The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

An analysis of the mathematical errors on the items of the descriptive assessment in the equation of a circle

원의 방정식의 서술형 평가에서 오류유형 분석

  • Received : 2014.10.21
  • Accepted : 2014.11.17
  • Published : 2014.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

This study was to investigate the types of errors and the frequency of errors to understand students' solving process on the descriptive items with the students of an excellent high school which located in a non-leveling local school district of Gyunggi Province. All 11 items were developed in the equation of a circle and 120 students who attended this high school participated in solving them. The result showed a tendency as follows: Logically invalid inference(Type A, 38.83%) of errors, Omission error of the problem solving process(Type B, 25%), Technical error(Type C, 15.67%), Wrong conclusion(Type D, 11.94%), Use of wrong theorem(Type E, 5.97%), and Use of wrong picture(Type F, 2.61%). The logically invalid inference the students showed with a largest tendency was made because of the lack of reflection. This meant that this error could be corrected in a little treatment of carefulness.

Keywords

References

  1. 교육과학기술부 (2012). 수학과 교육과정 해설서, 서울:교육과학기술부. (Ministry of Education (2012). The Curriculum of Mathematics, Seoul: the Author.)
  2. 경기도 교육청 (2013). 창의 지성 역량을 키우는 수업 평가: 2013 중등 서술형 논술형 평가 예시자료, 경기도: 경기도 교육청. (Gyungi Provincial Office of Education (2013). An assessment of math classes to raise the power of creativity & intelligence: Some examples for descriptive or essay types of items in 2013, Gyungi Province: Gyungi Provincial Office of Education.)
  3. 김래영, 이민희 (2013). 수학과 서술형 평가에 대한 중학교 교사들의 인식 연구, 수학교육학연구 23(4), 533-551. (Kim, R. Y., & Lee, M. H. (2013). Middle school mathematics teachers' perceptions of constructed-response assessments, Journal of Educational Research in Mathematics 23(4), 533-551.)
  4. 김래영, 김구연, 노선숙, 김민경, 전지훈, 김기영, 이민희.(2012). 중등 수학과 서술형평가 체계의 실제와 대안적 발전 방향 모색: 경기도 창의 서술형 평가와 미국 오하이오 주 평가를 중심으로, 수학교육논문집 26(3), 273-299, (Kim, R. Y., Kim, G., Noh, S., Kim, M. K., Jeon, J., Kim, K., Y., & Lee, M., H. (2012). Current status and future direction of constructed-response assessments, Communications of Mathematical Education 26(3), 273-299.)
  5. 김부미 (2004). 인지심리학의 관점에서 수학적 오류의 분석가능성 탐색, 수학교육학연구 14(3), 239-266. (Kim, B., M. (2004). Cognitive psychological approaches on analysing students' mathematical errors, Journal of Educational Research in Mathematics 14(3), 239-266.)
  6. 김차숙, 류희찬 (2003). 중학교 1학년 학생들의 일차방정식에 대한 오류 분석과 교정에 관한 연구, 대한수학교육학회 학술발표대회 (pp. 405-426). 숭실대학교. (Kim, C., & Ryu, H. (2003). A study on the analysis of errors and corrections in solving linear equation of the first graders in middle school. The Proceedings of Korea Society of Educational Studies in Mathematics((pp. 405-426). Seoul: Soongsil University.)
  7. 서울특별시교육청.서울특별시교육정보연구원 (2011). 수학과 서술형 평가 문항 자료집, 서울: 서울특별시교육정보연구원. (Seoul Education Research and Information Institute (2011). The Materials of Descriptive Problems of Mathematics, Seoul: Author.)
  8. 우정호 (2003). 학교수학의 교육적 기초, 서울대학교 출판부. (Woo, J. H. (2003). The Educational Foundation of School Mathematics, Seoul: Seoul National University.)
  9. 유희찬, 조완영, 조정묵, 임미선, 유익승, 한명주, 박원균, 남선주, 정선윤 (2012). 고등학교 수학, 서울: (주)미래엔 컬처그룹. (Woo, H. C., Jo, Y., Jo, J., Lim, M., Yoo, I., Han, M., Park, W., Nam, S. Jung, S. (2012). Mathematics of High School, Seoul: Future & Culture Ltd.)
  10. 윤인준, 고상숙 (2013). 탐구형 소프트웨어를 활용한 해석기하에서 학습부진학생들의 개념형성에 관한 연구, 한국학교수학회논문집 15(4), 643-671. (Yoon, I. J., & Choi-Koh, S. (2012). Skemp's concept development underachievers' analytic geometry using the exploratory software, Journal of the Korean School Mathematics Society 15(4), 643-671.)
  11. 이종희, 김부미 (2006). 일차방정식에서 오류 탐지-교정 학습법의 교수학적 효과 분석, 교과교육학연구 10(2), 461-483. (Lee, J. H., & Kim, B. M. (2006). The Effects of 'Error Detection-Correction Instruction' on Learning Linear Equations, Journal of Research in Curriculum Institution 10(2), 461-483.)
  12. 이지현, 김구연 (2013). 서술형 평가 문항 분석: 수학과 교육과정의 성격 및 목표와의 적합성을 중심으로, 한국학교수학회논문집 16(4), 899-925. (Lee, J., & Kim, G. (2013). An Examination of the Alignment between 2007 Mathematics Curriculum and Constructed-Response Assessment, Journal of the Korean School Mathematics Society 16(4), 899-925.)
  13. 한경민 (2013). 원의 방정식에서 오류유형 분석과 오류극복 학습에 관한 연구, 석사학위논문, 단국대학교. (Han, K. M. (2013). An Analysis on the Types of Errors in Mathematics and How to Overcome the Errors in the Area of the Equation of a Circle. Unpublished Thesis. Dankook University.)
  14. Artigue, M., & Viennor, L. (1987). Some aspects of students' conceptions and difficulties about differentials, Proceedings of the Second International Seminar Misconceptions and Educational Strategies in Science and Mathematic 3, 1-8.
  15. Clements, M. A. (1980). Analyzing children's errors on written mathematical tasks, Educational Studies in Mathematics 11, 1-21.
  16. Clements, M. A., & Del Campo, G. (1987). Fractional understanding of fractions: variations in children's understanding of fractional concepts, across embodiments, Proceedings of the Second International Seminar Misconceptions and Educational Strategies in Science and Mathematic 3, 98-110.
  17. Cornu, B. (1991). Limit In D. Tall (Ed.), Advanced Mathematical Thinking, Kluwer Academic Publishers.
  18. Hardar, N. M., Zaslavsky, O & Inbar, S. (1987). An empirical classification model for errors in high school mathematics, Journal for Research in Mathematics Education 18(1), 3-14. https://doi.org/10.2307/749532
  19. Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra, 4. Reston, VA: Author.
  20. Radatz, H. (1979). Error analysis in mathematics education, Journal for Research in Mathematics Education 10(3), 163-172. https://doi.org/10.2307/748804

Cited by

  1. Analysis of Constructed Response Items of High School Mathematics in the 2015 National Assessment of Educational Achievement vol.28, pp.2, 2014, https://doi.org/10.29275/jerm.2018.05.28.2.159