포물선의 동적 표현과 마이크로월드
Dynamic Representations of Parabolas in a Microworld
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In this paper, we discuss two representations of a curve. One is a static representation as set of points, the other is a dynamic representation using time parameter. And we suggest needs of designing a computer microword where we can represent a curve both statically and dynamically. We also emphasize the importance of translation activity from a static representation to a dynamic representation. For this purpose, we first consider constructionism and 'computers and mathematics education' as a theoretical backgrounds. We focus the curve of a parabola in this paper since this is common in mathematics curriculum and is related to realistic situation such as throwing ball. And we survey the mathematics curriculum about parabola representation. And we introduce JavaMAL microworld that is integrated microworld between LOGO and DGS. In this microworld, we represent a parabola using a dynamic action, and connect this dynamic parabola action to recursive patterns. Finally, we remake a parabola for a realistic situation using this dynamic representation. And we discuss the educational meaning of dynamic representation and its computer microworld.
Abstract
In this paper, we discuss two representations of a curve. One is a static representation as set of points, the other is a dynamic representation using time parameter. And we suggest needs of designing a computer microword where we can represent a curve both statically and dynamically. We also emphasize the importance of translation activity from a static representation to a dynamic representation. For this purpose, we first consider constructionism and 'computers and mathematics education' as a theoretical backgrounds. We focus the curve of a parabola in this paper since this is common in mathematics curriculum and is related to realistic situation such as throwing ball. And we survey the mathematics curriculum about parabola representation. And we introduce JavaMAL microworld that is integrated microworld between LOGO and DGS. In this microworld, we represent a parabola using a dynamic action, and connect this dynamic parabola action to recursive patterns. Finally, we remake a parabola for a realistic situation using this dynamic representation. And we discuss the educational meaning of dynamic representation and its computer microworld.
참고문헌 (28)
- 강옥기, "중학교 수학 9-가" (2003), (주)두산
- 강행고, "중학교 수학 9-가" (2003), (주)중앙교육진흥연구소
- 교육부, "중학교 교육 과정 해설(Ⅲ)" (1999), 대한교과서(주)
- 교육인적자원부, "수학 3-나" (2001), 대한교과서(주)
- 김남희, "수학교육과정과 교재연구" (2006), 경문사
- 김홍종, "미적분학 1" (2004), 서울대학교 출판부
- 김화경, "‘컴퓨터와 수학교육’ 학습-지도 환경에 관한 연구", 박사, 교육학, pp.2006
- 김화경, "Logo와 DGS의 매개 모델과 오류 사례", 수학교육학연구, 17(2), pp.111~125 (2007), 대한수학교육학회
- 남호영, "원뿔에서 태어난 이차곡선" (2001), 수학사랑
- 박윤범, "중학교 수학 9-가" (2003), 대한교과서(주)
- 우정호, "학교수학의 교육적 기초" (1998), 서울대학교 출판부
- 우정호, "수학 Ⅱ" (2003), 대한교과서(주)
- 임재훈, "수학 Ⅱ" (2003), (주)두산
- 이성묵, "중학교 과학 2" (2002), (주)금성출판사
- 이성묵, "중학교 과학 3" (2003), (주)금성출판사
- 이형주, "중학교 수학교과서와 과학교과서의 공통 용어 비교․분석", 석사, 교육학, pp.2006
- 조한혁, "컴퓨터와 수학교육", 수학교육, 42(2), pp.8~192 (2003), 한국수학교육학회
- Abelson, H., "Turtle geometry" (1980), MIT Press
- Ackerman, E.K., "Constructing knowledge and transforming the world;A learning zone of one's own: Sharing representations and flow in collaborative learning environments", pp.15~36 (2004), IOS Press
- Borba, M.C., "Humans-with-media and the reorganization of mathematical thinking" (2004), Springer
- Burton, D.M., "The history of mathematics: An introduction" (2007), McGraw-Hill
- Cho, H., "Mediating model between LOGO and DGS for planar curves", Proceeding of Psychology of Mathematics Education (2007)
- Dennis, D., "Historical perspectives for the reform of mathematics curriculum: geometric curve drawing devices and their role in the transition to an algebraic description of functions", 박사, pp.1995
- Osler, T.J., "Archimedes' quadrature of the parabola: A mechanical view", College Mathematics Journal, 37(1), pp.24~28 (2006)
- Papert, S., "Mindstorms: children, computers, and powerful ideas" (1980), Perseus Publishing
- Resnick, M., "Some reflections on designing construction kits for kids", Proceeding of interaction design and children conference (2005), Boulder, CO.
- Sherin, B., "Representing geometric constructions as programs: a brief exploration", International Journal of Computers for Mathematical Learning, 7(1), pp.101~115 (2002)
- Stillwell, J., "Mathematics and its history" (2001), Springer