References
- 교육부(1998). 초등학교 교육과정 해설(IV). 서울: 대한교과서주식회사.
- 교육부(2003). 수학 6-가. 서울: 대한교과서주식회사.
- 교육부(2003). 수학익힘책 6-가. 서울: 대한교과서 주식회사.
- 교육부(2015). 수학 6-2 교사용 지도서. 서울: 천재교육.
- 교육부(2015). 수학 6-2. 서울: 천재교육.
- 교육부(2015). 수학익힘책 6-2. 서울: 천재교육.
- 김수운(2004). 쌓기나무 단원의 수업 실행 연구 - 6단계를 중심으로 -. 청주교육대학교 교육대학원 석사학위논문.
- 이지윤(2015a). 공간 과제에서 인지 전략의 유형과 역할 - 시각적 변별과 기억 능력을 중심으로. 수학교육학연구, 25(4), 571-598.
- 이지윤(2015b). 3D 입체 변별 과제에서 공간 인지전략의 유형과 역할 - 체화된 3D 거북 표현식과 전략을 중심으로 -. 서울대학교 대학원 박사학위논문.
- 이지윤, 조한혁, 송민호(2013). 공간 시각화 과제에 체화된 거북 스킴 적용에 관한 연구. 수학교육, 52(2), 191-201.
- 이화진 외(2005). KICE 교수학습개발센터 콘텐츠 개발.운영-내용 교수법(PCK) 및 온라인 수업장학 지원 프로그램 개발을 중심으로. 연구보고 RRI 2005-1. 서울:한국교육과정평가원.
- 장유라(2010). 초등학교 수학수업에 있어서 수학적 의사소통에 관한 연구. 부산대학교대학원 석사학위논문.
- 장혜원(2015). 2학년 쌓기나무 수업에서의 수학적 의사소통 분석. 학교수학, 17(2), 223-239.
- 장혜원, 강종표(2007). 쌓기나무 지도를 위한 부분 제거법의 적용. 수학교육학연구, 19(3). 425-441.
- 조한혁, 송민호(2014). 실행식(Executable expression) 기반 SMART 스토리텔링 수학교육. 수학교육학연구, 24(2). 269-283.
- 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
- Bruner, J. (1967). Toward a theory of instruction. Cambridge, MA: The Belknap Press of Harvard University Press.
- Bruner, J. (1973). Beyond the information given. New York: W.W. Norton & Company Inc.
- 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.
- 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.
- 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).
- 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
- Ernest, P. (2010). Mathematics and Metaphor. An International Journal of Complexity and Education, 7(1), 98-104.
- 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
- 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
- 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.
- 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
- 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.
- 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
- Michaelides, M. P. (2002). Students' Solution Strategies in Spatial Rotation Tasks. Paper is the result of a Master's Thesis, University of Cambridge.
- 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
- 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
- Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Cambridge, Massachusetts: Perseus Publishing.
- 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
- Schultz, K. (1991). The contribution of solution strategy to spatial performance. Canadian Journal of Psychology, 45, 474-491. https://doi.org/10.1037/h0084301
- 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
- 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
- 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
- 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
- Vygotsky, L. S. (1978). Mind and society: The development of higher psychological processes. Cambridge: Harvard University Press.
- 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
- 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