참고문헌
- 변정호, 이일선, 권용주 (2011). 시선추적기를 활 용한 시선집중 및 배분 교수행동 패턴의 컨설팅사례연구. 학습자중심교과교육연구, 11(4), 173-199.
- 오지혜 (2011). 초등수학에서 등호 개념 지도를 위한 교사 지식에 관한 연구. 이화여자대학교 교육대학원 석사논문.
- Ashlock, Robert B.(2010). Error Patterns in Computation: Using Error Patterns To Help Each Student Learn. 10th Edition. Pearson Education. 남승인 외 6명 공역(2013). 예비교 사와 현직교사를 위한 초등수학 교수법 - 수학 오개념과 오류 바로잡기. 서울: 경문사.
- Behr, M., Erlwanger, S. & Nichols, E. (1980). How children view th equal sign. Mahematics Teaching, 92, 13-15.
- Broody, Arthur J., Coslick, Ronald T. (1998). Fostering children's mathematical Power. Lawrence Eribaum Associates, Inc. 권성룡 외 11인(2006). 수학의 힘을 길러주자. 왜? 어떻게?. 서울: 경문사.
- Chesney, D. L., McNeil, N. M., Brockmole, N. M., & Kelley, K. (2013). An eye for relations: eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence. Memory & cognition, 41, 1079-1095. https://doi.org/10.3758/s13421-013-0315-8
- Karatekin, C. (2007). Eye tracking studies of normative and atypical development. Development Review, 27, 283-348. https://doi.org/10.1016/j.dr.2007.06.006
- Kurz, T. L. (2013.) Using Technology to Balance Algebraic Explorations - Free, Web-based balance tools can help students visualize the concept of the equal sign as the pivot point of an equation. Teaching children mathematics, Vol. 19 No. 9, 554-562. https://doi.org/10.5951/teacchilmath.19.9.0554
- Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326. https://doi.org/10.1007/BF00311062
- McNeil, N. M., Allibali, M. W. (2004) You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science, 28, 451-466.
- McNeil, N. M., Chesney, D. L., Matthews, P. G. et al. (2012). It pay to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence. Journal of Educational Psychology, 104(4), 1109-1121. https://doi.org/10.1037/a0028997
- National Council of Teachers of Mathematics (2000) Principle and standards for school mathematics. Reston, VA: The Author. 류희찬․ 조완영․이경화․나귀수․김남균․방정숙 공역(2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
- Perry, M., Church, R. B., & Goldin-Meadow, S. (1988). Transitional knowledge in the acquisition of concepts. Cognitive Development, 3, 359-400. https://doi.org/10.1016/0885-2014(88)90021-4
- Sherman, J., Bisanz, J.(2009) Equivalence in Symbolic and Nonsymbolic Contexts: Benefits of Solving Problems With Manipulatives. Journal of Educational Psychology, volume 101, Number 1, 2009, 88-100. https://doi.org/10.1037/a0013156
- Suth, J., & Moyer-Packenham, P. S. (2007). Developing students' representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155.
- Tomas, L. E, & Lleras, A. (2007). Moving eyes and moving thought: On spatial compatibility between eye movements and cognition. Psychonomic Bulletin & Review, 14(4), 663-668. doi:10.3758/BF03196818.
- Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equations with one unknown. Educational Studies in Mathematics, 49(3), 341-359. https://doi.org/10.1023/A:1020229023965
- Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76-95. https://doi.org/10.1007/BF03217546