본문 바로가기
KERD
논문KCI 등재

Semiotic mediation through technology: The case of fraction reasoning

여승현
한국수학교육학회|2021.02|수학교육 (The Mathematical Education)|제60권 제1호|pp. 1-19|DOI https://doi.org/10.7468/mathedu.2021.60.1.1

0

조회

0

다운로드

5

인용

0

참고문헌

키워드

공학도구semiotic mediationfraction as measuredynamic technology측정으로서의 분수기호적 중재

초록

This study investigates students’ conceptions of fractions from a measurement approach while providing a technological environment designed to support students’ understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students’ constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field’s understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

Abstract

This study investigates students’ conceptions of fractions from a measurement approach while providing a technological environment designed to support students’ understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students’ constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field’s understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

참고문헌 (49)

  1. Alajmi, A. H., "How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait", Educational Studies in Mathematics, 79(2), pp.239~261 (2012)
  2. Arzarello, F., "Semiosis as a multimodal process", RLIME-Revista Latino americana de Investigaciónen Matemática Educativa, 9(1), pp.267~299 (2006)
  3. Arzarello, F., "Handbook of international research in mathematics education", pp.720~749 (2008), Erlbaum
  4. Bartolini Bussi, M. G., "Handbook of international research in mathematics education", pp.720~749 (2008), Erlbaum
  5. Battista, M. T., "Research on technology and the teaching and learning of mathematics: Cases and perspectives", pp.341~362 (2008), Information Age Publishing, Inc
  6. Behr, M. J., "Handbook of research on mathematics teaching and learning", pp.296~332 (1992), Macmilian Publishing Company
  7. "Common core state standards for mathematics" (2010)[URL]
  8. Davydov, V. V., "Soviet studies in mathematics education: Psychological abilities of primary school children in learning mathematics", pp.86~147 (1991), National Council of Teachers of Mathematics
  9. Dick, T. P., "Focus in high school mathematics: Technology to support reasoning and sense making" (2011), National Council of Teachers of Mathematics
  10. Dougherty, B. J., "Algebra in the early grades", pp.389~412 (2008), Lawrence Erlbaum Associates
  11. Empson, S. B., "Equal sharing and shared meaning : The development of fraction concepts in a first-grade classroom", Cognition and Instruction, 17(3), pp.283~342 (1999)
  12. Empson, S. B., "Fractions as the coordination of multiplicatively related quantities : Across-sectional study of children's thinking", Educational Studies in Mathematics, 63(1), pp.1~28 (2006)
  13. Empson, S. B., (2011), Heinemann
  14. Ginsburg, H., "Entering the child's mind : The clinical interview in psychological research and practice" (1997), Cambridge University Press
  15. Hollebrands, K. F., "The role of a dynamic software program for geometry in the strategies high school mathematics students employ", Journal for Research in Mathematics Education, 38(2), pp.164~192 (2007)
  16. Hunting, R. P., "Engaging whole-number knowledge for rational-number learning using a computer-based tool", Journal for Research in Mathematics Education, 27(3), pp.354~379 (1996)
  17. 강흥규, "양의 측정을 통한 자연수와 분수 지도의 교수학적 의의", 학교수학, 5(3), pp.6~399 (2003), 대한수학교육학회
  18. Kaur, H., "Two aspects of young children’s thinking about different types of dynamic triangles : Prototypicality and inclusion", ZDM, 47(3), pp.407~420 (2015)
  19. Kieren, T. E., "Number concepts andoperations in the middle grades", pp.162~181 (1988), Erlba
  20. Konold, C., "Understanding distributions by modeling them", International Journal of Computers for Mathematical Learning, 12(3), pp.217~230 (2007)
  21. Laborde, J. M., "Digital curricula in school mathematics", pp.53~74 (2016), Information Age Publishing, Inc
  22. 이지영, "분수의 다양한 의미에서 단위에 대한 초등학교 6학년 학생들의 이해 실태 조사", 수학교육학연구, 24(1), pp.83~102 (2014), 대한수학교육학회
  23. Mack, N. K., "Building on informal knowledge through instruction in a complex content domain : Partitioning, units, and understanding multiplication of fractions", Journal for Research in Mathematics Education, 32(3), pp.267~295 (2001)
  24. . Statute Notice of Ministryof Educatio (No. 2015-74), "Ministry of Education", 2015
  25. Moreno-Armella, L., "From static to dynamic mathematics : Historical and representational perspectives", Educational Studies in Mathematics, 68(2), pp.99~111 (2008)
  26. Morris, A. K., "A teaching experiment : Introducing fourth graders to fractions from the viewpoint of measuring quantities using Davydov’s mathematics curriculum", Focus on Learning Problems in Mathematics, 22(2), pp.33~84 (2000)
  27. Mortimer, E. F., "Conceptual profiles : A theory of teaching and learning scientific concepts" (2014), Springer
  28. Foundations for success: The final report of the National Mathematics Advisory Panel, "National Mathematics Advisory Panel", U.S. Department of Education, ~ (2008)
  29. Ng, O. L., "Young children reasoning about symmetry in a dynamic geometry environment", ZDM, 47(3), pp.421~434 (2015)
  30. 노정원, "기호적 중재를 통한 사각형의 성질 학습 사례 연구 - 성질 사이의 관계에 관한 추론을 중심으로", 학교수학, 21(1), pp.197~214 (2019), 대한수학교육학회[DOI]
  31. Olive, J., "Research on technology and the teaching and learning of mathematics: Research syntheses", pp.1~54 (2008), Information Age and the National Council of Teachers of Mathematics
  32. Saxe, G. B., "Towards curricular coherence in integers and fractions : A study of the efficacy of a lesson sequence that uses the number line as the principal representational context", ZDM, 45(3), pp.343~364 (2013)
  33. Schmittau, J., "The development of algebra in the elementary mathematics curriculum of VV Davydov", The Mathematics Educator, 8(1), pp.60~87 (2004)
  34. Schoenfeld, A. H., "Making mathematics work for all children : Issues of standards, testing, and equity", Educational Researcher, 31(1), pp.13~25 (2002)
  35. Schoenfeld, A. H., "Advances in Instructional Psychology (Volume 4)", pp.55~175 (1993), Erlbaum
  36. Sfard, A., "Thinking as communicating: Human development, the growth of discourses, and mathematizing" (2008), Cambridge University Press
  37. Simon, M. A., "Promoting a concept of fraction-as-measure : A study of the Learning Through Activity research program", The Journal of Mathematical Behavior, 52, pp.122~133 (2018)
  38. 손태권, "2015개정교육과정 분수의 덧셈과 뺄셈에 관한 수학 교과서 및 익힘책 분석", 학교수학, 22(3), pp.489~508 (2020), 대한수학교육학회
  39. Steffe, L. P., "Design and use of computer tools for interactive mathematical activity(TIMA)", Journal of Educational Computing Research, 27(1), pp.55~76 (2002)
  40. Streefland, L., "Fractions in realistic mathematics education" (1991), Kluwer
  41. Streefland, L., "Rational numbers: An integration of research", pp.289~325 (1993), Lawrence Erlbaum Associates, Inc
  42. Suh, J., "Examining technology uses in the classroom : Developing fraction sense using virtual manipulative concept tutorials", Journal of Interactive Online Learning, 3(4), pp.1~21 (2005)
  43. Thompson, P. W., "research companion to principles and standards for school mathematics", pp.95~113 (2003), The National Council of Teachers of Mathematics
  44. Vygotsky, L. S., "Mind in society" (1978), Harvard University Press
  45. Webel, C., "Using representations of fraction multiplication", Teaching Children Mathematics, 22(6), pp.366~373 (2016)
  46. 양은경, "개방형 기하 문제에서 학생의 드래깅 활동을 통해 나타난 수학적 추론 분석", 수학교육학연구, 24(1), pp.1~27 (2014), 대한수학교육학회
  47. Yeo, S., "Investigating children’s informal thinking : The case of fraction division", Journal of KSME Series D : Research in Mathematics Education, 22(4), pp.283~304 (2019)
  48. 여승현, "Integrating Digital Technology into Elementary Mathematics: Three Theoretical Perspectives", 수학교육연구, 23(3), pp.165~179 (2020), 한국수학교육학회[DOI]
  49. Yin, R. K., "Case study research: Design and methods" (2014), Sage

관련 논문AI추천

Investigating Children’s Informal Knowledge and Strategies: The Case of Fraction DivisionSheunghyun Yeo한국수학교육학회 · Mathematics Education Research and Practice2019 · 제22권 제4호Making Sense of Drawn Models for Operations of Fractions Involving Mixed Numbers노지화영남수학회 · East Asian Mathematical Journal2018 · 제34권 제2호단위분수에 대한 초등학교 3학년 학생들의 이해 분석: 지도 맥락과 시각적 표현의 관점에서임미인한국수학교육학회 · 수학교육2018 · 제57권 제1호An Analysis of Fraction Operation Sense to Enhance Early Algebraic Thinking방정숙, LEE, Jiyoung한국수학교육학회 · Mathematics Education Research and Practice2012 · 제16권 제4호A First Grade Teacher’s Challenge in Promoting Students’ Understanding of Unit IterationByungeun Pak한국수학교육학회 · Mathematics Education Research and Practice2022 · 제25권 제3호Elementary Preservice Teachers’ Noticing and Evaluation of Digital Mathematical Resources여승현한국수학교육학회 · Mathematics Education Research and Practice2023 · 제26권 제2호

이 간행물의 다른 논문 (5건)

유리수 지수 정의에 대한 교사 이해 분석신보미pp. 21-39메타분석을 통한 또래교수 수업이 수학 학업성취도와 정의적 영역에 미치는 효과조창호, 최송희, 김동중pp. 41-59수학 예비교사들이 과제의 인지적 노력 수준 변형에서 겪는 오류와 어려움강향임, 최은아pp. 61-76수업 설계안 구조 변화에 따른 예비교사들의 수업 설계 특징 분석한선영, 이선영pp. 77-110수학 교사의 교과서 이해 및 활용 의도 탐색조수현, 김구연pp. 111-131
원문 보기