[논문]기표의 구현과 수학적 이해: 경과시간을 중심으로

한채린

doi:10.7468/mathedu.2021.60.3.249

기표의 구현과 수학적 이해: 경과시간을 중심으로
Realization of signifiers and mathematics understanding: Focused on the elapsed time 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.3, 2021년, pp.249 - 264

한채린 (서울등촌초등학교)

초록
AI-Helper

이 연구는 사회문화적인 관점에서 경과시간이라는 수학적 대상을 구현하는 기표를 통해 학생들의 경과시간 이해를 탐색하였다. 연구 결과, 학생들은 주어진 기표에 따라 차별화된 방식으로 경과시간 과제를 수행하고 있음이 확인되었고, 개별적으로 구성된 학생들의 경과시간 구현 기표 수형도는 이들이 특히 아날로그 시계 기표에서 경험하는 차별화된 과제 수행을 설명해주었다.

Abstract ▼ AI-Helper

This article is devoted to investigating young learners' understanding of elapsed time from socio-cultural perspectives. The socio-cultural perspective benefits to access and personalize mathematics learning as how to have a mathematical object to be able to realize signifiers with the help of many other mathematical words and mediators. In terms of the realization of signifiers, I analyzed performances on elapsed time tasks of students in Grades 3 (n=115) and interviewed focal students. Quantitative analysis on students' performance identified that students perform differently when the task provided with the analog clock signifier. It suggested that students might think in a different way upon the given signifier even for the same elapsed time, especially when given as the analog clock. Qualitative analysis on focal students' interviews visualized how the students' understanding were different by displaying individual realization trees on elapsed time. The particular location of the analog clock signifier on each realization tree provided a personalized explanation about low performance on the task with analog clock signifier. The finding suggested that the realization of a specific signifier could be a key point in elapsed time understanding. I discussed why a majority of students face difficulty in elapsed time learning indicated analog clock and the advantage of moving elapsed time strands to higher grades in the school mathematics curriculum.

주제어

표/그림 (11)

그림 [Fig. 1] A realization tree of basic quadratic function(Nachlieli & Tabach, 2012, p.13)
그림 [Fig. 2] The hierarchical thinking involved in coordinating hours and minutes(Kamii & Russell, 2012, p. 299)
표 [Table 1] Four representations on elapsed time regarded in this study
그림 [Fig. 3] Example of elapsed time item across realized signifiers
표 [Table 2] Number of collected responses upon time-set items
그림 [Fig. 4] Boxplots of performance for elapsed time task by each realized signifier
표 [Table 3] One-way ANOVA results of the data regarding the realized signifier of elapsed time
그림 [Fig. 5] Ga-yeon's realization tree of the signifier "Elapsed time from 6:30 to 8:20"
그림 [Fig. 6] Mia's realization tree of the signifier "Elapsed time from 6:30 to 8:20"
그림 [Fig. 7] Seung-min's realization tree of the signifier "Elapsed time from 6:30 to 8:20"
그림 [Fig. 8] Seung-min's solutions for the elapsed time task represented by the analog clock signifier

참고문헌 (58)

Acredolo, C. (1989). Assessing children's understanding of time, speed, and distance interrelations. In I. Levin & D. Zakay (Eds.), Time and human cognition: A life-span perspective (pp. 219-257). Amsterdam, Netherlands: Elsevier Science.
Australian Curriculum, Assessment and Reporting Authority. (2012). Australian Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/
Buchholtz, N. (2019). Planning and conducting mixed methods studies in mathematics educational research. In G. Kaiser & N. Presmeg (Eds.), Compendium for early career researchers in mathematics education (pp. 131-152). Cham, Switzerland: Springer Nature.
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.
Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51-52, 45-65.
Cho, Y. M., & Lim, S. H. (2010). A study on textbooks of South Korea, Singapore, and Japan focused on the teaching of the time. J ournal of Elementary Mathematics Education in Korea, 14(2), 421-440.
Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. New York, NY: Routledge.
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: Sage Publications.
Crosby, A. W. (1997). The measure of reality: Quantification in Western Europe, 1250-1600. New York, NY: Cambridge University Press.
Earnest, D. (2015). From number lines to graphs in the coordinate plane: Investigating problem solving across mathematical representations. Cognition and Instruction, 33(1), 46-87.

상세보기
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.

상세보기
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

상세보기
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.

상세보기
Finnish National Board of Education (2016). National core curriculum for basic education 2014. Helsinki, Finland: Author.
Fivush, R., & Mandler, J. M. (1985). Developmental changes in the understanding of temporal sequence. Child Development, 56(6), 1437-1446.

상세보기
Friedman, W. J., & Laycock, F. (1989). Children's analog and digital clock knowledge. Child Development, 60(2), 357-371.

상세보기
Glas, C. A. (2019). Reliability issues in high-stakes educational tests. In B. P. Veldkamp & C. Sluijter (Eds.), Theoretical and practical advances in computer-based educational measurement (pp. 213-230). Cham, Switzerland: Springer International Publishing.
Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed method evaluation designs. Educational Evaluation and Policy Analysis, 11(3), 255-274.

상세보기
Hackenberg, A. J. (2013). The fractional knowledge and algebraic reasoning of students with the first multiplicative concept. The Journal of Mathematical Behavior, 32(3), 538-563.

상세보기
Hackenberg, A. J., Norton, A., & Wright, R. J. (2016). Developing fractions knowledge. London, UK: Sage Publications.
Hackenberg, A. J., & Tillema, E. S. (2009). Students' whole number multiplicative concepts: A critical constructive resource for fraction composition schemes. The Journal of Mathematical Behavior, 28(1), 1-18.

상세보기
Han, C. (2020). Making sense of time-telling classroom: Interplay of cognition, instruction, and tools. Unpublished doctoral dissertation, Seoul National University.
Han, C. (2021). A comparative analysis of the mathematics curriculum on time-related contents: Focusing on Korea, Japan, Australia, the United States, and Finland. Education of Primary School Mathematics, 24(3), 115-134.
Harner, L. (1982). Talking about the past and the future. In W. J. Friedman (Ed.), The developmental psychology of time (pp. 141-169). New York, NY: Academic Press.
Izsak, A., Jacobson, E., de Araujo, Z., & Orrill, C. H. (2012). Measuring mathematical knowledge for teaching fractions with drawn quantities. J ournal for Research in Mathematics Education, 43(4), 391-427.

상세보기
Kamii, C., & Russell, K. A. (2010). The older of two trees: Young children's development of operational time. Journal for Research in Mathematics Education, 41(1), 6-13.
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.

상세보기
Kwon, M. (2019). Second grade elementary school students' understanding of time and elapsed time. Journal of Educational Research in Mathematics, 49(4), 741-760.
Levin, I. (1989). Principles underlying time measurement: The development of children's constraints on counting time. In I. Levin & D. Zakay (Eds.), Time and human cognition (pp. 145-183). North Holland, Netherlands: Elsevier.
Long, K., & Kamii, C. (2001). The measurement of time: Children's construction of transitivity, unit iteration, and conservation of speed. School Science and Mathematics, 101(3), 125-132.

상세보기
Ministry of Education. (2015). Mathematics curriculum. Sejong, South Korea: Author.
Morse, J. M., & Niehaus, L. (2009). Mixed method design: Principles and procedures. Walnut Creek, CA: Left Coast Press.
Nachlieli, T., & Tabach, M. (2012). Growing mathematical objects in the classroom-The case of function. International Journal of Educational Research, 51-52, 10-27.
Nam, J., & Chang, H. (2016). Analysis on mathematical understanding of elementary school students about time. Journal of Elementary Mathematics Education in Korea, 20(3), 479-498.
Nam, J., & Chang, H. (2017). A comparative analysis of time in elementary mathematics textbooks. School Mathematics, 19(3), 513-531.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.
Pang, J., Kwon, M., Kim, M., Choi, I., & Jin, S. (2016). An analysis of length and time in the elementary mathematics textbooks: Focused on the instructional components of measurement and key competencies in mathematics. School Mathematics, 18(2), 301-322.
Park, J. (2016). Communicational approach to study textbook discourse on the derivative. Educational Studies in Mathematics, 91(3), 395-421.

상세보기
Piaget, J. (1969). The child's conception of time. New York, NY: Ballantine Books.
Richards, D. D. (1982). Children's time concepts: Going the distance. In W. J. Friedman (Ed.), The developmental psychology of time (pp. 13-45). New York, NY: Academic Press.
Russell, K. A., & Kamii, C. (2012). Children's judgments of durations: A modified replication of Piaget's study. School Science and Mathematics, 112(8), 476-482.

상세보기
Saxe, G. B. (2012). Cultural development of mathematical ideas: Papua New Guinea studies. Cambridge, UK: Cambridge University Press.
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences, 16(4), 565-613.

상세보기
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press.
Sfard, A. (2012). Developing mathematical discourse: Some insights from communicational research. International Journal of Educational Research, 51-52, 1-9.
Sfard, A. (2017). Ritual for ritual, exploration for exploration. In J. Adler & A. Sfard (Eds.), Research for educational change: Transforming researchers' insights into improvement in mathematics teaching and learning (pp. 41-63). London, UK: Routledge.
Siegler, R. S., & Richards, D. D. (1979). Development of time, speed, and distance concepts. Developmental psychology, 15(3), 288-298.

상세보기
Smith III, J. P., & Barrett, J. E. (2017). Learning and teaching measurement: Coordinating quantity and number. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 355-385). Reston, VA: National Council of Teachers of Mathematics.
Steffe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Differences, 4(3), 259-309.

상세보기
Steffe, L. P. (1994). Children's multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3-39). Albany, NY: SUNY Press.
Steffe, L. P. (2001). A new hypothesis concerning children's fractional knowledge. The Journal of Mathematical Behavior, 20(3), 267-307.

상세보기
Tabach, M., & Nachlieli, T. (2015). Classroom engagement towards using definitions for developing mathematical objects: The case of function. Educational Studies in Mathematics, 90(2), 163-187.

상세보기
Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Vygotsky, L. S. (1986). Thought and language (2nd ed.). Cambridge, MA: MIT Press.
Weingarden, M., Heyd-Metzuyanim, E., & Nachlieli, T. (2019). The realization tree assessment tool-examining explorative participation in mathematics lessons. The Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2019.100717.

상세보기
Williams, R. F. (2012). Image schemas in clock-reading: Latent errors and emerging expertise. Journal of the Learning Sciences, 21(2), 216-246.

상세보기
Yeo, S. (2021). Semiotic mediation through technology: The case of fraction reasoning. The Mathematical Education, 60(1), 1-19.
文部科學省. (2017). 小學校學習指導要領解設算數編. 文部科學省.

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