References
- 교육부(2015). 수학과 교육과정(교육부 고시 제2015-74호 별책8). 세종: 교육부.
- 교육부(2017). 수학 2-2. 서울: (주) 천재교육.
- 권미선(2019). 시각과 시간에 대한 초등학교 2 학년 학생들의 이해 실태 조사. 수학교육학연구, 29(4), 741-760.
- 한채린(2021a). 시각과 시간에 대한 수학과 교육과정 국제 비교 연구: 한국, 일본, 호주, 미국, 핀란드를 중심으로. 초등수학교육, 24(3), 115-134.
- 한채린(2021b). 기표의 구현과 수학적 이해: 경과시간을 중심으로. 수학교육, 60(3), 249-264.
- 한채린(2021c). '몇 시 몇 분 전'으로 시각 읽기에 얽힌 수학적 활동의 탐색. 학교수학, 23(3), 457-475.
- Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2012). Australian Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/
- Barnett, J. E. (1998). Time's pendulum: From sundials to atomic clocks, the fascinating history of timekeeping and how our discoveries changed the world. New York, NY: Plenum Press.
- Berliner, D. C. (1979). Tempus educare. In P. L. Peterson & H. J. Walberg (Eds.), Research on teaching: Concepts, findings, and implications (pp. 120-135). Berkeley, CA: McCutchan.
- Burny, E., Valcke, M., & Desoete, A. (2009). Towards an agenda for studying learning and instruction focusing on time-related competencies in children. Educational Studies, 35(5), 481-492. https://doi.org/10.1080/03055690902879093
- Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., Cirillo, M., ... & Bakker, A. (2020). Maximizing the quality of learning opportunities for every student. Journal for Research in Mathematics Education, 51(1), 12-25. https://doi.org/10.5951/jresematheduc.51.1.0012
- Clandinin, D. J., & Connelly, F. M. (2000). Narrative inquiry: Experience and story in qualitative research. San Francisco: Jossy-Bass Publisher.
- Cipolla, C. M. (1978). Clocks and culture, 1300-1700. New York, NY: Norton.
- Cohen, D. K., & Ball, D. L. (1999). Instruction, capacity, and improvement (CPRE Research Report RR-043). Philadelphia: Consortium for Policy Research in Education.
- Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. https://doi.org/10.3102/01623737025002119
- Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: Sage Publications.
- Dixon, J. K., Larson, M., Burger, E. B., Sandoval-Martinez, M. E., & Leinwand, S. J. (2015). Go math! grade 4 volume 2: Student edition. Orlando, FL: Houghton Mifflin Harcourt Publishing Company.
- Earnest, D. (2017). Clock work: How tools for time mediate problem solving and reveal understanding. Journal for Research in Mathematics Education, 48(2), 191-223. https://doi.org/10.5951/jresematheduc.48.2.0191
- Earnest, D. (2019). The invisible quantity: time intervals in early algebra/La cantidad invisible: los intervalos de tiempo en el algebra temprana. Infancia y Aprendizaje, 42(3), 664-720. https://doi.org/10.1080/02103702.2019.1615199
- Earnest, D. (2021). About time: Syntactically-guided reasoning with analog and digital clocks. Mathematical Thinking and Learning, https://doi.org/10.1080/10986065.2021.1881703
- Earnest, D., & Chandler, J. (2021). Making time: words, narratives, and clocks in elementary mathematics. Journal for Research in Mathematics Education, 52(4), 407-443. https://doi.org/10.5951/jresematheduc-2021-0020
- Earnest, D., Gonzales, A. C., & Plant, A. M. (2018). Time as a measure: Elementary students positioning the hands of an analog clock. Journal of Numerical Cognition, 4(1), 188-214. https://doi.org/10.5964/jnc.v4i1.94
- Ellis, A. B. (2007). Connections between generalizing and justifying: Students' reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194-229.
- Finnish National Board of Education (2016). National core curriculum for basic education 2014. Helsinki, Finland: Author.
- Friedman, W. J., & Laycock, F. (1989). Children's analog and digital clock knowledge. Child Development, 60(2), 357-371. https://doi.org/10.1111/j.1467-8624.1989.tb02721.x
- Hackenberg, A. J. (2010). Students' reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383-432. https://doi.org/10.1080/07370008.2010.511565
- Han, C. (2020). Making sense of time-telling classroom: Interplay of cognition, instruction, and tools. Unpublished doctoral dissertation, Seoul National University.
- Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549. https://doi.org/10.2307/749690
- Husen, T. (Ed.). (1967). International study of achievement in mathematics: A comparison of twelve countries (Vol. I). New York, NY: John Wiley & Sons.
- Kamii, C., & Russell, K. A. (2012). Elapsed time: Why is it so difficult to teach? Journal for Research in Mathematics Education, 43(3), 296-315. https://doi.org/10.5951/jresematheduc.43.3.0296
- Kurz, A. (2011). Access to what should be taught and will be tested: Students' opportunity to learn the intended curriculum. In S. N. Elliott, R. J. Kettler, P. A. Beddow, & A. Kurz (Eds.), The handbook of accessible achievement tests for all students: Bridging the gaps between research, practice, and policy (pp. 99-129). Springer. https://doi.org/10.1007/978-1-4419-9356-4_6
- Males, L. M., & Earnest, D. (2015, April). Opportunities to learn time measure in elementary curriculum materials. In D. Earnest, L. M. Males, C. Rumsey, & R. Lehrer (Discussants), The measurement of time: Cognition, instruction, and curricula. Symposium conducted at the 2015 Research Conference of the National Council of Teachers of Mathematics, Boston, MA.
- Monroe, E. E., Orme, M. P., & Erickson, L. B. (2002). Links to literature: working cotton: Toward an understanding of time. Teaching Children Mathematics, 8(8), 475-479. https://doi.org/10.5951/tcm.8.8.0475
- Moore, K. C. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83(2), 225-245. doi:10.1007/s10649-012-9450-6
- Moore, K. C., & Carlson, M. P. (2012). Students' images of problem contexts when solving applied problems. The J ournal of Mathematical Behavior, 31, 48-59. https://doi.org/10.1016/j.jmathb.2011.09.001
- National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers [CCSSO] (2010). Common core state standards for mathematics. Washington, DC: Authors.
- National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
- Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics. Dordrecht: Kluwer Academic Publishers.
- Smith, J. P., & Thompson, P. W. (2008). Quantitative reasoning and the development of algebraic reasoning. In D. W. Carraher, J. J. Kaput, & M. Blanton (Eds.), Algebra in the early grades (pp. 95-132). Mahwah, NJ, USA: Lawrence Erlbaum Associates.
- Sowder, L. (1988). Children's solutions of story problems. The Journal of Mathematical Behavior, 7, 227-238.
- Thompson, P. W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in collegiate mathematics education: Issues in mathematics education (pp. 21-44). Providence, RI, USA: American Mathematical Society.
- Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), WISDOMe Monographs: Vol. 1. New perspectives and directions for collaborative research in mathematics education (pp. 33-57). Laramie, WY, USA: University of Wyoming.
- Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.
- Williams, R. F. (2012). Image schemas in clock-reading: Latent errors and emerging expertise. Journal of the Learning Sciences, 21(2), 216-246. https://doi.org/10.1080/10508406.2011.553259
- Yerushalmy, M., & Shternberg, B. (2005). Chapter 3: Epistemological and cognitive aspects of time: A tool perspective. Journal for Research in Mathematics Education. Monograph XIII. Medium and meaning: Video papers in mathematics education research.
- Yin, R. K. (2014). Case Study Research Design and Methods (5th ed.). Thousand Oaks, CA: Sage.
- 文部科学省. (2017). 小学校学習指導要領. 文部科学省.