| 1 | Sintanjin Elementary School, SOUTH KOREA |
| 2 | Korea National University of Education, SOUTH KOREA |
| 1. | Alajmi, A. H. (2009). Addressing computational estimation in the Kuwaiti curriculum: Teachers’ views. Mathematics Teacher Education, 12(4), 263-283. |
| 2. | Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79, 239-261. |
| 3. | Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational numbers for teaching mathematics in grades 3-5. In R. I. Charles (Volume Ed.) & R. M. Zbiek (Series Ed.), Essential understandings series. Reston, VA: National Council of Teachers of Mathematics. |
| 4. | Blanton, M., Levi, L., Crites, T., & Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. In B. J. Dougherty (Volume Ed.) & R. M. Zbiek (Series Ed.), Essential understandings series. Reston, VA: National Council of Teachers of Mathematics. |
| 5. | Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann. |
| 6. | Charalambous, D., Delaney, S., Hsu, H., & Mesa, M. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning: An International Journal, 12(2), 117-151. |
| 7. | Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://corestandards.org/asset.... |
| 8. | Gojak, L. M. (2013). Making mathematical connections. Retrieved from http://www.nctm.org/News-and-C.... |
| 9. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011a). Study with your friends mathematics for elementary school 3-1. Takeshi, Nara: GAKKOHTOSHO. |
| 10. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011b). Study with your friends mathematics for elementary school 4-1. Takeshi, Nara: GAKKOHTOSHO. |
| 11. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011c). Study with your friends mathematics for elementary school 4-2. Takeshi, Nara: GAKKOHTOSHO. |
| 12. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011d). Study with your friends mathematics for elementary school 5-1. Takeshi, Nara: GAKKOHTOSHO. |
| 13. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011e). Study with your friends mathematics for elementary school 5-2. Takeshi, Nara: GAKKOHTOSHO. |
| 14. | Hitotsumatsu, S., Masaki, K., Akai, T., Okada, Y., Machida, S., Moriya, Y., et al. (2011f). Study with your friends mathematics for elementary school 6-1. Takeshi, Nara: GAKKOHTOSHO. |
| 15. | Ku, J., Kim, S., Lee, H. W., Cho, S., & Park, H. (2016). OECD programme for international students assessment: an analysis of PISA 2015 results [in Korean with English abstract]. KICE: Seoul. |
| 16. | Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13(9), 546-552. |
| 17. | Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM Mathematics Education, 40, 833-843. |
| 18. | Ministry of Education (MOE) (2015a). 5-2 Mathematics textbook (in Korean). Seoul, Korea: Chunjae Textbooks. |
| 19. | Ministry of Education (MOE) (2015b). 6-1 Mathematics textbook (in Korean). Seoul, Korea: Chunjae Textbooks. |
| 20. | Ministry of Education (MOE) (2016a). 3-1 Mathematics textbook (in Korean). Seoul, Korea: Chunjae Textbooks. |
| 21. | Ministry of Education (MOE) (2016b). 3-2 Mathematics textbook (in Korean). Seoul, Korea: Chunjae Textbooks. |
| 22. | Ministry of Education (MOE) (2016c). 4-1 Mathematics textbook (in Korean). Seoul, Korea: Chunjae Textbooks. |
| 23. | National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author. |
| 24. | Otto, A., Caldwell, J., Hancock, S. W., & Zbiek, R. M. (2011). Developing essential understanding of multiplication and division for teaching mathematics in grades 3-5. In E. C. Rathmell (Volume Ed.) & R. M. Zbiek (Series Ed.), Essential understandings series. Reston, VA: National Council of Teachers of Mathematics. |
| 25. | Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75, 211-246. |
| 26. | Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27. |
| 27. | Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics (9th edition). Hoboken, NJ: John Wiley & Sons. |
| 28. | Sanford, V. (1921). La Disme of Simon Stevin: The first book on decimals. The Mathematics Teacher, 14(6), 321-333. |
| 29. | Sang, K., Kwak, Y., Park, J. H., & Park, S. (2016). The trends in international mathematics and science study (TIMSS): findings from TIMSS 2015 for Korea [in Korean with English abstract]. KICE: Seoul. |
| 30. | Sherman, H. J., Richardson, L. I., & Yard, G. J. (2015). Teaching learners who struggle with mathematics: Responding with systematic intervention and remediation. Long Grove, IL: Waveland Press. |
| 31. | Siebert, D. (2002). Connecting informal thinking and algorithms: the case of division of fractions. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp.247-256). Reston, VA: NCTM. |
| 32. | Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp.153-161). Reston, VA: NCTM. |
| 33. | Son, J. W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117-142. |
| 34. | Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Greenwich, CT: Information Age Publishing. |
| 35. | Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2008). Elementary and middle school mathematics: Teaching developmentally (Seventh edition). Boston: Pearson Education. |
| 36. | Weiss, I. R., Pasley, J. D., Smith, P. S., Sanilower, E. R., & Heck, D. J. (2003). Looking inside the classroom: A study of K-12 mathematics and science education in United States. Chapel Hill: Horizon Research. |