. Journal for Research in Mathematics Education, 46(2), 196-243. https://doi.org/10.5951/jresematheduc.46.2.0196
- Herbel-Eisenmann, B. A. (2007). From intended curriculum to written curriculum: Examining the "voice" of a mathematics textbook. Journal for Research in Mathematics Education, 38(4), 344-369.
- Huntley, M. A. (2008). A framework for analyzing differences across mathematics curricula. Journal of Mathematics Education Leadership, 10(2), 10-17.
- Kieren, T. E. (1980). The rational number construct: Its elements and mechanisms. In T. E. Kieren (Ed.), Recent research on number learning (pp. 125-149). Columbus, OH: ERIC/SMEAC.
- Lamon, S. J. (2007). Rational numbers and proportional reasoning. In F. K. J. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte, NC: Information Age.
- Lamon, S. J. (2012). Teaching fractions and ratios for understanding (3rd ed.). New York: Routledge.
- Leong, Y. H., & Kaur, B. (2019). The enacted school mathematics curriculum. In T. L. Toh, B. Kaur, & E. G. Tay (Eds.), Mathematics education in Singapore (pp. 55-65). Springer Singapore. https://doi.org/10.1007/978-981-13-3573-0_4
- Leung, F. K. S. (2014). What can and should we learn from international studies of mathematics achievement? Mathematics Education Research Journal, 26(3), 579-605. https://doi.org/10.1007/s13394-013-0109-0
- Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234-241. https://doi.org/10.2307/749754
- Lee, M. Y., & Hackenberg, A. J. (2014). Relationships between fractional knowledge and algebraic reasoning: The case of Willa. International Journal of Science and Mathematics Education, 12(4), 975-1000. https://doi.org/10.1007/s10763-013-9442-8
- Lee, J., & Lee, M. Y. (2020). Pre-service teachers' exploration of model breaking points. International Journal of Science and Mathematics Education, 18, 549-575. https://doi.org/10.1007/s10763-019-09974-3
- Lee, M. Y., & Lee, J. (2021). Pre-service teachers' selection, interpretation, and sequence of fraction examples. International Journal of Science and Mathematics Education, 19(3), 539-558. https://doi.org/10.1007/s10763-020-10062-0
- Lee, J., & Lee, M. Y. (accepted). How elementary pre-service teachers use three fraction models: Their perceptions and difficulties. Journal of Mathematics Teacher Education.
- Ministry of Education. (2015). Mathematics curriculum. Ministry of Education of Korea Government.
- Ministry of Education. (2015). Suhak 3-1. Seoul, Korea: Ministry of Education.
- Ministry of Education. (2015). Suhak 3-2. Seoul, Korea: Ministry of Education.
- Ministry of Education-Singapore. (2012). Primary mathematics teaching and learning syllabus. Singapore: Curriculum Planning and Development Division.
- Mizzi, A., Choy, B. H., & Lee, M. Y. (2016). Textbook signatures: An exploratory study of the notion of fractions in Germany, Singapore, and South Korea. Paper presented at the 13th International Congress on Mathematical Education (ICME-13). Hamburg, Germany.
- National Mathematics Advisory Panel (2008). Report of the task group on conceptual skills and knowledge. Washington, DC: U.S. Department of Education.
- Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355. https://doi.org/10.1007/s10649-006-5423-y
- O'Keeffe, L., & O'Donoghue, J. (2015). A role for language analysis in mathematics textbook analysis. International Journal of Science and Mathematics Education, 13(3), 605-630. https://doi.org/10.1007/s10763-013-9463-3
- Pepin, B., Haggarty, L., & Keynes, M. (2001). Mathematics textbooks and their use in English, French and German classrooms: Away to understand teaching and learning cultures. ZDM, 33(5), 158-175.
- Petit, M. M., Laird, R., & Marsden, E. (2010). Informing practice: They "get" fractions as pies; now what? Mathematics Teaching in the Middle School, 16(1), 5-10. https://doi.org/10.5951/MTMS.16.1.0005
- Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In T. S. E. Wood, & D. V. E. Tirosh (Eds.), International handbook of mathematics teacher education (Vol. 2, pp. 1-35): Sense Publishers.
- Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the Learning Through Activity research program. The Journal of Mathematical Behavior, 52, 122-133. https://doi.org/10.1016/j.jmathb.2018.03.004
- Smith, J. P. (2002). The development of students' knowledge of fractions and ratios. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 3 - 17). Reston, Virginia: National Council of Teachers of Mathematics.
- Son, J. W., & Diletti, J. (2017). What can we learn from textbook analysis? In J.-W. Son, T. Watanabe, & J.-J. Lo (Eds.), What matters? Research trends in international comparative studies in mathematics education (pp. 3-32). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-51187-01
- Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
- Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3(3), 153-171. https://doi.org/10.1207/s1532690xci0303_1
- Usiskin, Z. (2013). Studying textbooks in an information age: A United States perspective. ZDM, 45(5), 713-723. https://doi.org/10.1007/s11858-013-0514-6
- Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the Book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-007-0844-0
- van de Walle, J., Karp, K. S., & Bam-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
- Vig, R., Murray, E., & Star, J. R. (2014). Model breaking points conceptualized. Educational Psychology Review, 26, 73-90. https://doi.org/10.1007/s10648-014-9254-6
- Wang, Y., Barmby, P., & Bolden, D. (2015). Understanding linear function: Acomparison of selected textbooks from England and Shanghai. International Journal of Science and Mathematics Education, 15(1), 131-153. https://doi.org/10.1007/s10763-015-9674-x
- Wong, K. Y. (2015). Effective mathematics lessons through an eclectic Singapore approach. World Scientific Publishing Co. Pte. Ltd.