Journal of Elementary Mathematics Education in Korea (한국초등수학교육학회지)

Korea Society of Elementary Mathematics Education (한국초등수학교육학회)
권호 표지

Geometry Education and Software: A Review

소프트웨어를 활용한 도형 교육 연구 동향 탐색

  • Received : 2020.01.16
  • Accepted : 2020.02.07
  • Published : 2020.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

The use of software is effective in developing mathematical understanding that provides mathematical problems and ensures mathematical communication. In particular, various software may provide all of the skills and conceptual activities students need to understand mathematical concepts. Based on these arguments, I analyze domestic prior studies based on the perspective of how the shape education using software affects mathematics learning. Based on the five categories of visualization, manipulation, cognitive tools, discourse promoters, and ways of thinking, domestic studies have shown that the number and categories of research related to shape education using software are limited. In addition, it was confirmed that previous studies in South Korea have been focused on the application of software rather than analysis of the changing aspects of learners' mathematics learning. These implications might be used as a basis for setting the direction of research on mathematics education related to the education of software utilization in the future.

소프트웨어의 활용은 학생들의 수학적 이해를 발전시키는데 효과적이다. 다양한 소프트웨어들은 학생들이 수학 개념을 이해하는 데 필요한 기술 및 개념 활동을 제공한다. 이러한 주장을 바탕으로 본 연구에서는 소프트웨어를 활용한 도형 교육이 수학 학습에 어떤 측면에 영향을 주는가라는 주제를 중심으로 국내 선행 연구를 분석하였다. 시각화, 조작, 인지 도구, 의사소통의 촉진제, 사고방식이라는 다섯 가지 범주를 기준으로 국내 연구들을 살펴본 결과, 소프트웨어를 활용한 도형 교육 관련 연구의 수, 범주가 제한적이라는 것을 알 수 있었다. 또한 국내 선행 연구들이 학습자의 수학 학습의 변화 측면 분석보다 소프트웨어 활용 자체에 중점을 두고 이루어져 왔음을 확인할 수 있었다. 이러한 시사점은 향후 소프트웨어 활용 도형 교육과 관련한 수학 교육 연구 방향을 설정하는데 근거 자료로 활용될 수 있다.

Keywords

References

  1. 고영해, 안재호, 박남제 (2011). LOGO 교육용 프로그래밍 언어를 이용한 프랙탈 기하이론 기반의 초등학교 컴퓨터교육 지도 방안. 한국정보기술학회논문지, 9(8), 151-163.
  2. 권오남, 김도연 (2018). 초등학생의 디지털 테크놀로지를 이용한 유리수 조밀성 탐구 사례 분석: 포괄적 유물론에서의 접근, 초등수학교육, 21(4), 375-395.
  3. 김경미 (2004). 객체지향형 교육용 프로그래밍 언어 '두리틀(Dolittle)'의 수학교육 활용. 고려대학교 대학원 석사학위논문.
  4. 김계남 (2014). 초등수학과 게임의 효과적인 접목을 위한 연구, 만화애니메이션 연구, 37, 393-411. https://doi.org/10.7230/koscas.2014.37.393
  5. 김은미 (2001). 구체적 조작물과 웹 기반 가상현실 프로그램 중심의 학습이 초등학교 남녀 학생의 공간시각화 능력에 미치는 효과. 이화여자대학교 수학교육학과 대학원 석사학위논문..
  6. 김주창 (2009). GSP 활용이 초등 수학 영재의 기하 학습에 미치는 효과. 춘천교육대학교 대학원 석사학위논문.
  7. 김태년, 김영미, 황대준 (2004). LTSA 기반 초등수학 안내시스템 설계에 관한 연구, 정보처리학회논문지A, 11(2), 223-230.
  8. 박종률, 이현수 (2012). 초등수학 영재학생의 자연수의 연산을 활용한 원형 디자인 -GSP를 활용한 원 디자인을 중심으로-, 초등수학교육, 15(1), 31-47.
  9. 배윤주, 박정아, 김성은, 두민영 (2019). 국내 스마트교육에 대한 연구동향 분석: 2011년-2018년을 중심으로, 교육문화연구, 25(3), 319-339.
  10. 성은모 (2015). 초등학생의 스마트미디어 활용능력 요인과 교과태도 및 학업성취도와의 관계, 교육정보미디어연구, 21(2), 215-243.
  11. 이용수, 김동혁, 고병오, 최의인 (2013). 웹을 기반으로 한 자기 주도적 MITS -초등 수학수와 연산 영역 중심-, 정보교육학회논문지, 8(3), 335-352.
  12. 이헌수.(2011) 테크놀로지를 활용한 수학 영재교육. 전남대학교 대학원 박사학위논문..
  13. 이헌수, 박종률, 이광호. (2009) 그래핑 계산기와 CBL을 활용한 1차 함수 탐구 - 초등 영재아를 중심으로 한 사례연구. 한국학교수학회논문집, 12(3), 347-364.
  14. 장인옥 (2013). 테크놀로지를 활용한 영재 교수-학습에서 '공동학습자'로서의 교사 역할, 영재와 영재교육, 12(3), 117-134.
  15. 조정수, 이은숙 (2013). 역동기하 환경에서 "끌기(dragging)"의 역할에 대한 고찰, 학교수학, 15(2), 481-501.
  16. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  17. Battista, M. T. (2007). The Development of geometric and spatial thinking. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Reston, VA: NCTM.
  18. Battista, M. T. (2009). Highlights of research on learning school geometry. In T. V. Craine & R. Rubenstein (Eds.), Understanding geometry for a changing world (pp. 91-108). Reston, VA: The National Council of Teachers of Mathematics.
  19. Ben-Zvi, D. (2000). Towards understanding the role of technological tools in statistical learning. Mathematical Thinking and Learning, 2(1 & 2), 127-155. https://doi.org/10.1207/S15327833MTL0202_6
  20. Borwein, J. M. (2005). The Experimental mathematician: The Pleasure of discovery and the role of proof. International Journal of Computers for Mathematical Learning, 10, 75-108. https://doi.org/10.1007/s10758-005-5216-x
  21. Borwein, J. M., & Bailey, D. H. (2003). Mathematics by experiment: Plausible reasoning in the 21st century. Natick, MA: AK Peters.
  22. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
  23. Brunton, G., Stansfield, C., & Thomas, J. (2012). Finding relevant studies. In S. Oliver. D. Gough & J. Thomas (Eds.), An introduction to systematic reviews (pp. 107-134). London, UK: SAGE Publications.
  24. Burger, W. F., & Shaughnessy, M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48. https://doi.org/10.2307/749317
  25. Chaplin, S. H., O'Connor, C., & Canavan-Anderson, N. (2009). Classroom discussions: Using math talk to help students learn (2nd ed.). Sausalito, CA: Math Solutions.
  26. Clements, D. (2004). Geometric and Spatial Thinking in Early Childhood Education. In D. H. Clements, J. Sarama, & A. M. DiBiase (Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education (pp. 267-297). Mahwah, NJ: Lawrence Erlbaum Associates.
  27. Clements, D. H., Sarama, J., & DiBiase, A. M. (2003). Engaging young children in mathematics: Standards for early childhood mathematics education.. Routledge.
  28. Clements, D. H., & Battista, M. T. (1994). Computer environments for learning geometry. Journal of Educational Computing Research, 10(2), 173-197. https://doi.org/10.2190/8074-298A-KTL2-UQVW
  29. Clements, D. H., Battista, M. T., & Sarama, J. (2001). Logo and geometry. Journal for Research in Mathematics Education. Monograph Series, 10, 1-177.
  30. Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461-555). New York, NY: Information Age publishing.
  31. Crompton, H., Grant, M. R., & Shraim, K. Y. (2018). Technologies to enhance and extend children’s understanding of geometry: A configurative thematic synthesis of the literature. Journal of Educational Technology & Society, 21(1), 59-69.
  32. Daher, W. M. (2011). Building mathematics cellular phone learning communities. International Journal of Interactive Mobile Technologies, 5(2), 9-16. Retrieved from http://online-journals.org/i-jim/article/viewArticle/1475 https://doi.org/10.3991/ijim.v5i2.1475
  33. Dick, T. (2007). Keeping the faith: Fidelity in technological tools for mathematics education. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Syntheses, cases, and perspectives (Vol. 2, pp.333-339). Charlotte, NC: Information Age.
  34. Duatepe-Paksu, A. (2009). Effects of drama-based geometry instruction on student achievement, attitudes, and thinking levels. The Journal of Educational Research, 102(4), 272-286. https://doi.org/10.3200/JOER.102.4.272-286
  35. Fesakis, G., Sofroniou, C., & Mavroudi, E. (2011). Using the internet for communicative learning activities in kindergarten: The Case of the "Shapes Planet." Early Childhood Education Journal, 38, 385-392. https://doi.org/10.1007/s10643-010-0422-0
  36. Fey, J. T., Atchison, W. F., Good, R. A., Heid, M. K., Johnson, J., & Kantowski, M. G. (1984). Computing and mathematics: The impact on secondary school curricula. Reston, VA: National Council of Teachers of Mathematics.
  37. Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199-219. https://doi.org/10.1007/s10857-007-9070-8
  38. Giaquinto, M. (2007). Visual thinking in mathematics: An Epistemological study. Oxford, UK: Oxford University press.
  39. Gutierrez, A. (1992). Exploring the links between van Hiele levels and 3-dimensional geometry. Structural Topology, 18, 31-48.
  40. Hill, H. C. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 430-511.
  41. Hoyles, C. (1995). Exploratory software, exploratory cultures? In C. Hoyles, A. di Sessa, R. Noss, & L. Edwards (Eds.), Computers and exploratory learning (pp. 199-219). Berlin, Germany: Springer Verlag.
  42. Hoyles, C., & Noss, R. (2003). Digital technologies in mathematics education. In M. A. Clements, A. Bishop, J. Kilpatrick,C. Keitel, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 323-350). Bordrecht, Netherlands: Kluwer Academic Press.
  43. Hwa, S. P. (2018). Pedagogical Change in Mathematics Learning: Harnessing the Power of Digital Game-Based Learning. Journal of Educational Technology & Society, 21(4), 259-276.
  44. Johnson-Gentile, K., Clements, D. H., & Battista, M. T. (1994). Effects of computer and noncomputer environments on students' conceptualizations of geometric motions. Journal of Educational Computing Research, 11(2), 121-140. https://doi.org/10.2190/49EE-8PXL-YY8C-A923
  45. Jones, K. (2011). The Value of learning geometry with ICT: Lessons from innovative educational research. In A. Oldknow & C. Knights (Eds.), Mathematics education with digital technology (pp. 39-45). New York, NY: Continuum.
  46. Kamina, P., & Iyer, N. N. (2009). From concrete to abstract: Teaching for transfer of learning when using manipulatives. In Proceedings of the Northeastern Educational Research Association (pp. 1-9). Rocky Hill, CT: NERA.
  47. Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515-556). Reston, VA: National Council of Teachers of Mathematics.
  48. Kim, R. (2014). Elementary teachers’ knowledge for teaching mathematics: A review. Mediterranean Journal of Social Sciences, 5(9), 428.
  49. Kim, R., & Albert, L. R. (2015). Mathematics teaching and learning: South Korean elementary teachers' mathematical knowledge for teaching. Springer, NY:U.S.A.
  50. Konstantopoulos, S. (2011). Teacher effects in early grades: Evidence from a randomized study. Teachers College Record, 113.
  51. Kop, R.-P., van den Berg, M. & Klein T. (2004). Survey naar de toepassing van ICT voor onderwijsdoeleinden in het hoger onderwijs [A survey into the application of ICT for educational purposes in higher education]. ICT-onderwijsmonitor studiejaar 2002/2003. Leiden: Research voor Beleid.
  52. Kordaki, M., & Potari, D. (2002). The effect of area measurement tools on student strategies: The role of a computer microworld. International Journal of Computers for Mathematical Learning, 7(1), 65-100. https://doi.org/10.1023/A:1016051411284
  53. Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006). Teaching and learning geometry with technology. In A. Gutierrez. & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275-304). Rotterdam, Netherlands: Sense Publishers.
  54. Lajoie, S. P., & Azevedo, R. (2006). Teaching and learning in technology-rich environments. In P. Alexander & P. Winne(Eds.), Handbook of educational psychology (2nd ed., pp. 803-821). Mahwah, NJ: Erlbaum.
  55. Mammana, M. F., Micale, B., & Pennisi, M. (2012). Analogy and dynamic geometry system used to introduce threedimensional geometry. International Journal of Mathematical Education in Science & Technology, 43(6), 818-830. https://doi.org/10.1080/0020739X.2012.662286
  56. Mariotti, M. A. (2000). Introduction to proof: The Mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1/2), 25-53. https://doi.org/10.1023/A:1012733122556
  57. Martin-Gutierrez, J., Gil, F. A., Contero, M., & Saorin, J. L. (2013). Dynamic three-dimensional illustrator for teaching descriptive geometry and training visualisation skills. Computer Applications in Engineering Education, 21(1), 8-21. https://doi.org/10.1002/cae.20447
  58. Meagher, M. (2006). Theoretical approaches to learning with digital technologies. In J. B. Lagrange, C. Hoyles, L. H. Son, & N. Sinclair (Eds.), Proceedings of the 17th ICMI Study Conference "Technology Revisited" (pp. 386-393). Hanoi, Vietnam: Hanoi University of Technology.
  59. Miyazaki, M., Kimiho, C., Katoh, R., Arai, H., Ogihara, F., Oguchi, Y., Morozumi, T., Kon, M., & Komatsu, K. (2012). Potentials for spatial geometry curriculum development with three-dimensional dynamic geometry software in lower secondary mathematics. International Journal for Technology in Mathematics Education, 19(2), 73-79.
  60. Oakley, A. (2012). Foreword. In D. Gough, S. Oliver, & J. Thomas (Eds.), An Introduction to systematic reviews (pp. vii-x). London, UK: SAGE Publications.
  61. Olive, J., & Lobato, J. (2008). The learning of rational number concepts using technology. In M. K. Heid & G. W. Blume(Eds.), Research on technology and the teaching and learning of mathematics: Synthesis, cases, and perspectives (Vol. 1, pp. 1-54). Charlotte, NC: Information Age.
  62. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York, NY: Basic Books.
  63. Pea, R. D. (1987). Cognitive technologies for mathematics education. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89-122). Hillendale, NJ: Erlbaum.
  64. Piaget, J. (1971). Biology and knowledge. Edinburgh, UK: Edinburgh University Press. (Original work published 1967)
  65. Piaget, J., & Inhelder, B. (1967). The Child's conception of space. (F. J. Langdon & J. L. Lunzer, Trans.). New York, NY: W. W. Norton & Company. (Original work published 1948)
  66. Sandelowski, M., Voils, C. J., Leeman, J., & Crandlee, J. L. (2011). Mapping the mixed methods- Mixed research synthesis terrain. Journal of Mixed Methods Research, 6(4), 317-331. https://doi.org/10.1177/1558689811427913
  67. Sarama, J., & Clements, D. (2002). Design of microworlds in mathematics and science education. Journal of Educational Computing Research, 27(1), 1-3. https://doi.org/10.2190/P9GT-RN11-3AY3-WBG6
  68. Sarama, J., & Clements, D. H. (2009)."Concrete" computer manipulatives in mathematics education. Child Development Perspectives, 3, 145-150. https://doi.org/10.1111/j.1750-8606.2009.00095.x
  69. Shafie, L. A., & Mansor, M. (2009). The Predicaments of Language Learners in Traditional Learning Environments. English Language Teaching, 2(2), 69-74.
  70. Sherman, M. (2002). An Examination of the role of technological tools in relation to the cognitive demand of mathematics task in secondary classrooms (Unpublished master's thesis). University of Pittsburgh, PA.
  71. Sinclair, N., & Robutti, O. (2013). Technology and the role of proof: The Case of dynamic geometry. In Third international handbook of mathematics education (pp. 571-596). New York, NY: Springer.
  72. Skemp, R. R. (1976/2006). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 12(2), 88-95. https://doi.org/10.5951/MTMS.12.2.0088
  73. Soto-Johnson, H., Cribari, R. D., & Wheeler, A. (2009). The Impact of written reflections in a geometry course for preservice teachers. Quaderni Di Ricerca in Didattica (matematica), 4(19), 65-73.
  74. Thomas, J., & Harden, A. (2008). Methods for the thematic synthesis of qualitative reserach in systematic reviews. BMC Medical Research Methodology, 8(45), 1-10. https://doi.org/10.1186/1471-2288-8-1
  75. Thomas, J., Harden, A., & Newman, M. (2012). Synthesis: Combining results systematically and appropriately. In S. Oliver. D. Gought (Ed.), An introduction to systematic reviews (pp. 179-226). Thousand Oaks, CA: SAGE Publications.
  76. Traxler, J. (2011). Context in a wider context. Medienpadagogik, 19. Retrieved from http://www.medienpaed.com/article/view/134
  77. Ubuz, B., & Ustun, I. (2004). Figural and conceptual aspects in defining and identifying polygons. Eurasian Journal of Educational Research, 16, 15-26.
  78. Van de Walle, J. A., & Lovin, L. H. (2006). Teaching student-centered mathematics: Grades 3-5 (Vol. 2). Boston, MA: Pearson.
  79. van Hiele, P. M. (1984). The Child's thought and geometry. In D. Geddes, D. Fuys, & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243-252). Brooklyn, NY: Brooklyn College. (Original work published 1957)
  80. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A Contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 77-101. https://doi.org/10.1007/BF03172796
  81. Vygotsky, L. S. (1978). Mind in society: The Development of higher psychological processes (A. Kozulin, Trans.). Cambridge, MA: Harvard University Press.
  82. Yeh, A. J., & Nason, R. A. (2004, November). Toward a semiotic framework for using technology in mathematics education: The Case of learning 3D geometry. Paper presented at the International Conference on Computers in Education, Melbourne, Australia.
  83. Yu, P., Barrett, J., & Presmeg, N. (2009). Prototypes and categorical reasoning: A Perspective to explain about interactive geometry objects. In T. V. Craine & R. Rubenstein (Eds.), Understanding geometry for a changing world (Seventy-first Yearbook ed., pp. 109-125). Reston, VA: The National Council of Teachers of Mathematics.
  84. Wayne, A. Y., & Young, P. (2003). Teacher characteristics and student achievement gains: A review. Review of Educational Research, 73(1), 89-122. https://doi.org/10.3102/00346543073001089
  85. Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A Perspective of constructs. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics in teaching and learning (pp. 1169-1208). Reston, VA: NCTM.