Browse > Article

An Analysis of 6th Graders' Fraction Operations and Schemes  

Han, Jeong Yee (Graduate School, Korea National University of Education)
Lee, Kwang Ho (Korea National University of Education)
Publication Information
School Mathematics / v.19, no.1, 2017 , pp. 59-75 More about this Journal
Abstract
This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.
Keywords
fraction operation; fraction scheme; partitioning; iterating; partitive unit fraction scheme; partitive fraction scheme;
Citations & Related Records
연도 인용수 순위
  • Reference
1 권성룡(2003). 초등학생의 분수이해에 관한 연구. 학교수학, 5(2), 259-273.
2 김유경, 방정숙(2012). 3학년 학생들의 전체-부분으로서의 분수에 대한 이해 분석. 수학교육학연구, 22(3), 311-329.
3 류희찬, 신준식(1995). 실제적 접근 방법을 통한 분수 지도 방법 연구. 수학교육학연구, 5(2), 201-214.
4 서동엽(2005). 분수의 역사발생적 지도 방안. 수학교육학연구, 15(3), 233-249.
5 심재방(2014). 단위화를 활용한 초등학교 4학년 분수 표현 및 크기 지도 방안. 한국교원대학교 대학원 석사학위논문.
6 안우환(2004). 논문 작성을 위한 교육통계. 경기: 한국학술정보(주).
7 이지영, 방정숙(2014). 분수의 다양한 의미에서 단위에 대한 초등학교 6학년 학생들의 이해 실태 조사. 수학교육학연구, 24(1), 83-102.
8 이혜민, 신인선(2011). 산술과 대수적 사고의 연결을 위한 분수 scheme에 관한 사례 연구. 초등수학교육, 14(3), 261-275.
9 임재훈, 홍진곤(1998). 조작적 구성주의와 사회적 구성주의에서 구성의 의미와 과정. 수학교육학연구, 8(1), 299-312.
10 정은실(2006). 분수 개념의 의미 분석과 교육적 시사점 탐구. 학교수학, 8(2), 123-138.
11 최근배(2010). 분할과 반복 조작을 통한 분수지도 탐구. 학교수학, 12(3), 411-424.
12 Hackenberg, A. J. (2007). Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior, 26(1), 27-47.   DOI
13 Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (3th ed.). New York: Routledge.
14 Lim, Y. J. & Lee, K. H. (in press). Partitioning strategies and fraction scheme of 5th graders. Information.
15 Norton, A. (2008). Josh's operational conjectures: Abductions of a splitting operation and the construction of new fractional schemes. Journal for Research in Mathematics Education, 39(4), 401-430.
16 Norton, A., & D’Ambrosio, B. S. (2008). ZPC and ZPD: Zones of teaching and learning. Journal for Research in Mathematics Education, 39(3), 220-246.
17 Norton, A., & Wilkins, J. L. M. (2009). A quantitative analysis of children's splitting operations and fraction schemes. Journal of Mathematical Behavior, 28, 150-161.   DOI
18 Norton, A., & Wilkins, J. L. M. (2010). Students’ partitive reasoning. Journal of Mathematical Behavior, 29, 181-194.   DOI
19 Norton, A., & Wilkins, J. L. M. (2013). Supporting Students’ Constructions of the Splitting Operation. Cognition and instruction, 31(1), 2-28.   DOI
20 Norton, A., & Wilkins, J. L. M. (2012). The splitting group. Journal for Research in Mathematics Education, 43(5), 557-583.   DOI
21 Norton, A., Wilkins, J. L. M., & Cong, X. (2016). A progression of fractions schemes that crosses chinese and US classrooms. Manuscript submitted for publication.
22 Olive, J., & Steffe, L. P. (2002). The construction of an iterative fractional scheme: The case of Joe. Journal of Mathematical Behavior, 20(4), 413-437.   DOI
23 Steffe, L. P. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 20(3), 267-307.   DOI
24 Steffe, L. P. (2003). Fractional commensurate, composition, and adding schemes learning trajectories of Jason and Laura: Grade 5. Journal of Mathematical Behavior, 22(3), 237-295.   DOI
25 Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129-162.   DOI
26 Steffe, L. P. (2010). The partitioning and fraction schemes. In L. P. Steffe, & J. Olive (Eds.), Children's fractional knowledge (pp. 315-340). New York: Springer.
27 Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal for Research in Mathematics Education, 30(4), 390-416.   DOI
28 Tzur, R. (2004). Teacher and students’ joint production of a reversible fraction conception. Journal of Mathematical Behavior, 23(1), 93-114.   DOI
29 Wilkins, J. L. M., & Norton, A. (2011). The splitting loope. Journal for Research in Mathematics Education, 42(4), 386-416.   DOI
30 von Glasersfeld, E. (1999). 앎과 학습의 길: 급진적 구성주의, (김판수, 박수자, 심성보, 유병길, 이형철, 임채성 외 공역). 서울: 원미사. (원작은 1995년 출판).