References
- 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(2), 239-261. https://doi.org/10.1007/s10649-011-9342-1
- Arzarello, F. (2006). Semiosis as a multimodal process. RLIME-Revista Latino americana de Investigacionen Matematica Educativa, 9(1), 267-299.
- Arzarello, F., & Robutti, O. (2008). Framing the embodied mind approach within a multimodal paradigm. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 720-749, 2nd ed.). Mahwah, NJ: Erlbaum.
- Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: artefacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 720-749, 2nd ed.). Mahwah, NJ: Erlbaum.
- Battista, M. T. (2008). Representations and cognitive objects in modern school geometry. In G. W. Blume, & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (pp. 341-362). Charlotte, NC: Information Age Publishing, Inc.
- Behr, M. J., Harel, G., Post, Th. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-332). New York, NY: Macmilian Publishing Company.
- 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, Retrieved from http://www.corestandards.org/wp-content/uploads/MathStandards.pdf
- Davydov, V. V., & Tsvetkovich, Z. H. (1991). The object sources of the concept of fraction. In V. V. Davydov (Soviet Edition Editor) & L. P. Steffe (English Language Editor), Soviet studies in mathematics education: Psychological abilities of primary school children in learning mathematics (pp. 86-147). Reston, VA: National Council of Teachers of Mathematics.
- Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to support reasoning and sense making. Reston, VA: National Council of Teachers of Mathematics.
- Dougherty, B. J. (2008). Measure up: A quantitative view of early algebra. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 389-412). New York, NY: Lawrence Erlbaum Associates.
- Empson, S. B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17(3), 283-342. https://doi.org/10.1207/S1532690XCI1703_3
- Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2006). Fractions as the coordination of multiplicatively related quantities: Across-sectional study of children's thinking. Educational Studies in Mathematics, 63(1), 1-28. https://doi.org/10.1007/s10649-005-9000-6
- Empson, S. B., & Levi, L. (2011). Extending Children's Mathematics: Fractions and Decimals: [innovations in Cognitively Guided Instruction]. Portsmouth, NH: Heinemann.
- Ginsburg, H. (1997). Entering the child's mind: The clinical interview in psychological research and practice. UK: Cambridge University Press.
- Hollebrands, K. F. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164-192.
- Hunting, R. P., Davis, G., & Pearn, C. A. (1996). Engaging whole-number knowledge for rational-number learning using a computer-based tool. Journal for Research in Mathematics Education, 27(3), 354-379. https://doi.org/10.2307/749369
- Kang, H. K., & Ko, J. H. (2003). The educational significance of the method of teaching natural and fractional numbers by measurement of quantity. School Mathematics, 5(3), 385-399.
- Kaur, H. (2015). Two aspects of young children's thinking about different types of dynamic triangles: Prototypicality and inclusion. ZDM, 47(3), 407-420. https://doi.org/10.1007/s11858-014-0658-z
- Kieren, T. E. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In J. Hiebert & M. J. Behr (Eds.), Number concepts andoperations in the middle grades (pp. 162-181). Hillsdale, NJ: Erlba
- Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12(3), 217-230. https://doi.org/10.1007/s10758-007-9123-1
- Laborde, J. M. (2016). Technology-enhanced teaching/learning at a new type with dynamic mathematics as implemented in the new Cabri. In M. Bates & Z. Usiskin (Eds.). Digital curricula in school mathematics (pp. 53-74). Charlotte, NC: Information Age Publishing, Inc.
- Lee, J., & Pang, J. (2014). Sixth grade students' understanding on unit as a foundation of multiple interpretations of fractions. Journal of Educational Research in Mathematics, 24(1). 83-102.
- Mack, N. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3), 267-295. https://doi.org/10.2307/749828
- Ministry of Education (2015). Mathematics curriculum. [Supplement 8]. Statute Notice of Ministryof Education (No. 2015-74). Seoul, South Korea: Ministry of Education.
- Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68(2), 99-111. https://doi.org/10.1007/s10649-008-9116-6
- Morris, A. K. (2000). A teaching experiment: Introducing fourth graders to fractions from the viewpoint of measuring quantities using Davydov's mathematics curriculum. Focus on Learning Problems in Mathematics, 22(2), 33-84.
- Mortimer, E. F., & El-Hani, C. N. (2014). Conceptual profiles: A theory of teaching and learning scientific concepts. New York, NY: Springer.
- National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
- Ng, O. L., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM, 47(3),421-434. https://doi.org/10.1007/s11858-014-0660-5
- Noh, J., Lee, K., & Moon, S. (2019). A case study on the learning of the properties of quadrilaterals through semiotic mediation: Focusing on reasoning about the relationships between the properties. School Mathematics, 21(1), 197-214. https://doi.org/10.29275/sm.2019.03.21.1.197
- Olive, J., & Lobato, J. (2008). The learning of rational number concepts using technology. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Research syntheses (pp.1-54). Charlotte, NC: Information Age and the National Council of Teachers of Mathematics.
- Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM, 45(3), 343-364. https://doi.org/10.1007/s11858-012-0466-2
- Schmittau, J., & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of VV Davydov. The Mathematics Educator, 8(1), 60-87.
- Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25. https://doi.org/10.3102/0013189X031001013
- Schoenfeld, A. H., Smith, J. P., & Arcavi, A. A. (1993). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in Instructional Psychology (Volume 4) (pp. 55-175). Hillsdale, NJ: Erlbaum.
- Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press.
- 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
- Son, T., Hwang, S., & Yeo, S. (2020). An analysis of the 2015 revised curriculum addition and subtraction of fractionsin elementary mathematics textbooks. School Mathematics, 22(3), 489-508. https://doi.org/10.29275/sm.2020.09.22.3.489
- Steffe, L. P., & Olive, J. (2002). Design and use of computer tools for interactive mathematical activity (TIMA). Journal of Educational Computing Research, 27(1), 55-76. https://doi.org/10.2190/GXQ4-60W8-CJY4-GKE1
- Streefland, L. (1991). Fractions in realistic mathematics education. Boston, MA: Kluwer.
- Streefland, L. (1993). Fractions: A realistic approach. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 289-325). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
- Suh, J., Moyer, P. S., & Heo, H. J. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. Journal of Interactive Online Learning, 3(4), 1-21.
- Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. Gary Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95-113). Reston, VA: The National Council of Teachers of Mathematics.
- Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
- Webel, C., Krupa, E., & McManus, J. (2016). Using representations of fraction multiplication. Teaching Children Mathematics, 22(6), 366-373. https://doi.org/10.5951/teacchilmath.22.6.0366
- Yang, E., & Shin, J. (2014). Students' mathematical reasoning emerging through dragging activities in open-ended geometry problems. Journal of Educational Research in Mathematics, 24(1), 1-27.
- Yeo, S. (2019). Investigating children's informal thinking: The case of fraction division. Journal of KSME Series D: Research in Mathematics Education, 22(4), 283-304.
- Yeo, S. (2020). Integrating digital technology into elementary mathematics: Three theoretical perspectives. Journal of KSME Series D: Research in Mathematics Education, 23(3), 165-179.
- Yin, R. K. (2014). Case study research: Design and methods (5th ed.). Thousand Oaks, CA: Sage.