DGS 동적 기하에서의 새로운 함수적 관점의 정의 = Functional Definitions in DGS Environments

다국어 초록 (Multilingual Abstract)

In this paper, we introduce new functional definitions for school geometry based on DGS (dynamic geometry system) teaching-learning environment. For the vertices forming a geometric figure, we first consider the relationship between the independent vertices and dependent vertices, and using this relationship and educational considerations in DGS, we introduce functional definitions for the geometric figures in terms of its independent vertices. For this purpose, we design a new DGS called JavaMAL MicroWorld. Based on the needs of new definitions in DGS environment for the student`s construction activities in learning geometry, we also design a new DGS based geometry curriculum in which the definitions of the school geometry are newly defined and reconnected in a new way. Using these funct onal definitions, we have taught the new geometry contents emphasizing the sequential expressions for the student`s geometric activities.

참고문헌 (Reference)

1 "학교수학에 제시된 정의에 관한 연구" 2001

2 "탐구형 소프트웨어를 활용한 기하학습내용의 구성방안 탐색" 대한수학교육학회 10 (10): 139-159, 2000

3 "탐구형 소프트웨어를 활용한 고등학교 해석 기하 교육에 관한 사례 연구" 한국수학교육학회 41 (41): 341-360, 2002

4 "컴퓨터와 수학교육" 한국수학교육학회 42 (42): 177-191, 2003

5 "Windows on mathematical meanings, Dordrecht, Netherlands" Kluwer Academic Publishers 1996

6 Goldenberg,, "What is dynamic geometry? In R. Lehrer & D. Chazan (Eds.) Designing learning environments for developing understanding of geometry and space." London: Lawrence Erlbaum Associates, Inc. 1998

7 "The role of definitions in teaching and learning of mathematics" Kluwer Academic Publishers 1991

8 "The role and function of a hierarchical classification of quadrilaterals For the Learning of Mathematics" 11-18, 1994

9 "The computer as a medium for exploring mathematics" MIT Press 1980

10 "Representing Geometric Constructions As Programs" 7 (7): 101-115, 2002

11 Jones,, "Providing a foundation for deductive reasoning" 44 : 55-85, 2000

12 "Problems of the plane representation of space geometry figures Educational Studies in Mathematics 19" k (k): 79-92, 1988

13 Edwards,, "Microworlds as representation." Berlin: Springer 1995

14 Freudenthal, "Mathematics as an educational task" 1973

15 King, J. R. &, "Geometry Turnned On!" The Mathematics Association of America. 1997

16 Duval,, "Geometrical pictures" Berlin: Springer. 1995

17 Mariotti,, "Defining in classroom activities" 34 : 219-248, 1997

18 Fou-Lai Lin, "Defining a Rectangle under a Social and Practical Setting by Two Seventh Graders," 34 : 17-28, 2002

19 "Connected mathematics - Building concrete relationship with mathematical knowledge Thesis of doctor of philosophy at the Massachusetts Institute of Technology" 1993

20 "Connected mathematics - Building concrete relationship with mathematical knowledge Thesis of doctor of philosophy at the Massachusetts Institute of Technology" 1993

21 "An Alternative Approach to Proof in Dynamic Geometry, In R. Lehrer & D. Chazan (Eds.) Designing learning environments for developing understanding of geometry and space." Lawrence Erlbaum Associates, Inc. 1998

22 "A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.) Designing learning environments for developing understanding of geometry and space" London: Lawrence Erlbaum Associates, Inc. 1998