References
- 권미숙, 김남균 (2009). 초등학교 6학년 학생들의 교과서 비례 문제 해결과 비례 추론에 관한 연구. 한국초등수학교육학회지, 13(2), 211-229.
- 고은성, 이경화 (2007). 초등학교 6학년 학생의 비례 추론 능력 분석. 수학교육학연구, 17(4), 359-380.
- 박지연, 김성준 (2016). 초등학교 6학년 학생들의 비례 추론 능력 분석 -'비교' 상황을 중심으로. 한국초등수학교육학회지, 20(1), 105-129.
- 안숙현, 방정숙 (2008). 5, 6, 7학년 학생들의 비례추론 능력 실태 조사. 수학교육학연구, 18(1), 103-121.
- 정영옥 (2015). 초등학교에서 비례 추론 지도에 관한 논의. 수학교육학연구, 25(1), 21-58.
- 정유경, 정영옥 (2015). 초등학생들의 비례추론 전략 분석 -6학년을 중심으로. 한국초등수학교육학회지, 19(4), 457-484.
- 정은실 (2013). 초등학교 수학교과서에서의 비례추론에 대한 연구. 수학교육학연구, 23(4), 505-516.
- Ben-Chaim, D., Keret, Y., Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers' content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10, 333-340. https://doi.org/10.1007/s10857-007-9052-x
- Cramer, K., & Post, T. (1993). Proportional reasoning. The Mathematics Teacher, 86(5), 404-407.
- 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). NY: Macmillan.
- Ekawati, R., Lin, F. & Yang, K. (2015). Primary teachers' knowledge for teaching ratio and proportion in Mathematics: The case of Indonesia. Eurasia Journal of Mathematics, Science & Technology Education, 11(3), 513-533. https://doi.org/10.12973/eurasia.2015.1354a
- Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel Publishing Company.
- Hull, L.S.H. (2000). Teachers' mathematical understanding of proportionality: Links to curriculum, professional development, and support. Unpublished doctoral dissertation, The University of Texas at Austin, Austin, TX.
- Lamon, S. J. (1993). Ratio and proportion: Children's cognitive and metacognitive processes. In T. P. Carpenter, E. Fennema, & T. A. Romberg(Eds.), Rational Numbers An Integration of Research (pp. 131-156). New Jersey, Hillsdale: Lawrence Erlbaum Associates, Publishers.
- Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte, NC: Information Age Publishing.
- Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261.
- Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Reston, VA: National Council of Teachers of Mathematics, INC.
- Lobato, J., & Ellis, A. B. (2010). Essential understandings: Ratios, proportions, and proportional reasoning. In R. M. Zbiek (Series Ed.), Essential understandings. Reston, VA: National Council of Teachers of Mathematics (NCTM).
- Lobato, J., Orrill, C., Druken, B., & Jacobson, E. (2011). Middle school teachers' knowledge of proportional reasoning for teaching. In Annual Meeting of the American Educational Research Association (AERA), ew Orleans, LA. Abstract retrieved from http://www.kaputcenter.umassd.edu/downloadsproducts/workshops/AERA2011/Lobato_Orrill_Druken_Erikson_AERA_2011.pdf.
- Nabors, W. K. (2003). From fractions to proportional reasoning: a cognitive schemes of operation approach. Journal of Mathematical Behavior, 22, 133-179. https://doi.org/10.1016/S0732-3123(03)00018-X
- NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM
- Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. In A. Coxford & A. Shulte (Eds.), The Idea of Algebra K-12 (1988 Yearbook, pp. 78-90). Reston, VA: National Council of Teachers of Mathematics.
- Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.2307/749486
- Van de Walle, J. A. (2008). 수학을 어떻게 가르칠 것인가. (남승인 외 역). 서울: 경문사. (영어 원작은 2004년 출판).