DOI QR코드

DOI QR Code

영재학교 학생의 GeoGebra를 활용한 과정 중심 평가 수행과제 탐구: 이차곡선 중심으로

Exploring gifted school students' process-based assessment performance using GeoGebra: Focused on the quadratic curves

  • 투고 : 2024.05.12
  • 심사 : 2024.06.18
  • 발행 : 2024.06.30

초록

본 연구에서는 영재학교 학생을 대상으로 GeoGebra를 활용한 과정 중심 평가 교수⋅학습 사례를 제시하였다. 영재교육의 가장 중요한 요소 중 하나인 창의성 측면에서 영재학교 학생 대상으로 과정 중심 평가는 매우 효과적일 수 있다. 그럼에도 불구하고 영재 학생들을 대상으로 하는 과정 중심 평가를 포함한 교수⋅학습 방법 및 자료 개발이 다소 미진한 상태이다. 연구자는 ◯◯영재학교 학생 79명을 대상으로 <기하> 교과의 이차곡선 관련 내용을 중심으로 GeoGebra를 활용한 실험수업을 8차시에 걸쳐 진행 후, 제시한 조건에 맞추어 GeoGebra를 활용하여 타원을 작도한 결과를 평가하였다. 학생들의 산출물을 토대로 GeoGebra의 구성단계와 구성단계 네비게이션바 기능을 활용하여 학생들의 작도 결과와 함께 그 해결 과정을 과정 중심으로 평가할 수 있었을 뿐만 아니라, 문제해결 과정에서 발견되는 개개인의 정의적 특성까지 일부 확인할 수 있었다. 또한 본 연구의 교수⋅학습 상황에서 학생들은 메타인지적 사고 활동을 할 수 있었으며, 수학적 창의성을 증진할 수 있는 수업 사례임을 확인할 수 있었다.

This study presented a case study of teaching and learning process-based assessment using GeoGebra for students at a gifted school. Process-based assessment can be very effective for gifted students in terms of creativity, which is one of the most important elements of gifted education. Nevertheless, the development of teaching and learning methods and materials including process-based assessment for gifted students have been still somewhat underdeveloped. The researcher conducted eight experimental lessons using GeoGebra centered on quadratic curves in the <Geometry> course for 79 students at an ◯◯ gifted and talented school, and then evaluated the results of students' ellipse constructions using GeoGebra according to the given conditions. Based on the students' output, it was possible to evaluate the students' construction results and the process of solving the problem in a process-based way by utilizing GeoGebra's construction protocol and construction protocol navigation bar functions, as well as to identify some of the defining characteristics of individuals found in the problem-solving process. In addition, In teaching and learning situation of this study students could perform metacognitive thinking activities, and it was confirmed that this was a teaching example that could promote mathematical creativity.

키워드

과제정보

본 연구는 2024년 인천과학예술영재학교 교내연구비로 수행되었음.

참고문헌

  1. Kwon, O. N., Cho, Y. M., Park, J. S., & Park, J. H. (2005). Cultivating Mathematical Creativity through Open-ended Appro aches: Development of a Program and Effectiveness Analysis. The Mathematical Education, 44(2), 307-323.
  2. Kwon, Y. S., & Ryu, S. R. (2013). The Effects of Inductive Activities Using GeoGebra on the Proof A bilities and Attitudes of Mathematically Gifted Elementary Students. Education of Primary School Mathematics, 16(2), 123-145. https://doi.org/10.7468/jksmec.2013.16.2.123
  3. Kim, K. S., & Han, I. K. (2007). A Study on Investigating Various Properties of Triangle's Escribed Circle and Tetrahedron's Escribed Sphere. Communications of mathematical education, 21(3), 385-406.
  4. Kim, M. J., Lee, J. H., & Kim, W. K. (2014). Development of teaching and learning materials by using GeoGebra and it's application effects for high school mathematically gifted students. Journal of the Korean School Mathematics Society, 17(3), 359-384.
  5. Kim, P. S., & Kim, N. R. (2016). A Study of Mathematically Gifted Student's Perception of Mathematical Creativity. Journal of Gifted/Talented Education, 26(4), 747-761. https://doi.org/10.9722/JGTE.2016.26.4.747
  6. Do, J. W., & Paik, S. Y. (2019). Aspects of Meta-affect in Problem-Solving Process of Mathematically Gifted Children. Journal of Elementary Mathematics Education in Korea, 23(1), 59-74.
  7. Maeng, H. J. (2013). Discussions on The Directions of Research and Development Tasks for Convergence Gifted Education. Journal of Gifted/Talented Education, 23(6), 981-1001. https://doi.org/10.9722/JGTE.2013.23.6.981
  8. Bae, J. H., & Ryu, S. R. (2016). A Comparison on the Relations between Affective Characteristics and Mathematical Reasoning Ability of Elementary Mathematically Gifted Students and Non-gifted Students. Education of Primary School Mathematics, 19(2), 161-175. https://doi.org/10.7468/jksmec.2016.19.2.161
  9. Paik, S. Y. (2016). Teaching & Learning of Mathematical Problem-Solving. Seoul: Kyungmoon
  10. Yang, K. Y., & Lim, M. R. (2018) An Analysis on the Inquiry Activities of Quadratic Surface Applying GeoGebra. Journal of Gifted/Talented Education, 28(4), 439-458. https://doi.org/10.9722/JGTE.2018.28.4.439
  11. Yang, S. H. (2012). A Study on the Role and Utilization of GeoGebra in Teaching and Learning of Mathematics. Doctoral dissertation, Sungkyunkwan University.
  12. Yang, S. H. (2014). A Case Study for Creativity Assessment of Problem Solving Process of Mathematically Gifted High School Students Utilizing Construction Protocol of GeoGebra. Journal of Gifted/Talented Education, 24(6), 897-916. https://doi.org/10.9722/JGTE.2014.24.6.897
  13. Yang, S. H., & Kang, O. K. (2011). Instruction method for Quadratic Curve Based on Dynamic Visual Representation by applying GeoGebra. School Mathematics, 13(3), 447-468.
  14. Oh, S. Y., & Kwon, N. Y. (2022). Difficulties and differences in perception and performance on process-based assessment for high school mathematics teacher. The Mathematical Education, 61(2), 239-256. https://doi.org/10.7468/MATHEDU.2022.61.2.239
  15. Lee, D. W., Koh, H. K., & Yoo, M. H. (2012). Math Teaching Method and Classroom Environment Preferred by Gifted High School Students. Journal of Gifted/Talented Education, 22(1), 23-37. https://doi.org/10.9722/JGTE.2012.22.1.023
  16. Lee, S. H., Lee, J. H., & Kim, W. K. (2012). The Effects of Using GeoGebra on the Mathematical Thinking in the Optimization Problems of Regional Inequalities - Focus on level curve-. Korean Journal of Teacher Education, 28(4), 1-44.
  17. Lee, S. N., Yi, S. H., & Han, S. S. (2009). Comparison of Mathematically Gifted Students and Non-gifted Students in Perception of Learning Environments and Affective Characteristics. Korean Journal of Child Studies, 30(5), 1-13.
  18. Lee, E. H., & Ryu, S. R. (2014). Comparative Study between Gifted Math Elementary Students and Non-Gifted Students in Emotional Intelligence and Creative Nature. School Mathematics, 16(1), 181-199.
  19. Lee, J. Y., & Choi, J. H. (2013). The Effects of 4D-Frame Teaching upon Mathematically Gifted Elementary S tudents' Mathematical Creativity and Spatial Sense. Education of Primary School Mathematics, 16(1), 1-20. https://doi.org/10.7468/jksmec.2013.16.1.001
  20. Lee, J. W., Shin, J. H., & Lee, S. J. (2013). An analysis of characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Journal of the Korean School Mathematics Society, 16(3), 539-560.
  21. Lee, H. R., & Choi, J. H. (2013). Comparative Study between Mathematically Gifted Elementary Students and Non-Gifted Students in Communication Skills and Self-Directed Learning Ability. School Mathematics, 15(3), 585-601.
  22. Jun, S. M., & Yoo, W. S. (2011). An Analysis on the Development Tendency of Teaching and Learning Materials for the Gifted Students in the Middle School. Communications of Mathematical Education, 25(1), 79-97. https://doi.org/10.7468/JKSMEE.2011.25.1.079
  23. Heo, N. G. (2014). A Study on Construction of Tangent Line of Quadratic Curves Through Geometric Method. Journal of Science Education for the Gifted, 6(3), 125-133.
  24. Heo, N. G. (2017). Analogical Reasoning in Construction of Quadratic Curves. Journal of Educational Research in Mathematics, 27(1), 51-67.
  25. Hong, J. K., & Kang, E. J. (2009). An Analysis on Thinking Processes of Mathematical Gifted Students Using Think-aloud Method. The Journal of Educational Research in Mathematics, 19(4), 565-584.
  26. Whang, W. H., & Cha, S. G. (2002). A Study on the Effectiveness of Dynamic Geometry Software in Solving High School Analytic Ge ometry Problems. The Mathematical Education, 41(3), 341-360.