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Comparison and Analysis among Mathematical Modeling, Mathematization, and Problem Solving  

Kim, In-Kyung (Department of Mathematics Education, Cheongju University)
Publication Information
Journal for History of Mathematics / v.25, no.2, 2012 , pp. 71-95 More about this Journal
Abstract
Nowadays, the big issues on mathematics education are mathematical modeling, mathematization, and problem solving. So, this paper looks about these issues. First, after 1990's, the researchers interested in mathematical model and mathematical modeling. So, this paper looks about mathematical model and mathematical modeling. Second, it looks about Freudenthal' mathematization after 1970's. And then, it compared with mathematical modeling. Also, it looks about that problem solving focused on mathematics education since 1980's. And it compared with mathematical modeling.
Keywords
mathematical modeling; mathematization; problem solving;
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1 강옥기, 수학적 모델링의 정교화 과정 연구, 수학교육학연구, 수학교육학연구 20(2010), No.1, pp. 73-84.
2 권기석, 박배훈, 고등학교에서 수학적 모델링의 활용에 관한 연구, 수학교육 36(1997), No.2, pp. 149-159.
3 김선희, 김기연, 수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석, 학교수학 6(2004), No.3, pp. 283-299.
4 김성준, 학교 대수 도입과 관련된 논의, 학교수학 4(2002), No.1, pp. 29-47.
5 류성림, 이산수학에서의 수학적 모델링, 청람수학교육 11(2003), pp. 127-165.
6 류희찬, 수학교육에서 '모델링' 지도의 의미와 방안, 청람수학교육 11(2003), pp. 1-19.
7 손홍찬, 류희찬, 수학적 모델링에서 스프레드시트 환경이 수학적 모델의 정교화 과정에 미치는 역할, 학교수학 9(2007), No.4, pp. 467-486.
8 신은주, 권오남, 탐구지향 수학적 모델링에 관한 연구, 수학교육학연구 11(2001), No.1, pp. 157-177.
9 신은주, 이종희, 중학생들의 모델링 활동에서 메타인지 분석에 관한 사례연구, 수학교육학연구 14(2004a), No.4, pp. 403-419.
10 신은주, 이종희, 모델 개발과정에서 도구를 조작하는 활동분석, 학교수학 6(2004b), No.4, pp. 389-409.
11 우정호 역, 어떻게 문제를 풀 것인가? Polya 저, (주) 천재교육, 1999.
12 우정호, 정영옥, 박경미, 이경화, 김남희, 나귀수, 임재훈 역, 수학적 발견 I, II, 서울 : 교우사, 2005.
13 장혜원, 중등 수학의 대수와 함수 영역에서의 모델링, 청람수학교육 11(2003), pp. 41-65.
14 정영옥, Freudenthal의 수학화 학습- 지도론 연구, 서울대학교 대학원 박사학위논문, 1997.
15 조완영, 미적분 영역에서의 모델링, 청람수학교육 11(2003), pp. 167-187.
16 주미경, 모델링 지도에 관한 고찰, 대한수학교육학회논문집 1(1991), No.1, pp. 53-61.
17 황혜정, 수학적 모델링의 이해- 국내 연구 결과 분석을 중심으로, 학교수학 9(2007), No.1, pp. 65-97.
18 황혜정, 나귀수, 최승현, 박경미, 임재훈, 서동엽, 수학교육신론, 서울 : 문음사, 2007.
19 J. De Lange, & H. B. Verhage, Math A and achievement testing, in proceedings of the 11th international conference for the Psychology of Mathematics Education (1987), Vol.3, pp. 243-248.
20 H. M. Doerr, & L. English, "A modeling perspective on students'mathematical reasoning about data". Journal of Research in Mathematics Education 34(2003), No.2, pp. 110-136.   DOI   ScienceOn
21 J. A. Dossey, S. McCrone, F. R. Goirdano, & M. D. Weir, Mathematics methods and modeling for today's mathematics classroom, CA: Brookscole, 2002.
22 L. English, & B. Sriraman, "Problem solving for the 21st century, in Sriraman, B. & English, L." (Eds.) Theories of mathematics education, NY: Springer, 2010, pp. 263-290.
23 G. Kaiser, & B. Sriraman, "A global survey of international perspectives on modeling in mathematics education", Zentralblatt fur Didaktik der Mathematik 38(2006), No.2, pp. 281-292.   DOI
24 H. Freudenthal, Mathematics as an educational task, Dordrecht : Kluwer Academic Publishers, 1973.
25 H. Freudenthal, Revisiting mathematics education, Dordrecht : Kluwer Academic Publishers, 1991.
26 T. Johnson, & R, Lesh, "A models and modeling perspective on technology-based representational media, In R. Lesh, & H. Doerr", Beyond constructivism-models and modeling perspectives on mathematics problem solving, learning, and teaching, Lawrence Erlbaum Associates, Inc. NJ., 2003, pp. 35-58.
27 R. Lesh, K. Cramer, H. M. Doerr, T. Post, & J. S. Zawojewski, "Model development sequences, In R. Lesh, & H. Doerr", Beyond constructivism-models and modeling perspectives on mathematics problem solving, learning, and teaching, Lawrence Erlbaum Associates, Inc. NJ., 2003, pp. 35-58.
28 R. Lesh, & H. M. Doerr, "Symbolizing, communicating, and mathematizing: Key components of models and modeling, In P. Cobb & E. Yackel", (Eds.) Symbolizing and communicating in mathematics classrooms, Mahwah, NJ: Lawrence Erlbaum Associates, 1998.
29 R. Lesh, & H. M. Doerr, Beyond constructivism-models and modeling perspectives on mathematics problem solving, learning, and teaching, Lawrence Erlbaum Associates, Inc. NJ., 2003a.
30 R. Lesh, & H. M. Doerr, "In what ways does a models and modeling perspective move beyond constructivism? In R. Lesh, & H. Doerr", Beyond constructivismmodels and modeling perspectives on mathematics problem solving, learning, and teaching, Lawrence Erlbaum Associates, Inc. NJ., 2003b, pp. 519-556.
31 R. Lesh, H. M. Doerr, G. Carmona, & M. Hjalmarson, "Beyond constructivism", Mathematical thinking and learning 5(2003), No.2, pp. 211-234.   DOI   ScienceOn
32 R. Lesh, & L. English, "Trends in the evolution of models & modeling perspectives on mathematical learning and problem solving", ZDM 2005, Vol. 37(6).
33 D. Maki, & M. Thompson, Mathematical models and applications, with emphasis on the social, life, and management sciences, (2nd ed.) Englewood Cliffs, NJ: Prentice-Hall, 1973.
34 A. Schoenfeld, "On mathematics as sense-making: an informal attack on the unfortunate divorce of formal and informal mathematics, In J. Voss, D. Perkins, & J. Segal", (Eds.) informal reasoning and education, Hillsdale, NJ: Lawrence Erlbaum, 1991, pp. 311-343.
35 N. Mousoulides, B. Sriraman, & C. Christou, "From problem solving to modelingthe emergence of models and modeling perspectives", Nordic Studies in Mathematics Education 12(2007), No.1, pp. 23-47.
36 NCTM, Curriculum and evaluation standards for school mathematics, Reston, VA: The National Council of Teachers of Mathematics, 1989.
37 G. Polya, Mathematical Discovery, NY: John Wiley & Sons, Inc., 1962.
38 F. Swetz, & J. S. Hartzler, (Eds.) Mathematical modeling in the secondary school curriculum, NCTM., 1991.
39 A. Treffers, Three dimension, D. Reidel Publishing Company, 1987.
40 J. Zawojewski, & R. Lesh, "A models and modeling perspectives on problem solving. in R. Lesh, & H. Doerr", Beyond constructivism-models and modeling perspectives on mathematics problem solving, learning, and teaching, NJ: Lawrence Erlbaum Associates, Inc., 2003, pp. 317-336.