중·고등학생의 사각형에 대한 개념 정의 이해와 개념 이미지 분석
An analysis on concept definition and concept image on quadrangle of middle and high school students
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초록
이 연구의 목적은 중학생과 고등학생의 사각형에 대한 개념 정의 이해 정도를 분석하고 개념 이미지에 대한 현상을 탐색하는 것이다. 이를 위해검사 도구를 개발하고 중학교 2학년 60명, 중학교 3학년 63명, 고등학교 1학년 65명을 대상으로 검사하고, 일부의 학생을 면담하였다. 연구 결과는다음과 같다. 첫째, 학년이 올라감에 따라 자연적으로 사각형의 개념 정의에 대한 이해도가 향상된다고 볼 수 없다. 특히, 모든 학년에서 다른사각형과 비교하여 마름모 개념 정의에 대한 이해도가 가장 낮은 것으로 나타났다. 둘째, 정사각형에 대한 개념 정의는 여학생이 남학생보다 더 잘이해하지만, 사다리꼴, 평행사변형, 마름모, 직사각형에 대한 개념 정의에 대한 이해 정도는 성별로 차이가 없는 것으로 나타났다. 셋째, 사각형 개념정의를 이해하지 못하는 학생은 학년이 올라갈수록 개념 이미지의 영향을 점점 더 크게 받는 것으로 나타났다. 넷째, 학년이 올라갈수록 학생의사각형에 대한 개념 이미지 형성에 개념 정의의 영향은 줄어들고 교과서나 교사의 영향이 증가하는 경향을 보여주었다.
Abstract
The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9th graders and 65 10th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.
참고문헌 (38)
- 장현석, "원기둥을 이용한 중학생의 공간기하 이해 능력 분석", 수학교육, 59(2), pp.113~130 (2020), 한국수학교육학회[DOI]
- 조영미, "우리나라 초등학교 수학에서 사각형의 상호 관계 지도 변천 재음미 - 1차에서 3차 교육과정까지의 변화를 중심으로-", 학교수학, 12(3), pp.389~410 (2010), 대한수학교육학회
- 최수임, "정의하기와 이름짓기를 통한 도형의 이해 고찰 -초등학교 4학년 도형 영역을 중심으로-", 한국학교수학회논문집, 15(4), pp.719~745 (2012), 한국학교수학회
- Clements, D. H., "Handbook of research on mathematics teaching and learning", pp.420~464 (1992), Macmillan
- Davis, R. B., "The notion of limit : some seemingly unavoidable misconception stages", The Journal of Mathematical Behavior, 5(3), pp.281~303 (1986)[DOI]
- Fischbein, E., "The theory of figural concepts", Educational Studies in Mathematics, 24, pp.139~162 (1993)[DOI]
- Fischbein, E., "Concepts and figures in geometrical reasoning", International Journal of Science Education, 20(10), pp.1193~1211 (1998)[DOI]
- Fujita, T., "Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon", The Journal of Mathematical Behavior, 31, pp.60~72 (2012)[DOI]
- Fujita, T., "Learners’ understanding of the definitions and hierarchical classification of quadrilaterals : towards a theoretical framing", Research in Mathematics Education, 9(1), pp.3~20 (2007)[DOI]
- Ha, Y-J., "A study on the teaching and learning of quadrilaterals by using symmetry", Master, pp.2018
- 한혜숙, "The Geometer's Sketchpad를 활용한 8학년 학생들의 사각형 학습", 한국학교수학회논문집, 11(3), pp.513~541 (2008), 한국학교수학회
- Hershkowitz, R., "Visualization in geometry : two sides of the coin", Focus on Learning Problems in Mathematics Winter Edition, 11(1), pp.61~76 (1989)
- 황성환, "Gender differences in Korean elementary students: An analysis of TIMSS 2011 and 2015 fourth grade mathematics assessment", 수학교육, 59(3), pp.217~235 (2020), 한국수학교육학회[DOI]
- 김지원, "초등학교 2학년 학생들의 삼각형에 대한 개념 이미지 분석", 학교수학, 18(2), pp.425~440 (2016), 대한수학교육학회
- Kim, H-J., "An analysis on the teaching quadrilaterals in the elementary school mathematics textbooks", Education of Primary School Mathematics, 11(2), pp.141~159 (2008)
- Lee, J. K., "A study of Korea middle school students’ cognitive level of geometry and geometry curriculum based on van Hiele theory", Educational Research Institute Dongguk University, 17, pp.55~85 (2006)
- Lee, S. Y., "Correlation between the mathematical problem-solving and language skills in context: compared according to gender", Master, pp.2008
- Mesquita, A. L., "On conceptual obstacles linked with external representations in geometry", Journal of Mathematical Behavior, 17(2), pp.183~195 (1998)[DOI]
- Monaghan, F., "What difference does it make? Children views of the difference between some quadrilaterals", Educational Studies in Mathematics, 42(2), pp.179~196 (2000)[DOI]
- Na, H-L., "Analysis on the conceptualizing process of the fourth grade elementary student in relation to the quadrilaterals in the dynamic geometry environment", Master, pp.2013
- Principles and standards for school mathematics, "National Council of Teachers of Mathematics.", National Council of Teachers of Mathematics, ~ (2000)
- 노정원, "기호적 중재를 통한 사각형의 성질 학습 사례 연구 - 성질 사이의 관계에 관한 추론을 중심으로", 학교수학, 21(1), pp.197~214 (2019), 대한수학교육학회[DOI]
- 노영아, "도형 영역의 오류 유형과 원인 분석에 관한 연구 -초등학교 4학년을 중심으로-", 한국초등수학교육학회지, 11(2), pp.199~216 (2007), 한국초등수학교육학회
- Okazaki, M., "Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland", Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 4, pp.41~48 (2007)
- Piaget, J., "L'Image mentale chezl' enfant. E tudes ur le Ddveloppemendt es Representationlsm agees" (1966), Presses Universitaires de France
- Piaget, J., "child's conception of geometry" (1960), Basic Books
- "Rectangle and rhombi: how well do pre-service teachers know them? Issues in the undergraduate mathematics preparation of school teachers, 1, content knowledge" (2007)[URL]
- Robert, A., "The teaching and learning of mathematics at university level" (2001), Kluwer Academic Publishers
- Rosch, E., "Family resemblances : studies in the internal structures of categories", Cognitive Psychology, 7, pp.573~605 (1975)[DOI]
- Ryu, H. J., "Mathematics and curriculum and textbook analysis 2009 on triangle and square", Journal of Elementary Education Research, 25(1), pp.71~91 (2009)
- Shin. Y. J., "An analysis of concept images of quadrilaterals of second-year elementary students", Master, pp.2017
- Sierpinska, A., "Humanities students and epistemological obstacles related to limits", Educational Studies In Mathematics, 18, pp.371~397 (1987)[DOI]
- Sierpinska, A., "Some remarks on understanding in mathematics", For the Learning of Mathematics, 10, pp.24~36 (1990)
- Tall, D., "Concept image and concept definition in mathematics with particular reference to limit and continuity", Educational Studies in Mathematics, 12, pp.151~169 (1981)[DOI]
- Van Hiele, P. M., "English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele", pp.243~242 (1985), Brooklyn College, School of Education
- Vinner, S., "Concept definition, concept image and the notion of function", International Journal of Mathematical Education in Science and Technology, 14, pp.293~305 (1983)[DOI]
- Vinner, S., "Advanced mathematical thinking", pp.65~81 (1991), Kluwer Academic Publishers
- Vygotsky, L. S., "The collected works of L. S. Vygotsky", pp.39~285 (1987), Plenum Press