우리나라 수학교육에서 공학 활용의 역사와 현황 = Trend and Prospect on Using Technology in Mathematics Education in Korea

다국어 초록 (Multilingual Abstract)

As teachers need to understand how to select and use technology in mathematics education, analysis on history, characteristics, and effects of various technology used in school mathematics will facilitate effective use of technology.
This thesis aims to analyze through literary studies the history, characteristics, and effects of using spreadsheets Excel, dynamic geometry softwares GSP, Cabri and CAS, the most commonly used technology in teaching and learning mathematics in Korea.
And we also study the current trends on using technology in mathematics education in Korea by investigating research trend, secondary mathematics curriculums past and present in Korea, mathematics textbooks, and classroom environments.

국문 초록 (Abstract)

이 논문에서는 우리나라 학교수학의 교수·학습에서 가장 많이 사용되고 있는 공학적 도구들로 스프레드시트인 엑셀, 역동적 기하 소프트웨어인 GSP, Cabri, 그리고 CAS를 중심으로 이것들이 수학교육에서 활용되어온 역사와 특징 그리고 그것이 미친 영향을 살펴본다. 그리고 우리나라 수학교육에서 공학적 도구의 활용을 교육과정 상의 변화, 교과서에서의 변화, 현직교사의 연수와 예비교사의 교육과정, 그리고 교실 등의 물리적 환경 등을 통하여 그 현황을 파악하고 미래의 수학교육에서 공학 활용에 대한 방향을 제시한다.

참고문헌 (Reference)

1 이정례, "학교수학 교수․학습에서 기술공학의 활용 연구" 한국수학교육학회 24 (24): 29-48, 2010

2 안대영, "통계에서 엑셀의 교수학적 활용 가능성" 8 : 317-330, 1999

3 김미화, "중등 수학과 교과서에서 공학적 도구 활용의 변화 분석" 전북대학교 교육대학원 2011

4 김영진, "중등 수학 교사의 공학 관련 현직 연수 실태 분석 및 개선 방안 연구" 대한수학교육학회 38 : 37-48, 2010

5 박경미, "우리나라 초․중등학교 수학교육 발전 방안 기획 연구" 한국과학창의재단 2010

6 이정용, "엑셀 매크로(MACRO) 기능을 이용한 통계학 참여수업의 예" 한국통계학회 21 (21): 355-359, 2008

7 손홍찬, "스프레드시트 환경에서 모델링 활동을 통한 수학적 발견과 정당화" 대한수학교육학회 7 (7): 427-444, 2005

8 류희찬, "수학교육에서의 컴퓨터의 활용: 현황과 과제" 1997

9 NCTM, "수학교육과정과 평가의 새로운 방향" 경문사 1989

10 교육인적자원부, "수학과 교육과정(교육부 고시 제 2007-79호 [별책 8])"

11 교육부, "수학과 교육과정(교육부 고시 제 1997-15호 [별책 8])"

12 교육부, "수학과 교육과정(교육부 고시 제 1997-14호)"

13 이창현, "반힐레 이론과 GSP를 활용한 중학교 기하영역에 관한 연구 - 8-나 단계의 사각형의 성질을 중심으로 -" 한국수학교육학회 49 (49): 85-109, 2010

14 김남희, "문제해결력 신장을 위한 Cabri3D의 교육적 활용" 대한수학교육학회 16 (16): 345-366, 2006

15 강순자, "공간 능력을 신장하기 위한 기하학습자료 개발: GSP를 이용하여 정다면체 구성" 38 (38): 179-187, 1999

16 한세호, "고등학교 수학학습에서 컴퓨터대수체계(CAS)의 도구발생" 건국대학교 대학원 2007

17 김남희, "‘문제해결’ 관점에서의 GSP활용" 대한수학교육학회 4 (4): 8-125, 2002

18 "http://www.t3ww.org"

19 "http://www.lkl.ac.uk"

20 Goldenberg, E. P., "What is dynamic geometry?, in Designing learning environments for developing understanding of geometry and space" Lawrence Erlbaum 351-368, 1998

21 Heid, M. K, "Theories for Thinking about the Use of CAS in Teaching and Learning Mathematics, in Computer Algebra Systems in Secondary School Mathematics Education" National Council of Teachers of Mathematics 73-88, 2003

22 Healey, L, "The role of peer group discussion in mathematical environment(Final Report to the Leverhulme Trust)" London University, Institute of Education. 1990

23 Hollebrands, K, "The role of a dynamic software program for geometry in high school students developing understandings of geometric transformations" 695-706, 2002

24 Leung, F. K. S, "The impact of information and communication technology on our understanding of the nature of mathe- matics" 26 (26): 2006

25 Neuwirth, E., "The active modeler: Mathematical modeling with Microsoft Excel. Belmont" Brooks Cole Publishing Company 2004

26 NCTM, "Technology-supported mathe- matics learning environments, sixty- seventh yearbook" National Council of Teachers of Mathematics 2005

27 Smith, R. S, "Teaching precalculus with a spreadsheet, in Proceedings of the Fifth Annual International Conference on Technology in Collegiate Mathematics" Ad- dison—Wesley 1992

28 Laborde, C., "Teaching and learning geometry with technology, in Handbook of research on the psychology of mathematics education: Past, present and future" Sense Publishers 275-304, 2006

29 Mullis, I., "TIMSS 1999 Inter- national Mathematics Report" International Study Center 2000

30 Baker J. E, "Spreadsheets in education-the first 25 Years" 1 (1): 18-43, 2003

31 Bialas, Piotr, "Spreadsheet use in an elementary statistics course" Columbia University Teachers College. 2001

32 Morishita, E., "Spreadsheet fluid dyna mics for aeronautical course problems" 17 (17): 294-311, 2001

33 Wilson, K, "Spread- sheet generalizing and paper and pencil generalizing" 441-448, 2004

34 Sutherland,R, "Some unanswered questions on the teaching and learning of algebra" 11 (11): 40-46, 1991

35 Heid, M. K, "Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool" 19 : 3-25, 1988

36 Christou, "Proofs through exploration in dynamic geometry environments" 215-222, 2004

37 De Villiers, M.D, "Proof in dynamic geometry" 2007

38 NCTM, "Principles and standards for school mathematics" National Council of Teachers of Mathematics 2000

39 Miyazaki, M., "Potentials of spatial geometry curriculum development with three-dimensional dynamic geometry software in lower secondary mathematics" 2008

40 Freudenthal, H, "Mathematik als padgogische Aufgabe" Klertt Stuienbucher 1979

41 Hershkowitz, R., "Mathematics curriculum development for computerized environments: A designer-researcher-teacher-learner activity, in Handbook of International Research in Mathematics Education" Lawrence Erlbaum 657-694, 2002

42 Laborde, C, "Integration of technology in the design of geometry tasks with Cabri- geometry" 6 : 283-317, 2001

43 Masalski, W. J, "How to use the spreadsheet as a tool in the secondary school mathematics classroom" NCTM 1999

44 Beare, R, "How spreadsheets can aid a variety of mathematical learning activities from primary to tertiary level. Technology in mathematics teaching: A bridge between teaching and learning. B" B. Jaworski 1993

45 계영희, "GSP를 활용한 한국 전통문양의 테셀레이션 작도" 한국수학사학회 21 (21): 71-80, 2008

46 신양재, "GSP를 활용한 열린 기하 수업에 관한 연구" 8 : 303-315, 1999

47 김부윤, "GSP4를 이용한 이차곡선과 Cycloid에 관한 지도 방안" 15 : 261-271, 2003

48 Bennett,D, "Exploring geometry with the geometer's sketchpad" Key Curriculum Press 1997

49 "DSSResources.COM, A Brief History of Spreadsheets"

50 Teasley, S. D., "Cons- turcting a Joint Problem Space: the Computer as a Tool for Sharing Knowledge, in Computers as Cognitive Tools" Chapman & Hall 229-258, 1993

51 Kilpatrick, Jeremy, "Computers and Curriculum Change in Mathematics, in Learning from Computers: Mathematics Education and Technology" Springer-Verlag 203-221, 1993

52 Friedlander, A, "Cognitive processes in a spreadsheet environment" 337-344, 1999

53 "Cabri3D v2"

54 "Cabri history"

55 Kutzler, Bernhard, "CAS as pedagogical tools for teaching and learning mathematics, in Computer Algebra Systems in Secondary School Mathematics Education" National Council of Teachers of Mathematics 73-88, 2003

56 Friedlander, A, "An excellent bridge to algebra" 91 (91): 382-383, 1998

57 Goldenberg, E. P, "Algebra and Computer Algebra, in Computer Algebra Systems in Secondary School Mathematics Education" National Council of Teachers of Mathematics 73-88, 2003

58 Sutherland, R., "A spread- sheet approach to solving algebra problems" 12 : 353-383, 1993

59 Arzarello, F., "A cognitive analysis of dragging practices in Cabri environments" 34 (34): 66-72, 2002