1. Aoyama, S. (2013). Wariai no mikata kangaekata wo sodateru shidou no kuhuu: Suutyokusenzu jou de taiou suru suuryou wo sousa suru katsudou wo tooshite [Lessons designed for developing the concepts and ideas of ratio and rate: Through manipulation of corresponding numbers and quantities on the number line diagrams]. Journal of Japan Society of Mathematical Education, 95(10), 2–10.
2. Bass, H. (2015). Quantities, numbers, number names, and the real number line. In X. Sun, B. Kaur, & J. Novotná (Eds.), Conference proceedings of ICMI Study 23: Primary mathematics study on whole numbers (pp. 10–19), June 3–7, University of Macau, Macao, China.
3. Beckmann, S., & Izsák, 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.
4. Christou, C., & Philippou, G. (2002). Mapping and development of intuitive proportional thinking. Journal of Mathematical Behavior, 20, 321–336.
5. Clark, F., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1–5. Journal for Research in Mathematics Education, 27(1), 41–51.