Analysis of problem solving competency and types of tasks in elementary mathematics textbooks: Challenging/Thinking and inquiry mathematics in the domain of number and operation |
Yeo, Sheunghyun
(University of Alabama)
Suh, Heejoo (Sungkyunkwan University) Han, Sunyoung (Sungkyunkwan University) Kim, Jinho (Daegu National University of Education) |
1 | Han, H., Choi, H., Kim, S., & Lee, J. (2017). The perceptions of pre-service mathematics teachers' mathematical problem posing and problem posing strategies. Journal of Learner-Centered Curriculum and Instruction, 17(22), 325-352. DOI |
2 | Bae, J. H., & Park, M. (2016). The effects of reflective problem posing activities on students' problem solving ability and attitudes toward mathematics. Journal of Elementary Mathematics Education in Korea, 20(2), 311-331. |
3 | Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83, 37-55. DOI |
4 | Brannick, M. T., & Prince, C. (1997). An overview of team performance measurement. In M. T.Brannick, E. Salas, & C. Prince (Eds.), Team performance assessment and measurement: Theory methods and applications (pp. 3-16). Mahwah: Lawrence Erlbaum Associates. |
5 | Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students' mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401-421. DOI |
6 | Choi, Y. S., & Bae, J. S. (2004). Effects of teaching with problem posing on mathematical problem solving ability and attitude in elementary school mathematics. Journal of Elementary Mathematics Education in Korea, 8(1), 23-43. |
7 | Choi, H. J., & Kim, S. L. (2011). Activities of mathematical problem posing using real-life materials. Journal of Elementary Mathematics Education in Korea, 15(1), 121-139. |
8 | Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. Elementary School Jurnal, 103(3), 287-311. DOI |
9 | Ministry of Education (2019d). Korean national elementary mathematics workbook 4-2. Seoul: Chunjae Education. |
10 | Ministry of Education (2019e). Korean national elementary mathematics 5-1. Seoul: Chunjae Education. |
11 | Jitendra, A. K., Griffin, C., Deatline-Buchman, A.,Dipipi-Hoy, C., Sczesniak, E., Sokol, N. G., & Xin, Y. P. (2005). Adherence to mathematics professional standards and instructional design criteria for problem-solving in mathematics. Exceptional Children, 71(3), 319-337. DOI |
12 | Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521-1540. DOI |
13 | Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52(3), 243-270. DOI |
14 | Hesse, F., Care, E., Buder, J., Sassenberg, K., &Griffin, P. (2015). A framework for teachable collaborative problem solving skills. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching 21st century skills (pp. 37-56). Dordrecht: Springer. |
15 | Hildebrandt, M. (2008). Defining profiling: A new type of knowledge? In M. Hildebrandt & S. Gutwirth (Eds.), Profiling the European citizen (pp. 17-45). Rotterdam, Netherlands: Springer. |
16 | Jay, E. S., & Perkins, D. N. (1997). Problem finding: The search for mechanism. In M. A. Runco (Ed.), The creativity research handbook (pp. 257-293). Cresskill, New Jersey: Hampton Press. |
17 | Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press, Inc. |
18 | Lee, D. H. (2017). The analysis of problem posing cases of pre-service primary teacher. School Mathematics, 19(1), 1-18. |
19 | Kilpatrick, J. (2009). A retrospective account of the past 25 years of research on teaching mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspective (pp. 1-15). NY: Lawrence Erlbaum Associates, Inc. |
20 | Kim, K. O., & Rye, S. R. (2009). The effects of the situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes. School Mathematics, 11(5), 665-683. |
21 | Lee, C., & Yun, M. (2020). Delphi method looking for factors of collaborative problem solving competencies and collaborative metacognition in mathematics. Journal of Learner-Centered Curriculum and Instruction, 20(23), 693-719. |
22 | Remillard, J., van Steenbrugge, H., & Bergqvist,T. (2014). A cross-cultural analysis of the voice of curriculum materials. In K.Jones, C. Bokhove, G. Howson, & L. Fan (Eds.), Proceedings of the International Conference on Mathematics Textbook Research and Development (pp.395-400). University of South Hampton. |
23 | Suh, H., Lee, S. Y., & Han, S. (2019). Educative supports for high school geometry instruction: An examination of, and suggestions for teachers' guides. School Mathematics, 21(3), 531-559. DOI |
24 | National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. |
25 | Ministry of Education (2019f). Korean national elementary mathematics workbook 5-2. Seoul: Chunjae Education. |
26 | Gracin, D. (2018). Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples. International Journal of Mathematical Education in Science and Technology, 49(7), 1003-1024. DOI |
27 | Griffin, P., Care, E., & McGaw, B. (2012). Thechanging role of education and schools. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching 21st century skills (pp. 1-15). Heidelberg: Springer. |
28 | Kim, J. S. (1998). A study on the problems in the school textbooks from a problem solving point of view. The Journal of Curriculum Studies, 16(2), 205-223. |
29 | Ministry of Education (2019g). Korean national elementary mathematics 6-1. Seoul: Chunjae Education. |
30 | Ministry of Education (2019h). Korean national elementary mathematics workbook 6-2. Seoul: Chunjae Education. |
31 | National Research Council. (2011). Assessing 21st century skills. Washington, DC: National Academies Press. |
32 | Nylund, K. L., Asparouhov, T., & Muthen, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixturemodeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535-569. DOI |
33 | Yoon, S. A., & Paik, S. (2010). A study to improve teaching methods of mathematical problem posing in elementary mathematics. The Journal of Korea Elementary Education, 21(1), 25-47. DOI |
34 | van Zanten, M., & van den Heuvel-Panhuizen, M. (2018). Opportunity to learn problem solving in Dutch primary school mathematics textbooks. ZDM, 50(5), 827-838. DOI |
35 | Kim, H, M., & Han, S. Y. (2018). A study on the development of assessment tool for mathematics problem solving competency. School Mathematics, 20(1), 83-105. DOI |
36 | Song, M. J., & Park, J. S. (2005). The effects of development and application of problem posing program on mathematics learning achievements, attitude and interest. Journal of Elementary Mathematics Education in Korea, 9(1), 1-18. |
37 | Xia, X., Lu, C., & Wang, B. (2008). Research on mathematics instruction experiment based on problem posing. Journal of Mathematics Education, 1(1), 153-163. |
38 | Yun, M. R., & Park, J. S. (2008). The effects of problem posing program through structure-centered cooperative learning on mathematics learning achievements and mathematical disposition. Journal of Elementary Mathematics Education in Korea, 12(2), 101-124. |
39 | World Economic Forum. (2016, January). The future of jobs: Employment, skills and workforce strategy for the fourth industrial revolution. Geneva, Switzerland: World Economic Forum. |
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),1-18 DOI |
41 | Kim, H. Y., Huh, N., Noh, J. H., & Kang, O. K. (2012). Teachers' perceptions and applications of key competency-based learning and instruction in mathematics classroom. Journal of the Korean School Mathematics Society, 15(4), 605-625. |
42 | Anderson, J. R., Lee, H. S., & Fincham, J. M.(2014). Discovering the structure of mathematical problem solving. NeuroImage,97, 163-177. DOI |
43 | Cai,J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., ... & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers' conceptions on problem posing and lesson design. International Journal of Educational Research, 102, 101404. DOI |
44 | 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. DOI |
45 | Choi & Pang (2018). Research on the instructional strategies to foster problem solving ability as mathematical subject competency in elementary classrooms. Education of Primary School Mathematics, 21(3), 351-374. DOI |
46 | Darling-Hammond, L., Hyler, M., & Gardner, M.(2017). Effective teacher professional development. Palo Alto, CA: Learning Policy Institute. |
47 | Kim, J. H., & Kim, I. K. (2011). Future research topics in the filed of mathematical problems solving: Using delphi method. Journal of Elementary Mathematics Education in Korea, 14(2), 187-206. |
48 | Kim, Y. M., & Lee, C. H. (2014). Analysing high school students' mathematical belief system and core belief factors. Journal of Korea Society Educational Studies in Mathematics, 16(1), 111-133. |
49 | Kim, J. W., Pang, J. S., & Hwang, J. N. (2020). An analysis of mathematics competencies in elementary mathematics textbooks for fifth and sixth grade. Mathematics Education, 59(2), 147-166. |
50 | Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259-274. DOI |
51 | Kwon, J. R. (2020). International comparison of ways in which competencies is reflected in mathematics curriculum: Focused on France, Australia and British Columbia in Canada. Communications of Mathematical Education, 34(2), 135-160. |
52 | Lee, M. (2019). Analysis of Discourses in Collaborative Problem Solving Using Mathematics History. Journal of Learner-Centered Curriculum and Instruction, 19(16), 311-333. |
53 | Jader, J., Lithner, J., & Sidenvall, J. (2020). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51(7), 1120-1136. DOI |
54 | Drake, C., Land, T. J., & Tyminski, A. M. (2014).Using educative curriculum materials to support the development of prospective teachers' knowledge. Educational Researcher, 43(3), 154-162. DOI |
55 | Fiore, S., & Schooler, J. W. (2004). Process mapping and shared cognition: Teamwork and the development of shared problem models. In E. Salas & S. M. Fiore (Eds.), Team cognition: Understanding the factors that drive process and performance (pp. 133-152). Washington, DC: American Psychological Association. |
56 | Hesse, F., Buder, J. Care, E., Griffin, P., & Sassenberg, K. (2012). Draft: A Framework for teachable collaborative problem solving skills. ATC21S: Australia, Melbern. Retrieved from: http://atc21s.org/wp-content/uploads/2014/01/white-paper7-Framework-for-Teachable-Collaborative-ProblemSolving-Skills_DRAFT.pdf |
57 | Jung, S. G., & Park, M. (2010). The effects of the mathematical problem generating program on problem solving ability and learning attitude. Journal of Elementary Mathematics Education in Korea, 14(2), 315-335. |
58 | Son, T., Hwang, S., & Yeo, S. (2020). An analysis of the 2015 revised curriculum addition and subtraction of fractions in elementary mathematics textbooks. School Mathematics, 22(3), 489-508. DOI |
59 | Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521-539. DOI |
60 | Silver, E. A., Mamona-Downs, J., Leung, S. S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27(3), 293-309. DOI |
61 | Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform: An analysis of demands and opportunities for teacher learning. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 37-55). NewYork: Routledge. |
62 | Organisation for Economic Cooperation and Development. (2018). The future of education and skills: Education 2030. OECD Education Working Papers. |
63 | Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. DOI |
64 | United Nations Educational, Science and Cultural Organization. (2017). Education for sustainable development goals: Learning Objectives. Paris, France: UNESCO. |
65 | Ministry of Education (2015b). Mathematics curriculum. Ministry of Education Notice 2015-74 [supplement 8]. |
66 | Kim, S. (2019). An analysis of actual application of primary mathematics textbooks in respect to core competency: Focused on the 2015 revision curriculum. Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology, 9(4), 55-67. DOI |
67 | Kim, S. B., & Hwang, H. J. (2015). An investigation on the application for problem generation and problem reformulation by pre-service teachers. Communications of Mathematical Education, 29(3), 533-551. DOI |
68 | Kim, J. K., & Lim, M. K. (2001). An effect coming to the problem solving ability from the problem posing activity by presenting the problem situation. Journal of Elementary Mathematics Education in Korea, 5, 77-98. |
69 | Klein, C., DeRouin, R. E., & Salas, E. (2006). Uncovering workplace interpersonal skills: A review, framework, and research agenda. In G. P. Hodgkinson & J. K. Ford (Eds.), International review of industrial and organisational psychology (pp. 80-126). New York: Wiley. |
70 | Organisation for Economic Cooperation and Development.. (2014). PISA 2012 results: Creative problemsolving: Students' skills in tackling real-life problems (Volume, V). Paris: OECD Publishing. |
71 | Oh, Y., & Jeon, Y.(2018). The effect of problem-posing activities on the affective domain of mathematics. Journal of the Korea Contents Association, 18(2), 541-552. DOI |
72 | Park, H. Y., & Lim, H. (2014). Analyzing features of collaborative problem solving competencies in PISA and ATC21S : Implications for instruction and assessment in Korea. Journal of Learner-Centered Curriculum and Instruction, 14(9), 439-462. |
73 | Organisation for Economic Cooperation and Development.. (2013). PISA 2015 collaborative problem solving framework. Paris: OECD. Retrieved from http://www.oecd.org/pisa/pisaproducts/Draft%20PISA%202015%20Collaborative%20Problem%20Solving%20Framework%20.pdf. |
74 | Oh, D. G., & Kim, S. L (2010). The effect of problem posing activities using fairy tale on mathematical attitude and academic achievement. East Asian Mathematical Journal, 26(4), 509-533. |
75 | Oh, Y., & Park, J. (2019). Exploring the task types of mathematical modeling applied to elementary school. The Journal of Korea Elementary Education, 30(1), 87-99. DOI |
76 | Pang, J. S. & Kim, S. H. (2006), An analysis on contents related to problem solving in the 7th elementary mathematics curriculum and instructional materials. School Mathematics, 8(3), 341-364. |
77 | Park, K., Lee, H., Park, S., Kang, E., Kim, S., Lim, H.,...& Yeo, M.(2015). A study on the development of proposal of mathematics curriculum revision II. Korea Foundation for the Advancement of Science and Creativity research report BD15120005. |
78 | Polya, G. (1980). On solving mathematical problems in high school. In S. Krulik (Ed.), Problem solving in school mathematics(pp. 1-2). Reston, Virginia: NCTM. |
79 | Remillard, J. T., & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM, 46(5), 705-718. DOI |
80 | Davis, E. A., Palincsar, A. S., Smith, P. S., Arias,A. M., & Kademian, S. M. (2017). Educative curriculum materials: Uptake, Impact, and Implications for Research and Design. Educational Researcher, 46(6), 293-304. DOI |
81 | Dillenbourg, P., & Traum, D. (2006). Sharing solutions: Persistence and grounding in multi-modal collaborative problem solving. The Journal of the Learning Sciences, 15, 121-151. DOI |
82 | Yimer, A., & Ellerton, N. F. (2010). A five-phase model for mathematical problem solving: Identifying synergies in pre-service-teachers' metacognitive and cognitive actions. ZDM, 42(2), 245-261. DOI |
83 | Salas, E., Cooke, N. J., & Rosen, M. A. (2008). On teams, teamwork, and team performance: Discoveries and developments. Human Factors: The Journal of the Human Factors and Ergonomics Society, 50, 540-547. DOI |
84 | Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28. |
85 | Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 97(3), 75-80. |
86 | Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis. New York: Cambridge University Press. |
87 | Fan, L., & Zhu, Y. (2007). Representation ofproblem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics, 66(1), 61-75. DOI |
88 | Fiore, S. M., Rosen, M. A., Smith-Jentsch, K. A.,Salas, E., Letsky, M., & Warner, N. (2010). Toward an understanding of macro cognition in teams: Predicting processes in complex collaborative contexts. Human Factors, 52, 203-224. DOI |
89 | Graesser, A. C., Foltz, P. W., Rosen, Y., Shaffer, D.W., Forsyth, C., & Germany, M.-L. (2018). Challenges of assessing collaborative problem solving. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching 21st century skills (pp. 75-91). Heidelberg: Springer. |
90 | Li, X., Song, N., Hwang, S., & Cai, J.(2020).Learning to teach mathematics through problem posing: teachers' beliefs and performance on problem posing. Educational Studies in Mathematics, 107(1), 1-23. |
91 | Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students' mathematical learning. In M. Hoines y A. Fuglestad (Eds.), Proceedings of the 28th annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257-264). Bergen, Noruega: Bergen University College. |
92 | Linzer, D. A., & Lewis, J. B. (2011). poLCA: An R package for polytomous variable latent class analysis. Journal of statistical software, 42(1), 1-29. |
93 | Mayer, R. E., Sims, V., & Tajika, H. (1995). Brief note: A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460. DOI |
94 | Ministry of Education (2015a). 2015 revised curriculum. Ministry of Education Notice 2015-80 [supplement 1]. |
95 | Ministry of Education (2019a). Korean national elementary mathematics 3-1. Seoul: Chunjae Education. |
96 | Ministry of Education (2019b). Korean national elementary mathematics workbook 3-2. Seoul: Chunjae Education. |
97 | Ministry of Education (2019c). Korean national elementary mathematics 4-1. Seoul: Chunjae Education. |
98 | Ball, D. L, & Cohen, D. K. (1996). Reform by the book: What is-or might be-the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-14. DOI |
99 | Bae, H. J., & Lee, D. H. (2016). An analysis on statistical units of elementary school mathematics textbook. ournal of Elementary Mathematics Education in Korea, 20(1). 55-69. |