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http://dx.doi.org/10.7858/eamj.2020.013

A Study of Modelling Task for Mathematical Modelling in the Secondary Schools  

Oh, Chun Young (Department of Mathematics of Education Chonnam National University)
Publication Information
East Asian mathematical journal / v.36, no.2, 2020 , pp. 147-172 More about this Journal
Abstract
The purpose of this study is to provide to understand correctly for teachers and pre-service teachers who have the wrong conception of mathematical modeling. We present the differences modeling problems and general application problems to identify between general application and modeling problems. We propose the entire process from modeling tasks development to solve the problems of mathematical modeling. Additionally, the entire process of the possible solutions was concluded for the presented modeling problems. We proposed what students and teachers should perform at each stage of each phase of the modeling cycle. The concrete tasks were suggested for teachers and students at each phase of modeling cycles, with the specific role of the teacher in the overall process for students' modeling activities.
Keywords
Mathematical modeling; Modeling problems; Modeling cycle;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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1 Maass K.,(2010), Classification scheme for modelling tasks, J Math Didakt 31: 285-311.   DOI
2 Maria L.H., Levy R. Felton-Koestler M. D. & Zbie R. M(2016), Mathematical modeling in the high school curriculum, Mathematics Teacher, 110(5).
3 Malkevitch J. (2012), http://www.ams.org/publicoutreach/feature-column/fc-2012-09
4 Markham, T., John L. & Jason R. (2003), Project-based Learning Handbook: A Guide to Standards Focused Project-Based Learning for Middle and High School Teachers. Novato, CA: Buck Institute for Education.
5 NCTM (2016), Mathematical modeling and mathematical mathematics, NCTM.
6 Niss, M. Blum W. & Galbraith P. (2007), Modelling and applications in mathematics education, The 14th ICMI Study, springer.
7 Niss, M. (2015) Mathematical competencies and PISA, K. stacey, R. Turner (eds.), Assessing Mathematical Literacy, pp.35-55, DOI 10.1007/978-3-319-10121-7_2, Springer International Publishing Switzerland.
8 Oliveira A. M. & Barbosa J. C., (2008). The teachers' tensions in mathematical modelling practice, Mathematical applications and modelling in the teaching and learning of mathematics, Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematical ducation in Monterrey, Mexico, July 6-13,
9 권기석, 박배훈 (1997), 고등학교에서 수학적 모델링의 활용에 관한 연구, 한국 수학교육학회지 시리즈 A, <수학교육> 36(2), 149-159.
10 김휴진(2009), 중학생들의 수학적 모델링 과정 분석과 SOLO 분류법을 활용한 평가, 석사학위 논문, 이화여자대학교.
11 박선영.한선영.(2018), 수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용, 한국 수학교육학회지 시리즈 A, <수학교육>, 57(3), 289-309.
12 박슬희.(2013), 중학생의 수학적 모델링 정교화 과정에 관한 사례 연구, 석사학위논문, 교원대학교 교육대학원.
13 서지희 윤종국 이광호(2013), 중학교 3학년 수학 영재 학생들을 위한 수학적 모델링 교수.학습 자료의 개발 및 적용: 쓰나미를 소재로, 대한수학교육학회, 학교수학, 15(4), 785 -799.
14 손홍찬, 류희찬(2007). 수학적 모델링에서 스프레드시트 환경이 수학적 모델의 정교화 과정에 미치는 역할, 대한수학교육학회, 학교수학, 9(4), 467-486.
15 이기열, 이병수(1999), 수학적 모델링을 통한 학습지도, 한국수학교육학회지 시리즈 E: 수학교육 논문집, 9, 187-201.
16 인은경(2010), 실생활 문제를 수학적 모델링을 통한 미분 지도에 관한 연구, 석사학위논문, 인하대학교 교육대학원.
17 정미라(2015), 고등학교 학생들의 수학적 모델링 과정에서 나타난 메타인지 사례 연구, 석사학위 논문, 이화여자대학교.
18 정해윤, 이경화, 백도현, 정진호, 임경석(2018), 수학적 모델링 관점에 의한 <수학과제 탐구> 과목용 과제의 설계, 대한수학교육학회, 학교수학, 20(1), 149-169,
19 한선영, 김선희 (2017). 수학과제 탐구 수업방안 연구 보고서, 한국 창의재단.
20 교육부(2015). 2회 수학교육 종합계획(2015 - 2019), 교육부
21 황혜정.민아람, (2008).2007년 이후 국내 논문 결과에 근거한 수학적 모델링 탐색, 한국수학교육학회지 시리즈 E: 수학교육 논문집, 32(2) 225-244..
22 황혜정(2007), 수학적 모델링의 이해-국내 연구 결과 분석을 중심으로- 대한수학교육학회, 9(1), 65-97. Mar. 2007
23 Haines. C. R. & McDuffie A. R., (2016), Annual perspectives to mathematics education, Mathematical Modeling and Modeling Mathematics, NCTM.
24 Dunya B. A., Diefes-Dux H. A., Kartal O. & Zawojewski, J. S. (2016), "The relationship between students' performance on conventional standardized mathematics assessments and complex mathematical modeling problems." International Journal of Research in Education and Science (IJRES) 2(1) : 239-52.
25 Freudenthal, H. (1968). How to teach mathematics so as to be useful, ICME-1 Lecture.
26 GAIMME(2016), Guidelines for Assessment and Instruction in Mathematical Modeling Education,(GAIMME). Boston/Philadelphia, SIAM and COMAP.
27 Gould, H., (2013), Teachers' conceptions of mathematical modeling, Columbia University, Degree of Doctor of Philosophy.
28 Gould, H., Diane R. M. &, Sanfratello A., (2012), Teachers College Mathematical Modeling Handbook, COMAP.
29 Jacob P. & Zwaneveld B. (2012), The many faces of the mathematical modeling cycle, Journal of mathematical Modelling and Application, 1(6), 3-21.
30 Kaiser G., (2005), Mathematical Modelling in School-Examples and Experiences, Mathematikunterricht im Spannungsfeld von Evolution und Evaluation: Hans-Wolfgang Henn, Division-Verlag Franzbecker, pp.99-108.
31 Kaiser G. & Stender. P, (2013), Complex modelling problems in co-operative, self-directed learning Environments. In Teaching Mathematical Modelling: Connecting to Research and Practice, edited by Gloria Stillman, Gabriele Kaiser, Werner Blum, and Jill Brown, pp. 277 93. Dordrecht, The Netherlands: Springer.
32 Lesh R. A. (2003), How mathematizing reality is different from realizing mathematics, Susan J. Lamon Willard A. Parker (Eds.), Mathematical Modeling: A way of life, ICTMA 11, Horwood Publishing Limited.
33 Zawojewski, J., Lesh S., Richard A., & English, L. D. (2003), A Models and modeling perspective on the role of small group learning activities. In Lesh, Ricjard A. & Doerr, Helen M. (Eds.) Beyond Constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching. Lawrence Erlbaum Associates, Mahwah, N.J., pp. 337-358.
34 Pollak, H., (2007). Mathematical modeling: A conversation with Henry Pollak. In Modelling and Applications in Mathematics Education: The 14th ICMI Study, edited by Nemer Blum, Peter, L. Galbraith, Hans-Wolfgang Henn, and Mogens Niss, pp. 109-20. New York: Springer.
35 Schoenfeld A. H. (2013), Mathematical modeling, sense making, and the common core state standards, Proceedings from the Teachers College Mathematical Modeling Oktoberfest.
36 Smith & Morgan (2016), Curricular orientations to real-world contexts in mathematics. The Curriculum Journal, 27(1), 24-45.   DOI
37 Pardalos, P. M. & Hearn. D. W. (2004), Modeling languagesin mathematical optimization, Applied Optimization, 88, models and history of modeling, Schichl, H., Kluwer Academic Publishers.
38 Voskoglou M. G, & Phil M.(2011), Mathematical modelling in classroom: The importance of validation of the constructed model, School of Technological Applications, 263-34 Patras, Greece. http://eclass.teipat.gr/RESE-STE101/document
39 Blomhoj M., (2008), Different perspectives in research on the teaching and learning mathematical modelling-categorizing the TSG21 papers. Proceedings from Topic Study Group 21,at the 11th International Congress on Mathematical Education in Monterrey, Mexico, July 6-13, 2008.
40 홍정희, 송순희(1994), 수학적 모델링을 활용한 수학 탐구수업 효과의 고찰, 수학교육, 34(1), 93-96.
41 Blum, W.(2011), Can modelling be Taught and Learnt? Some Answers from Empirical Research. In Gabriele Kaiser, Werner Blum, Rita Borromeo Ferri, Gloria Stillman (Eds.). Trends in Teaching and Learning of Mathematical Modelling ICTMA 14, pp. 15-30. New York: Springer.
42 Blum W. & Ferri R. B.,(2009), Mathematical modelling: Can It be taught and learnt? Journal of Mathematical Modelling and Application., 1(1), 45-58
43 Blum & Ferri (2016), Advancing the teaching of mathematical modeling: research-based concepts and examples, Annual Perspectives in Mathematics Education: Mathematical Modeling and Modeling Mathematics(NCTM),65-76.
44 Blum, W. & Leiss, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 222-231). Chichester: Horwood.
45 Carlson, M. A., Wickstrom, M. H. Elizabeth A. B. & Elizabeth W. F.,.(2016), "A case for Mathematical modeling in the elementary school classroom." Annual Perspectives in Mathematics Education (APME) : Mathematical Modeling and Modeling Mathematics, edited($^{\circ}C$ & by Christian R. Hirsch, pp. 121-29. Reston, Va. : National Council of Teachers of Mathematics(NCTM).
46 김민경 홍지연 & 김혜원(2010). 수학적 모델링 적용을 위한 문제 상황 개발 및 적용. 한국수학교육학회지 시리즈 E: 수학교육 논문집, 49(3), 313-328.
47 김인경 (2012), 수학적 모델링과 수학화 및 문제해결 비교 분석, 한국 수학사학회지, 25(2), 71-95.
48 김민경, 민선희 & 강선미 (2009), 초등 교사들의 수학적 모델링에 대한 인식조사 연구, 한국수학교육학회지, 12(4), 411-431.