초등학교 3학년 학생의 수학적 문제 해결에서의 표상과 표상의 정교화 과정 분석
An Analysis of Third Graders' Representations and Elaborating Processes of Representations in Mathematical Problem Solving
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Abstract
This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.
참고문헌 (31)
- "초등학교 교육 과정 해설(Ⅳ)-수학, 과학, 실과-," (1999), 대한교과서 주식회사.
- "초등학교 수학 교수-학습에서의 수학적 상징화에 관한 연구" (2002)
- "표현의 문제에 대한 수학 교육적 고찰 함수 영역을 중심으로" (1992)
- "수학 학습에서의 표현 및 표상에 관한 연구 표상 모델 개발을 중심으로" (1997)
- "Toward a theory of instruction Belknap Press of Harvard University Press" (1966)
- "From representations to symbolizing Comments on semiotics and mathematical learning Symbolizing and communicating in mathematics classrooms pp", pp.17~36 (2000), Lawrence Erlbaum Associates
- "Using a translation model for curriculum development and classroom instruction", pp.449~463 (2002), Lawrence Erlbaum Associates Inc
- "the use of diagrams as tools for thinking The roles of representation in school mathematics pp National Council of Teachers of Mathematics", pp.77~89, Inc
- "Pedagogical considerations concerning the problem of representation Problems of representation in the teaching and learning of mathematics pp", pp.109~122 (1987), In C Lawrence Erlbaum Associates Inc
- "An important process for teaching and learning mathematics", 7(5), pp.88~292 (2001)
- "Representation in mathematical learning and problem solving Handbook of international research in mathematics education pp", Lawrence Erlbaum Associates Inc
- "System of representations and the development of mathematical concepts The roles of representation in school mathematics pp National Council of Teachers of Mathematics", pp.1~23 (2001), Inc
- "Working group on representations and mathematics visualization Teaching and Learning of Mathematics 16", 16(4), pp.10~20 (1998)
- "Exploring the use of new representations as a resource for teacher learning", 103(1)
- "Geometry problem solving of Korean middle school students An analysis of representation and transfer The University of Pittsburgh" (1988), Unpublished doctoral dissertation
- "An argument to include representation in standards 2000" (2001)
- "Representation and abstraction in young children's numerical reasoning The roles of representation in school mathematics pp National Council of Teachers of Mathematics", pp.24~34 (2001), Inc
- "Creative problem solving in school mathematics" (1983), Houghton Mifflin Company
- "Key components of models and modeling Symbolizing and communicating in mathematics classrooms pp", pp.361~383 (2000), Lawrence Erlbaum Associates
- "Preschoolers' developing knowledge of the pan balance From new representation to transformed problem solving", pp.31~93 (1993)
- "National Council of Teachers of Mathematics Principles and standards for school mathematics National Council of Teachers of Mathematics" (2000), Inc
- "The role of representations in developing mathematical understanding Theory into Practice 40", 40(2), pp.118~127 (2001)
- "It’s not just" (2002)
- "Representation as a vehicle for solving and communicating Mathematics Teaching in the Middle School 9", 9(1), pp.38~43 (2003)
- "The use of symbols and diagrams as indicators of mathematical cognition", 34(5), pp.406~432 (2003)
- "The teaching of thinking and problem solving Handbook of percepion and cognition", pp.409~449 (1994), Academic Press Inc
- "Representations in the mathematics classroom The culture of the mathematics classroom pp", pp.308~343 (1997), Cambridge University Press
- "Grade 6 students' preinstructional use of equations to describe and represent problem situations", 31, pp.89~112 (2000)
- "A versatile theory of visualization andsymbolization in mathematics Paper presented at the Commission Internationale pour l'É" (1994)
- "The micro- developmen of young children's problem solving strategies when tackling addition tasks Psychology of Mathematics Education 25", 25(4), pp.391~399 (2001)
- "A models and modeling perspective on the role of small group learning activities", pp.317~336 (2003), Lawrence Erlbaum Associates Inc
