Browse > Article

A Study on Setting of Mathematical modelling Task Space and Rating Scheme in its Complexity  

Shin, Hyun Sung (Kangwon National University)
Choi, Heesun (EBS)
Publication Information
Journal of the Korean School Mathematics Society / v.19, no.4, 2016 , pp. 357-371 More about this Journal
Abstract
The purpose of this study was to decide the task space and Rating Scheme of task difficulty in complicated mathematical modelling situations. One of main objective was also to conform the validation of Rating Scheme to determine the degree of difficulty by comparing the student performance with the statement of the theoretical model. In spring 2014, the experimental setting was in Modelling Course for 38 in-service teachers in mathematics education. In conclusions, we developed the Model of Task Space based on their solution paths in mathematical modelling tasks and Rating Scheme for task difficulty. The Validity of Rating Scheme to determine the degree of task difficulty based on comparing the student performance gave us the meaningful results. Within a modelling task the student performance verifies the degree of difficulty in terms of scoring higher using solution approaches determined as easier and vice versa. Another finding was some relations among three research topics, that is, degree of task difficulty on rating scheme, levels of students performance and numbers of specific heuristic. Those three topics showed the impressive consistence pattern.
Keywords
Mathematical modelling task space; task difficulty; rating scheme for task difficulty; specific heuristic;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 김민경, 민선희, 강선미 (2009). 초등교사들의 수학적 모델링에 대한 인식 조사 연구. 한국학교수학회논문집, 12(4), 411-431.
2 신현성 (2001). 수학적 모델링을 통한 교육과정의 구성원리. 한국학교수학회논문집, 4(2), 27-32.
3 신현성, 이명화 (2011). 실세계 상황에서 수학적 모델링 과제설정 효과. 한국학교수학회논문집, 14(4), 423-442.
4 신현성, 한혜숙 (2009) 한국과 미국의 교과서 체제 비교분석. 한국학교수학회논문집, 12(2), 309-325.
5 Blum, W. (1993). Mathematical modelling in mathematics education and instruction. Teaching and learning mathematics in context, 3-14.
6 Blum, W., & Leiss, D. (2005). "Filling Up"-the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In CERME 4-Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1623-1633).
7 Caldwell, J. H., & Goldin, G. A. (1979). Variables affecting word problem difficulty in elementary school mathematics. Journal for Research in Mathematics Education, 323-336.
8 Cauzinille-Marmeche, E., & Julo, J. (1998). Studies of micro-genetic learning brought about by the comparison and solving of isomorphic arithmetic problems. Learning and Instruction, 8(3), 253-269.   DOI
9 Cohors-Fresenborg, E., Sjuts, J., & Sommer, N. (2004). Komplexitat von Denkvorgangen und Formalisierung von Wissen. In Mathematische Kompetenzen von Schulerinnen und Schulern in Deutschland (pp. 109-144). VS Verlag fur Sozialwissenschaften.
10 Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95.   DOI
11 Galbraith, P. L., Henn, H. W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education: The 14th ICMI study (Vol. 10). Springer Science & Business Media.
12 Goldin, G. A., & Luger, G. P. (1975). Problem structure and problem solving behavior. In Proceedings of the 4th international joint conference on Artificial intelligence-Volume 1 (pp. 924-931). Morgan Kaufmann Publishers Inc..
13 Graumann, G. (2002). Mathematikunterricht in der Grundschule. Julius Klinkhardt.
14 Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children's experience. In Modelling and applications in mathematics education (pp. 89-98). Springer US.
15 Knifong, J. D., & Holtan, B. (1976). An analysis of children's written solutions to word problems. Journal for Research in Mathematics Education, 106-112.
16 Jerman, M. (1974). Problem length as a structural variable in verbal arithmetic problems. Educational Studies in Mathematics, 5(1), 109-123.   DOI
17 Kaiser, G. (2013). Introduction: ICTMA and the teaching of modeling and applications. In Modeling students' mathematical modeling competencies (pp. 1-2). Springer Netherlands.
18 Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for research in mathematics education, 163-180.
19 Lesh, R., & Fennewald, T. (2010). Introduction to Part I Modeling: What Is It? Why Do It?. In Modeling students' mathematical modeling competencies (pp. 5-10). Springer US.
20 Lester, F. K. (1978). Mathematical problem solving in the elementary school: Some educational and psychological considerations. In Mathematical problem solving: Papers from a research workshop (pp. 53-86). ERIC Center Columbus.
21 Linville, W. J. (1969). The Effects of Syntax and Vocabulary upon the Difficulty of Verbal Arithmetic Problems with Fourth Grade Students.
22 National Council of Teachers of Mathematics [NCTM] (2000). Principle and Standards for School Mathematics. VA: NCTM
23 Newell, A., & Simon, H. A. (1972). Human problem solving (Vol. 104, No. 9). Englewood Cliffs, NJ: Prentice-Hall.
24 Niss, M. (2001). Issues and Problems of Research on the Teaching and Learning of Applications and Modelling (pp. 72-88). Matos et al., loc. cit.
25 Silver, E. A., & Marshall, S. P. (1990). Mathematical and scientific problem solving: Findings, issues, and instructional implications. Dimensions of thinking and cognitive instruction, 1, 265-290.
26 Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of experimental psychology: Learning, memory, and cognition, 17(3), 398.   DOI
27 Reit, X. R., & Ludwig, M. (2015). Thought structures as an instrument to determine the degree of difficulty of modelling tasks. In CERME 9-Ninth Congress of the European Society for Research in Mathematics Education (pp. 917-922).
28 Silver, E. A. (1981). Recall of mathematical problem information: Solving related problems. Journal for research in mathematics education, 54-64.
29 Stavy, R., & Tirosh, D. (1993). When analogy is perceived as such. Journal of Research in Science Teaching, 30(10), 1229-1239.   DOI
30 Varaki, B. S., & Earl, L. (2006). Math modeling in educational research: An approach to methodological fallacies. Australian journal of teacher Education, 31(2), 3.
31 vom Hofe, R., Jordan, A., Hafner, T., Stolting, P., Blum, W., & Pekrun, R. (2009). On the Development of Mathematical Modelling Competencies The PALMA Longitudinal Study. Mathematical applications and modelling in the teaching and learning of mathematics, 47.
32 Zawojewski, J. S., & McCarthy, L. (2007). Numeracy in Practice. Principal Leadership, 7(5), 32-37.