References
- Kwon, S. Y. (2003). A study on elementary school students' understanding of fraction. School Mathematics, 5(2), 259-273.
- Ministry of Education (2015). Elementary mathematics curriculum: Notice 2015-80. Seoul: Ministry of Education.
- Ministry of Education (2016). Elementary mathematics 4-1 teacher's guide. Seoul: Chunjae Education.
- Ministry of Education (1997). Elementary mathematics curriculum. Seoul: Author.
- Kim, M. (2010). An analysis on cognitive obstacles while doing addition and subtraction with fractions. Unpublished Master Thesis at Seoul National University of Education.
- Kim, M. J. (2007). Understanding of the construct polygons by using teaching aids. Unpublished Master Thesis at Hongik University.
- Kim, S. M. (2010). The effect of learner-centered lesson on creative problem solving ability in science, academic achievement in science, attitude toward science. Ewha Womans University.
- Kim, J. H. (2004). Practical Using of Tangram for Inducing Motivation and Improving Creativity.
- Kim, J. H. (2020a). Tasks with the various entry and exit points for implementing learner-centered instruction in a mixed-ability classroom. Explorations into Future Education, 41(1), 32-45.
- Kim, J. (2020b). Mathematics classroom where students feel happy: 3rd grade 1st semester addition and subtraction. Gyengki : Gyoyuggwahagsa.
- Kim, J. H. (2004). Instructional materials for learner-centered mathematics instruction. 37, 169-185.
- Kim, J. H. (2015). Elementary school figure exploration (with GeoGebra): 3rd and 4th graders. Seoul: Gyowoosa.
- Kim, J. H. (2018a). Reexamines some important terminologies for implementing learner-centered instruction. Korean Journal of Educational Research, 39(2), 1-11.
- Kim, J. H. (2018b). Mathematics classroom where students feel happy: 1st grade 1st semester operation instructions. Gyengki: Gyoyuggwahag-sa.
- Kim, J. H. (2020). Implementation of learner-centered instruction: Focused on the open-ended task with several results. Korean Journal of Educational Research, 40(2), 1-10.
- Kim, J. & Kim, S. M. (2013). Learner-centered mathematics teaching and learning from a constructionist' perspective. In Kim, J., Chang, K., Han, I., and Go, H., Constructivism and Korea mathematics education (pp. 45-64). Seoul : Kyongmoonsa.
- Kim, J., Lee, S. M., & Kim, S. R. (2010). Achievement of students who have learner-centered instruction for multiplication units. Journal of Elementary Mathematics Education in Korea, 14(1), 136-151.
- Kim, C. H. (2004). Research for the diagnostic and prescription of fractional addition and subtraction. Gyeongin National University of Education.
- Nam, H. S. (2002). Developing a program of teaching unlike-denominator fractional operations. Seoul National University of Education.
- Roh, Y. A. & Ahn, B. G. (2007). Analysis on error of fourth grade student in geometric domain. Journal of Elementary Mathematics Education in Korea, 11(2), 199-216.
- Ryu, H. C. (2004). How to use inquiry type software in mathematics education. The 14th Mathematics Education Seminar, Institute for Mathematics Education, Korea National University of Education, 56-73.
- Park, K. S. (1996). Some characteristics that can be found in mathematics teaching and learning in elementary schools in Korea. Research in Mathematics Education, 6(2), 99-113.
- Park, S. S. (1993). The effects of elaboration on logical reasoning of 4th grade children. Korea National University of Education.
- Pang, J. S., Kim, S. H., & Park, K. R. (2006). Development of teaching and learning materials to establish knowledge of elementary school teachers' mathematics and teaching methods. 2005 Subject Joint Research Results Report. KRF-2005-030-B00045, 1943-2029.
- Oh, S. H. (2000). A study on effectiveness of a fraction operation program using cusenaire rods. Unpublished master thesis, Korea National University of Education.
- Lee, E. S. (2016). Effects of mathematical instructions based on constructivism on leaners' knowledge generation level and reasoning ability. Unpublished master thesis, Daegu National University of Education
- Lee, J. E. (2005). Study on transition of teacher knowledge of fractions. Unpublished doctoral dissertation, Korea National University of Education.
- Lee, H. J. (1999). Constructivism and construction of curriculum. Journal of the Elementary Education Society, 2, 35-61.
- Lim, Jiye. (2017). An analysis of the examples of triangles and quadrangles generated by elementary school mathematics textbooks, teachers, and students. Unpublished master thesis, Seoul National University of Education.
- Jung, S. Y. (2017). The analysis of influencing on figure conceptual formation and mathematical tendency using GeoGebra in mathematics. Unpublished master thesis, Seoul National University of Education.
- Jung, E. S. (2005). A scheme of the instruction of geometry concepts through the example and counterexample. Unpublished master thesis, Gyeongin National University Education.
- Jeong, E. S. (2009). An comparative analysis of fraction concept in mathematics textbooks of Korea and Singapore. Mathematics Education, 19(1), 25-43.
- Jung, H. (2013). Effects of mathematical instructions based on constructivism on learners' reasoning ability. Unpublished master thesis, Daegu National University of Education.
- Cho, S. Y. (2011). Effects of mathematical instructions based on constructivism on learners' reasoning ability. Unpublished master thesis, Daegu National University of Education.
- Jo, Y. R. (2018). Effects of learner-centered mathematical instructions on learners′mathematical achievement and attitude toward mathematics - Focus on dividing fractions of the 6th Grade. Unpublished master thesis, Daegu National University of Education.
- Choi, Y. J. (2005). Study on the teaching methods of fractions concept through the analysis of misconcepts of fractions. Unpublished master thesis, Jeon-ju National University of Education
- Hwang, S. N. (2015). Effects of the leaner-centered mathematical activity on student's mathematical thinking and mathematical learning attitude. Unpublished master thesis, Ewha Womans University
- Hwang, H. J., Kim, J., Ko, H. K., & Suh, B. E. (2014, Eds). Principles and application learning and teaching of mathematics. Seoul: Kyungmoonsa.
- Barnett-Clark, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understandings of rational numbers for teaching mathematics in grades 3-5. Reston, VA: NCTM Press.
- Bezuk, N. S., & Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 118-136). New York: Macmillan.
- Black, P., Harrison, C., Lee, C., Marshall, B., & William, D. (2003). Assessment for learning: Putting it into practice. New York: Open University Press.
- Burns, M. (2001). Lessons for introducing fractions to grades 4-5. Sausalito, CA: Math Solutions Publications.
- Burns, M. (2003). Lessons for extending fractions to grades 5. Sausalito, CA: Math Solutions Publications.
- Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645. https://doi.org/10.1177/016146810811000302
- Chapin, S. H., O'Connor, C. & Anderson, N. C. (2013). Classroom discussions in math: A teacher's guide for using talk moves to support the Common Core and more, Grades K-6: A multimedia professional learning resource (3rd Ed.). Sausalito, CA: Math Solutions Publications.
- Charalambous, C. Y. & Pitta-Pantazi, D. (2015). Perspectives on priority mathematics education: Unpacking and understanding a complex relationship linking teacher knowledge, teaching, and learning. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed.) (pp. 19-59). New York, NY: Routledge.
- Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula 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
- Kim & Yeo (2019). Teaching practices for all learners in the mathematics classroom. Research in Mathematical Education, 22(2), 123-134. https://doi.org/10.7468/jksmed.2019.22.2.123
- Kim, J., Colen, Y., & Colen, J. (2013). Reform based instruction in Korea. In J. Kim, Han, I., Park, M., & Lee, J. (Eds.), Mathematics education in Korea: Curriculum and teaching and learning practices (pp. 104-129). Singapore: World Scientific Press.
- Levi, L., & Empson, S. B. (2011). Extending children's mathematics: Fractions and decimals. Portsmouth: Heinemann.
- NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.
- NCTM (2000). Principles and standards for school mathematics. Reston, VA: Author.
- Payne, J., Towsley, A., & Huinker, D. (1990). Fractions and decimals. In J. Payne & C. E. Clements (Eds.), Mathematics for the young child (pp. 175-200). Reston, VA: NCTM Press.
- Rectanus, C. (1994). Math by all means: Geometry grades 3-4. Math Solutions Publications.
- Reys, R., Lindquist, M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics. John Wiley & Sons.
- Schuster, L. (2009). A month-to-month guide: Fourth-grade math. Sausalito, CA, Math Solutions Publications.
- Silver, E. A., & Peterson, R. (1985). Decision systems for inventory management and production planning. Hoboken, NJ: John Wiley & Sons Inc.
- Skemp, R. R. (1987). The psychology of learning mathematics. London: Penguin Group.
- Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80. https://doi.org/10.1080/1380361960020103
- Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. https://doi.org/10.3102/00028312033002455
- von Glasersfeld, E. (1987). The construction of knowledge: Contributions to conceptual semantics. Salinas, CA: Intersystems Publications.
- Watson, A. & Ohtani, M. (Eds.) (2015). Task design in mathematics education. New York: Springer.
- Yeh, C., Ellis, M. W., & Hurtado, C., K. (2017). Reimagining the mathematics classroom: Creating and sustaining productive learning environments. Reston, VA: National Council of Teachers of Mathematics Press.