School Mathematics (대한수학교육학회지:학교수학)

The Korea Society of Educational Studies in Mathematics (대한수학교육학회)
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Educational Application of Turtle Representation System for Linking Cube Mathematics Class

연결큐브 수업을 위한 거북표현체계의 활용

  • Received : 2016.05.10
  • Accepted : 2016.06.13
  • Published : 2016.06.30
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Abstract

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

2009 개정 교육과정에서는 공간 감각의 향상을 위해 초등학교 6학년 수학 교과서에 '연결큐브'를 사용한 활동을 새롭게 도입하고 의사소통과 구체적 조작을 통한 교수 학습 방법을 강조하였다. 교사들을 대상으로 한 설문과 면담 분석 결과 공간 대상에 대한 표현 체계의 부재로 연결큐브 수업의 문제해결과 의사소통 측면에서 교사가 지도하는데 많은 어려움이 있음을 확인하였다. 본 연구에서는 이런 어려움을 해소하기 위한 대안으로 '거북표현체계'를 제시하고, 교사를 대상으로 설문과 검사를 실시하였다. 그 결과 문제해결과 의사소통 측면에서 거북표현체계의 효과와 유용성을 확인할 수 있었다.

Keywords

References

  1. 교육부(1998). 초등학교 교육과정 해설(IV). 서울: 대한교과서주식회사.
  2. 교육부(2003). 수학 6-가. 서울: 대한교과서주식회사.
  3. 교육부(2003). 수학익힘책 6-가. 서울: 대한교과서 주식회사.
  4. 교육부(2015). 수학 6-2 교사용 지도서. 서울: 천재교육.
  5. 교육부(2015). 수학 6-2. 서울: 천재교육.
  6. 교육부(2015). 수학익힘책 6-2. 서울: 천재교육.
  7. 김수운(2004). 쌓기나무 단원의 수업 실행 연구 - 6단계를 중심으로 -. 청주교육대학교 교육대학원 석사학위논문.
  8. 이지윤(2015a). 공간 과제에서 인지 전략의 유형과 역할 - 시각적 변별과 기억 능력을 중심으로. 수학교육학연구, 25(4), 571-598.
  9. 이지윤(2015b). 3D 입체 변별 과제에서 공간 인지전략의 유형과 역할 - 체화된 3D 거북 표현식과 전략을 중심으로 -. 서울대학교 대학원 박사학위논문.
  10. 이지윤, 조한혁, 송민호(2013). 공간 시각화 과제에 체화된 거북 스킴 적용에 관한 연구. 수학교육, 52(2), 191-201.
  11. 이화진 외(2005). KICE 교수학습개발센터 콘텐츠 개발.운영-내용 교수법(PCK) 및 온라인 수업장학 지원 프로그램 개발을 중심으로. 연구보고 RRI 2005-1. 서울:한국교육과정평가원.
  12. 장유라(2010). 초등학교 수학수업에 있어서 수학적 의사소통에 관한 연구. 부산대학교대학원 석사학위논문.
  13. 장혜원(2015). 2학년 쌓기나무 수업에서의 수학적 의사소통 분석. 학교수학, 17(2), 223-239.
  14. 장혜원, 강종표(2007). 쌓기나무 지도를 위한 부분 제거법의 적용. 수학교육학연구, 19(3). 425-441.
  15. 조한혁, 송민호(2014). 실행식(Executable expression) 기반 SMART 스토리텔링 수학교육. 수학교육학연구, 24(2). 269-283.
  16. Ben-Chaim, D., Lappan, G., & Houang, R. T. (1989). Adolescents' ability to communicate spatial information: Analyzing and effecting students' performance. Educational Studies in Mathematics, 20(2), 121-146. https://doi.org/10.1007/BF00579459
  17. Bruner, J. (1967). Toward a theory of instruction. Cambridge, MA: The Belknap Press of Harvard University Press.
  18. Bruner, J. (1973). Beyond the information given. New York: W.W. Norton & Company Inc.
  19. Cho, H. H., Lee, J. Y., & Song, M. H. (2012). Construction and design activities through Logo-based 3D microworld. Proceedings of the 2nd International Constructionism Conference 2012 held at Athens, Greece; August 21-25, 2012(pp.565-569). Athens, Greece.
  20. Cho, H. H., Lee, J. Y., Shin, D. J., & Woo, A. S. (2011). MCY-Mentoring Activities by Creating and Communicating Mathematical Objects. Journal of the Korean Society of Mathematical Education Series D: Research in Mathematics Education, 15(2), 141-158.
  21. Cho, H. H., Cho, H. I., Lee, C. H., Lee, E. J. & Jeong, H. R. (2016). 3D turtle coding activities for Korean Primary education. Proceedings of the 4th International Constructionism Conference 2016 held at Bangkok, Thailand; February 1-5, 2016(pp.22-29).
  22. Clements, D. (1999). Concrete manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60. https://doi.org/10.2304/ciec.2000.1.1.7
  23. Ernest, P. (2010). Mathematics and Metaphor. An International Journal of Complexity and Education, 7(1), 98-104.
  24. Gorgorio, N. (1998). Exploring the functionality of visual and non-visual strategies in solving rotation problems. Educational Studies in Mathematics, 35, 207-231. https://doi.org/10.1023/A:1003132603649
  25. Hegarty, M., Stieff, M. & Dixon, B. L. (2013). Cognitive change in mental models with experience in the domain of organic chemistry. Journal of Cognitive Psychology, 25(2), 220-228. https://doi.org/10.1080/20445911.2012.725044
  26. Hershkowitz, R., Ben-Chaim, D., Hoyles, C., Lappan, G., Mitchelmore, M., & Vinner, S. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.). Mathematics and cognition: a research synthesis by the international group for the psychology of mathematics education. 70-95. Cambridge University Press.
  27. Hoyles, C., & Noss, R. (2003). "What can digital technologies take from and bring to research in mathematics education?" In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.). Second International Handbook of Mathematics Education, Kluwer Academic Publishers, Dordrecht, 323-349
  28. Kamii, C., Kirkland, L., & Lewis, B. (2001). Representation and abstraction in young children's numerical reasoning. In A. Cuoco (Ed.). The Roles of Representation in School Mathematics (pp. 24-34). Reston, VA: NCTM.
  29. Lajoie, S. P. (2003). Individual differences in spatial ability_Developing technologies to increase strategy awareness and skills. Educational Psychologist, 38(2), 115-125. https://doi.org/10.1207/S15326985EP3802_6
  30. Michaelides, M. P. (2002). Students' Solution Strategies in Spatial Rotation Tasks. Paper is the result of a Master's Thesis, University of Cambridge.
  31. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197. https://doi.org/10.1023/A:1014596316942
  32. Noss, R. (2001). For a Learnable Mathematics in the Digital Culture. Educational Studies in Mathematics 48, 21-46. https://doi.org/10.1023/A:1015528224870
  33. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Cambridge, Massachusetts: Perseus Publishing.
  34. Sack, J. J. (2013). Development of a top-view numeric coding teaching-learning trajectory within an elementary grades 3-D visualization design research project. The Journal of Mathematical Behavior, 32(2), 183-196. https://doi.org/10.1016/j.jmathb.2013.02.006
  35. Schultz, K. (1991). The contribution of solution strategy to spatial performance. Canadian Journal of Psychology, 45, 474-491. https://doi.org/10.1037/h0084301
  36. Shepard, R. N. & Metzler, J. (1971). Mental Rotation of Three-Dimensional Objects. Science, 171(3972), 701-703. https://doi.org/10.1126/science.171.3972.701
  37. Stieff, M., Ryu, M., Dixon, B., & Hegarty, M. (2012). The role of spatial ability and strategy preference during spatial problem solving in organic chemistry. Journal of Chemical Education, 89, 854-859. https://doi.org/10.1021/ed200071d
  38. Stieff, M. (2007). Mental rotation and diagrammatic reasoning in science. Learning and Instruction, 17, 219-234. https://doi.org/10.1016/j.learninstruc.2007.01.012
  39. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three dimensional spatial visualization. Perceptual and Motor Skills, 47, 599-604. https://doi.org/10.2466/pms.1978.47.2.599
  40. Vygotsky, L. S. (1978). Mind and society: The development of higher psychological processes. Cambridge: Harvard University Press.
  41. Wraga, M., Shephard, J. M., Church, J. A., Inati, S. & Kosslyn, S. M. (2005). Imagined rotations of self versus objects: an fMRI study. Neuropsychologia, 43, 1351-1361. https://doi.org/10.1016/j.neuropsychologia.2004.11.028
  42. Zacks, J. M., Vettel, J. M., & Michelon, P. (2003). Imagined viewer and object rotations dissociated with event-related FMRI. Journal of Cognitive Neuroscience, 15(7), 1002-1018. https://doi.org/10.1162/089892903770007399