van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35.
Sinicrope, R., Mick, H., & Kolb, J. (2002). Fraction division interpretations. In B. Litwiller, & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 Year Book (pp. 153–161). Reston, VA: National Council of Teachers of Mathematics.
Schwartz, J. L. (1988). Intensive quantity and referent transforming arithmetic operations. In J. Hiebert, & M. Behr (Eds.), Number concepts and operations in the middle grades (Vol. 2, pp. 41-52). Reston, VA: Erlbaum.
Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15(5), 381-403.
Ng, S. F., & Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313.
Murata, A. (2008). Mathematics teaching and learning as a mediating process: The case of tape diagrams. Mathematical Thinking and Learning, 10(4), 374-406.
Middleton, J. A., van den Heuvel-Panhuizen, M., & Shew, J. A. (1998). Using Bar Representations as a Model for Connecting Concepts of Rational Number. Mathematics Teaching in the Middle School, 3(4), 302-311.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
Lamon, S. J. (2007). Rational numbers and proportional reasoning. In F. K. J. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Charlotte, NC: Information Age
Kaput, J. (1985). Multiplicative Word Problems and Intensive Quantities: An Integrated Software Response (Technical Report 85-19). Cambridge, MA: Educational Technology Center.
K chemann, D., Hodgen, J., & Brown, M. (2014). The use of alternative double number lines as models of ratio tasks and as models for ratio relations and scaling. In S. Pope (Ed.), Proceedings of the 8th British Congress of Mathematics Education (BCME8) (pp. 231-238). BSRLM: University of Nottingham.
K chemann, D., Hodgen, J., & Brown, M. (2011). Using the double number line to model multiplication. Paper presented at Seventh Annual Congress of the European Society for Research in Mathematics Education, Rzesz w, Poland.
Instructional-design theories and models, volum Ⅱ: A new paradigm of instructional theory. NJ: Lawrence Erlbaum Associates. 최욱, 박인우, 변호승, 양영선, 왕경수, 이상수 외 3인 공역 (2005). 교수설계 이론과 모형
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel Publishing Company.
Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics in grades 6–8. Reston, VA: National Council of Teachers of Mathematics. 박정숙, 강현영, 고은성, 이동환 공역(2016). 비, 비례, 비례 추론의 필수 이해
Developing essential understanding of functions for teaching mathematics in grades 9-12. Reston, VA: National Council of Teachers of Mathematics. 조완영, 권나영, 이동흔 공역(2017). 함수의 필수 이해
Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. Retrieved from http://www. corestandards.org/assets/CCSSI_Math%20Standards.pdf
Children's mathematics: Cognitively guided instruction. Reston, VA: National Council of Teachers of Mathematics. 김수환, 박영희, 백선수, 이경화, 한대희 공역(2006). 어떻게 수학을 배우지?
Beckmann, S., & Izs k, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17-38.
Beck, P. S., Eames, C. L., Cullen, C. J., Barrett, J. E., Clements, D. H., & Sarama, J. (2014). Linking children’s knowledge of length measurement to their use of double number lines. Proceedings of PME 38 and PME-NA 36, 2, 105-112.