References
- 교육인적자원부 (2007). 수학과 교육과정. 교육인적자원부.
- 고은성․이경화 (2007). 초등학교 6학년 학생의 비례 추론 능력 분석 : 2명의 사례 연구. 대한수학교육학회지 수학교육연구 17(4), 359-380.
- 권미숙․김남균 (2009). 초등학교 6학년 학생들의 교과서 비례 문제 해결과 비례 추론에 관한 연구. 한국초등수학교육학회지 13(2), 211-229.
- 김민경․권혁진 (2010). 수학 문제 해결에서 학업성취도에 따른 표상 활용 능력과 특징 분석. 한국수학교육학회지 시리즈 E <수학교육 논문집> 24(2), 475-502.
- 김숙진 (2011). 초등학교 학생들의 비례 추론 능력에 시각적 표현이 미치는 영향 : 5, 6학년을 대상으로. 경인교육대학교 석사학위논문.
- 박경은 (2004). 수학적 표상 활동 : 문헌 연구를 중심으로. 고려대학교 석사학위논문.
- 박정숙 (2008). 학생들의 문제해결전략 유형과 비례상황 인지와의 관계. 한국학교수학회논문집 11(4), 609-627.
- 박정숙 (2009). 학생의 비례추론의 분석 모형과 특성 분석. 서울대학교 박사학위논문.
- 이종욱 (2006). 4학년 아동의 비와 비례 개념 분석. 대한수학교육학회지 수학교육연구 16(2), 157-177.
- 정은실 (2003). 비 개념에 대한 역사적, 수학적, 심리적 분석. 대한수학교육학회지 <학교수학> 5(4), 421-440.
- Bruner, J. S. (1967). Toward a theory of instruction, London : Oxford University Press.
- Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp.159-178), New York: Macmillan.
- Heller et al. (1989). Proportional reasoning : The effect of two context variables, rate type, and problem setting. Journal of Research in Science Teaching, 26(3), 205-220. https://doi.org/10.1002/tea.3660260303
- Jane-Jane Lo & Watanabe, T. (1997). Developing Ratio and Proportion Schemes: A Story of a Fifth Grader. Journal for Research in Mathematics Education, 28(2), 216-236. https://doi.org/10.2307/749762
- Karplus, R., Pulos, S., & Stage, E. (1983). Early adolescents' proportional reasoning in 'rate' problems. Educational Studies in Mathematics, 14(3), 219-233. https://doi.org/10.1007/BF00410539
- Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp.235-287), Albany: State University of New York Press.
- Lamon, S. (1989). Ratio and proportion: Preinstructional cognitions. PhD Thesis, University of Wisconsin, Madison.
- Lamon, S. (1993). Ratio and proportion: connecting content and children''s thinking. Journal for Research in Mathematics Education, 24(1), 41-61. https://doi.org/10.2307/749385
- Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester Jr. (Ed), Second handbook of research on mathematics teaching and learning (pp.629-667), Reston, VA: NCTM.
- Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In M. Behr, & J. Hiebert (Eds.), Number concepts and operations in the middle grades (pp.93-118), Hillsdale, NJ: Lawrence Erlbaum Associates.
- Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children's proportional reasoning. Journal of Mathematical Behavior, 22, 335-368. https://doi.org/10.1016/S0732-3123(03)00025-7
- National Council of Teachers of Mathematics (2000). Principles and Standards for school mathematics. Reston, VA: Author.
- Singh, P. (2000). Understanding the Concepts of Proportion and Ratio Constructed by Two Grade Six Students. Educational Studies in Mathematics, 43(3), 271-292. https://doi.org/10.1023/A:1011976904850
- Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181-204. https://doi.org/10.1007/BF02400937
- Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57-86. https://doi.org/10.1207/s1532690xci2301_3
- Van Dooren, W., Bock, D. D., Evers, M., & Verschaffel, L. (2009). Students' overuse of proportionality on missing-value problems: How numbers may change solutions. Journal for Research in Mathematics Education, 40(2), 187-211.