초등 영재학급 학생의 분수 감각과 분수 조작 능력 사례연구
A Case Study on the Fractional Sense and Fraction Operation Ability of Elementary Gifted Class Students
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This study is a case study that considered fractional senses and fraction operation abilities for 107 gifted students in elementary school classes. In order to find out the fractional sense, in the first question comparing the sizes of fractions 2/3 and 4/5, the students showed a variety of strategies, but the utilization rate of strategies excluding reduction to a common denominator did not exceed 50%. The second question can be solved by using the first question. It is a problem of finding two fractions by selecting four from six numbers 1, 3, 4, 5, 6, and 7 to create two fractions of which sum does not exceed 1. The percentage of correct answers to this question was about 27% (29 out of 107). Only 5 out of 29 students found answers using the first question, and the rest of the students sought answers through trial and error in various calculations. It shows that the item arrangement method from a deductive perspective has no significant effect on elementary school students. The percentage of correct answers was about 27% in the questions to find out the fraction operation ability-the question of drawing a 4/3 bar using a given 3/8-sized bar and 30.7% (23 out of 75) of the students who had wrong answers showed insufficient splitting operation. In addition, it has been shown that the operation of partitioning and iterating to form numerical senses and fractional concepts related to the fractions of the students has no significant impact.
Abstract
This study is a case study that considered fractional senses and fraction operation abilities for 107 gifted students in elementary school classes. In order to find out the fractional sense, in the first question comparing the sizes of fractions 2/3 and 4/5, the students showed a variety of strategies, but the utilization rate of strategies excluding reduction to a common denominator did not exceed 50%. The second question can be solved by using the first question. It is a problem of finding two fractions by selecting four from six numbers 1, 3, 4, 5, 6, and 7 to create two fractions of which sum does not exceed 1. The percentage of correct answers to this question was about 27% (29 out of 107). Only 5 out of 29 students found answers using the first question, and the rest of the students sought answers through trial and error in various calculations. It shows that the item arrangement method from a deductive perspective has no significant effect on elementary school students. The percentage of correct answers was about 27% in the questions to find out the fraction operation ability-the question of drawing a 4/3 bar using a given 3/8-sized bar and 30.7% (23 out of 75) of the students who had wrong answers showed insufficient splitting operation. In addition, it has been shown that the operation of partitioning and iterating to form numerical senses and fractional concepts related to the fractions of the students has no significant impact.
참고문헌 (33)
- 강완, "분수의 크기 비교 지도 방법의 교수학적 변환 분석", 초등교육연구원, 14(1), pp.35~64 (2003), 한국초등교육 서울교육대학교
- 권성룡, "초등학생의 분수이해에 관한 연구", 학교수학, 5(2), pp.259~273 (2003)
- 교육부, "수학 5-1" (2019), 천재교육
- 교육부, "교사용 지도서 수학 5-1" (2019), 천재교육
- 김유경, "3학년 학생들의 전체-부분으로서의 분수에 대한 이해분석", 수학교육학연구, 22(3), pp.311~329 (2012)
- 김유경, "초등학생들의 분수의 크기 비교 전략 분석", 수학교육학연구, 26(4), pp.663~682 (2016)
- 류지연, "분수와 소수에 대한 수 감각 향상 프로그램 개발 연구-초등학교 고학년을 중심으로-", 한국초등수학교육학회 연구발표대회 논문집, pp.188~241 (2012)
- 방정숙, "몫으로서의 분수에 관한 초등학교 수학과 교과용도서분석", 수학교육학연구, 24(2), pp.165~180 (2014)
- 서동엽, "분수의 역사발생적 지도 방안", 수학교육학연구, 15(3), pp.233~249 (2005)
- 선춘화, "초등학교 6학년 학생의 수감각 실태조사", 수학교육, 44(4), pp.587~602 (2005)
- 신보희, "분수감각의 개념과 교수전략 고찰", 증거기반 교육연구, 3(1), pp.89~104 (2022)
- 이지영, "분수의 다양한 의미에서 단위에 대한 초등학교 6학년학생들의 이해 실태조사", 수학교육학연구, 24(1), pp.83~103 (2014)
- 이호수, "몫으로서의 분수와 분배전략", East Asian Math. J., 38(4), pp.379~396 (2022)
- 정은실, "분수 개념의 의미 분석과 교육적 시사점 탐구", 학교수학, 8(2), pp.123~138 (2006)
- 최근배, "분할과 반복 조작을 통한 분수지도 탐구", 학교수학, 12(3), pp.411~424 (2010)
- 한정이, "초등학교 6학년 학생들의 분수 조작 및 스킴 분석", 학교수학, 19(1), pp.59~75 (2017)
- 함혜림, "연산자 분수에 대한 고찰", 교육논총, 34(3), pp.181~213 (2014)
- Baroody, A. F., "수학의 힘을 길러주자 왜? 어떻게?" (2006), 경문사
- Faulkner V., "The components of number sense: An instructional model for teachers", Teaching Exceptional Children, 41(5), pp.24~30 (2009)
- Fennell, F., "Fractional Sense : Foundational Understandings", Journal of Learning Disabilities, 50(6), pp.648~650 (2017)
- McIntosh, A., "A proposed framework for examining basic number sense", For the Learning of Mathematics, 12(3), pp.2~8 (1992)
- Norton, A. H., "ZPC and ZPD : Zones of Teaching and Learning", J ournal for Research in Mathematics Education, 39(3), pp.220~246 (2008)
- Norton, A. H., "Modeling Students'Mathematics using Steffe- 's Fraction Schemes", Teaching Children Mathematics, pp.48~54 (2008)
- Norton, A., "A quantitative analysis of children's splitting operations and fraction schemes", The J ournal of Mathematical Behavior, 28, pp.150~161 (2009)
- Olive, J, "Bridging the Gap: Using Interactive Computer Tools to Build Fraction Schemes", Teaching Children Mathematics, pp.356~361 (2002)
- Reys, R. E., "Relationship between computational performance and number sense among sixth and eighth grade students in Taiwan", J ournal for Research in Mathematics Education, 29(2), pp.225~237 (1998)
- Siebert, D., "Creating, Naming, and Justifying Fractions", Teaching Children Mathematics, pp.394~400 (2006)
- Steffe, L. P., "A new hypothesis concerning children’s fractional knowledge", The J ournal of Mathematical Behavior, 20, pp.267~307 (2002)
- Steffe, L. P., "Fractional commensurate, composition, and adding schemes Learning trajectories of Jason and Laura : Grade 5", The Journal of Mathematical Behavior, 22, pp.237~295 (2003)
- Yang, D. C., "A study of the per formance of 5th graders in number sense and its relationship to achievement in mathematics", International J ournal of Science and Mathematics Education, 6, pp.789~807 (2007)
- von Glasersfeld, E., "Radical constructivism: A way of knowing and learning" (1995), Routledge Falmer
- Wenrick, M. R, "Elementary Students’ Use of Relationships and Physical Models to Understand Order and Equivalence of Rational Numbers", Doctor, pp.2003
- Wilkins, J. L. M., "The splitting loope", J ournal for Research in Mathematics Education, 42, pp.386~416 (2011)