1 |
Lin, C. Y., Becker, J., Byun, M. R., Yang, D. C., & Huang, T. W. (2013). Preservice teachers' conceptual and procedural knowledge of fraction operations: A comparative study of the United States and Taiwan. School Science and Mathematics, 113(1), 41-51.
DOI
|
2 |
Luo, F., Lo, J. J., & Leu, Y. C. (2011). Fundamental fraction knowledge of preservice elementary teachers: A cross-national study in the United States and Taiwan. School Science and Mathematics, 111(4), 164-177.
DOI
|
3 |
Ministry of Education (2019). 5-2 Mathematics textbook. Seoul, Korea: Chunjae Textbooks.
|
4 |
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.
|
5 |
Osana, H. P., & Pelczer, I. (2015). A review on problem posing in teacher education. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing (pp. 469-492). Springer.
|
6 |
Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics (11th ed.). John Wiley & Sons.
|
7 |
Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.
DOI
|
8 |
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
|
9 |
Adu-Gyamfi, K., Schwartz, C. S., Sinicope, R., & Boss, M. J. (2019). Making sense of fraction division: Domain and representation knowledge of preservice elementary teachers on a fraction division task. Mathematics Education Research Journal, 31, 507-528.
DOI
|
10 |
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407.
DOI
|
11 |
Bansilal, S., & Ubah, I. (2020). The use of cross multiplication and other mal-rules in fraction operations by pre-service teachers. The Journal of Mathematical Behavior, 58, 100781.
DOI
|
12 |
Baumanns, L., & Rott, B. (2021). Rethinking problem-posing situations: A review. Investigations in Mathematics Learning, 13(2), 59-76.
DOI
|
13 |
Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM Mathematics Education, 37(3), 149-158.
DOI
|
14 |
Yeo, S., & Webel, C. (2022). Elementary students' fraction reasoning: a measurement approach to fractions in a dynamic environment. Mathematical Thinking and Learning, 1-27.
|
15 |
Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102,101391.
DOI
|
16 |
Webel, C., & DeLeeuw, W. W. (2016). Meaning for fraction multiplication: Thematic analysis of mathematical talk in three fifth grade classes. The Journal of Mathematical Behavior, 41, 123-140.
DOI
|
17 |
Webel, C., Krupa, E., & McManus, J. (2016). Using representations of fraction multiplication. Teaching Children Mathematics, 22(6), 366-373.
DOI
|
18 |
Wilkins, J. L. (2008). The relationship among elementary teachers' content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139-164.
DOI
|
19 |
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students' understandings of fractions. Educational Studies in Mathematics, 64(3),293-316
DOI
|
20 |
Chong, Y. O. (2013). Teaching multiplication with whole numbers in elementary school mathematics: Focusing on the introduction of the concept of multiplication and multiplication facts. School Mathematics, 15(4), 889-920.
|
21 |
Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.276-295). Simon & Schuster Macmillan.
|
22 |
Isik, C., & Kar, T. (2012). The analysis of the problems posed by the pre-service teachers about equations. Australian Journal of Teacher Education, 37(9), 93-113.
|
23 |
Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. Technology in Mathematics Education, 4(7), 518-525.
|
24 |
Ticha, M., & Hospesova, A. (2013). Developing teachers' subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133-143.
DOI
|
25 |
Tobias, J. M. (2012). Prospective elementary teachers' development of fraction language for defining the whole. Journal of Mathematics Teacher Education, 16(2), 85-103.
DOI
|
26 |
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J.M. (2019). Elementary and middle school mathematics: Teaching developmentally (9th ed.). Pearson.
|
27 |
Izsak, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95-143.
DOI
|
28 |
Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (3th ed.). Routledge.
|
29 |
Kar, T., & Isik, C. (2014). Analysis of problems posed by pre-service primary teachers about adding fractions in terms of semantic structures. International Electronic Journal of Mathematics Education, 9(2), 135-146.
DOI
|
30 |
Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70(3), 259-274.
DOI
|
31 |
Lee, S. J., & Shin, J. (2011). Preservice teachers' key developmental understandings (KDUs) for fraction multiplication. Journal of the Korean School Mathematics Society, 14(4), 477-490.
|
32 |
Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1-7.
DOI
|
33 |
Watanabe, T. (2003). Teaching multiplication: An analysis of elementary school mathematics teachers' manuals from Japan and the United States. The Elementary School Journal, 104(2), 111-125.
DOI
|
34 |
Viera, A. J., & Garrett, J. M. (2005). Understanding inter observer agreement: The kappa statistic. Fam Med, 37(5), 360-363.
|
35 |
Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
DOI
|
36 |
Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM Mathematics Education, 40(5), 833-843.
DOI
|
37 |
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum.
|
38 |
Noh, J., Ko, H. K., & Huh, N. (2016). An analysis of pre-service teachers' pedagogical content knowledge about story problem for division of fractions. Elementary Mathematics Education, 19(1), 19-30.
|
39 |
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
DOI
|
40 |
Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101-118.
DOI
|
41 |
Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers'mathematical understanding exhibited in problem posing and problem solving. ZDM Mathematics Education, 53(4), 937-949.
DOI
|
42 |
Yeo, S. (2019). Investigating children's informal knowledge and strategies: The case of fraction division. Research in Mathematical Education, 22(4), 283-304.
DOI
|
43 |
Silver, E. A., & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
DOI
|
44 |
Son, T., & Hwang. S. (2021). Examining teachers' noticing competency on students' problem-solving strategies: Focusing on errors in fraction addition and subtraction with uncommon denominators problems. The Mathematical Education, 60(2), 229-247.
DOI
|
45 |
Steffe, L. P., & Olive, J. (2010). Children's fractional knowledge. Springer.
|
46 |
Stoyanova, E. (1998). Problem posing in mathematics analyses classrooms. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp. 164-185). MASTEC, Edith Cowan University.
|
47 |
Yeo, S. (2021). Semiotic mediation through technology: The case of fraction reasoning. The Mathematical Education, 60(1), 1-19.
DOI
|
48 |
Yim, J. (2012). Models and the algorithm for fraction multiplication in elementary mathematics textbooks. School Mathematics, 14(1), 135-150.
|
49 |
Hospesova, A., & Ticha, M. (2015). Problem posing in primary schoolteacher training. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing (pp. 433-447). Springer.
|
50 |
Lee, J., & Pang, J. (2019). A comparative analysis of fraction multiplication in Korean and Japanese elementary mathematics textbooks: Focused on quantitative reasoning. Journal of Educational Research in Mathematics, 29(4), 831-854.
DOI
|
51 |
Son, J. W., & Lee, J. E. (2016). Pre-service teachers' understanding of fraction multiplication, representational knowledge, and computational skills. Mathematics Teacher Education and Development, 18(2), 5-28.
|