교구를 활용한 탐구기반 외심 학습
Inquiry-Based Learning of Circumcenter Using Teaching Tools
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The purpose of this study is to analyze middle school students’ learning characteristics they showed on the inquiry-based learning process of circumcenter using various teaching tools, and then to identify the effects of using teaching tools in the middle school students’ learning process of circumcenter. For this purpose, we developed teaching materials for inquiry-based learning of circumcenter using textbook, origami, ruler and compass, GeoGebra and sand experiment. Then we applied them on the learning process of circumcenter for five groups of middle school students. From the analyzing of audio/video materials and documents which are collected from the process of participants’ inquiry-based learning of circumcenter, we identified the following results. First, inquiry-based learning of circumcenter using various teaching tools promoted mathematical discourses among participants of this study. For example, they conjectured mathematical properties or justified their opinions after manipulated teaching tools in the process of learning circumcenter. Second, inquiry-based learning of circumcenter using various teaching tools promoted participants’ divergent thinking. They tried many inquiry methods to find new mathematical properties relate to circumcenter. For example, they tried many inquiry methods to know whether there is unique circle containing four vertices of given quadrangles. Third, we found several didactic implications relate to inquiry-based learning of circumcenter using various teaching tools which are due to characteristics of teaching tools themselves. Participants showed several misconceptions about mathematical properties during they participated inquiry-based activity for learning of circumcenter using various teaching tools. We identified their misconceptions were not due to any other variables containing their learning characteristics but to characteristics of teaching tools.
Abstract
The purpose of this study is to analyze middle school students’ learning characteristics they showed on the inquiry-based learning process of circumcenter using various teaching tools, and then to identify the effects of using teaching tools in the middle school students’ learning process of circumcenter. For this purpose, we developed teaching materials for inquiry-based learning of circumcenter using textbook, origami, ruler and compass, GeoGebra and sand experiment. Then we applied them on the learning process of circumcenter for five groups of middle school students. From the analyzing of audio/video materials and documents which are collected from the process of participants’ inquiry-based learning of circumcenter, we identified the following results. First, inquiry-based learning of circumcenter using various teaching tools promoted mathematical discourses among participants of this study. For example, they conjectured mathematical properties or justified their opinions after manipulated teaching tools in the process of learning circumcenter. Second, inquiry-based learning of circumcenter using various teaching tools promoted participants’ divergent thinking. They tried many inquiry methods to find new mathematical properties relate to circumcenter. For example, they tried many inquiry methods to know whether there is unique circle containing four vertices of given quadrangles. Third, we found several didactic implications relate to inquiry-based learning of circumcenter using various teaching tools which are due to characteristics of teaching tools themselves. Participants showed several misconceptions about mathematical properties during they participated inquiry-based activity for learning of circumcenter using various teaching tools. We identified their misconceptions were not due to any other variables containing their learning characteristics but to characteristics of teaching tools.
참고문헌 (73)
- 강윤수, "삼각형의 내 · 외심 지도방법 연구", 한국학교수학회논문집, 12(3), pp.171~188 (2009), 한국학교수학회
- 고상숙, "교구를 활용한 중학교 공간능력 향상을 위한 수업에서 학습의 효과", 수학교육, 48(1), pp.1~20 (2009), 한국수학교육학회
- 권은정, "종이접기를 통한 수학학습 지도에 관한 사례연구 : 중학교 삼각형의 성질을 중심으로", 석사, 수학교육, pp.2006
- 김부윤, "수학이 있는 종이접기" (2012), 수학사랑
- 신현용, "학교수학에서의 정당화 지도의 필요성 및 가능성에 관한 연구", 대한수학회논문집, 19(4), pp.585~599 (2004), 대한수학회
- 원보영, "교과서에서의 컴퓨터 활용에 대한 개선방안 연구 : 중학교 2학년 교과서 기하단원 중심으로", 석사, 수학교육, pp.2011
- 이강섭, "교구를 활용한 활동에서 창의성 평가를 위한 학생들의 반응 유형 분석", 수학교육, 46(2), pp.227~237 (2007), 한국수학교육학회
- 이민혜, "수학교구를 활용한 삼각형의 내외심 지도방안 연구", 석사, pp.2014
- 조완영, "7차 수학과 교육과정 작도 영역의 교과서와 수업사례 분석", 학교수학, 4(4), pp.5~613 (2002), 대한수학교육학회
- 한인기, "삼각형의 접기 활동과 논증의 연계 가능성에 관한 연구", 수학교육, 41(1), pp.6~90 (2002), 한국수학교육학회
- Almasi, J., "The nature of fourth graders’sociocognitive conflicts in peer led and teach led discussions of literature", Reading Research Quarterly, 30, pp.314~351 (1995)
- Arzarello, F., "A cognitive analysis of dragging practices in Cabri environments", ZDM – The International Journal on Mathematics Education, 34(3), pp.66~72 (2002)
- Ball, D., "International handbook of teachers and teaching", pp.769~818 (1997), Kluwer
- Barrow, L. H., "A brief history of inquiry : From Dewey to standards", Journal of Science Teacher Education, 17, pp.265~278 (2006)
- Brenner, M. E., "Learning by understanding : The role of multiple representations inlearning algebra", American Educational Research Journal, 34(4), pp.663~689 (1997)
- Buteau, C., "Integrating computer algebra systems in post-secondary mathematics education : Preliminary results of a literature review", International Journal for Technology in Mathematics Education, 17(2), pp.57~68 (2010)
- Cazden, C. B., "Classroom discourse: the language of teaching and learning" (1988), Heinemann
- Charalambous, C. Y., "Mathematical knowledge for teaching and task unfolding : An exploratory study", Elementary School Journal, 110(3), pp.247~278 (2010)
- Charalambous, C. Y., "Preservice teachers’mathematical knowledge for teaching and their performance in selected teaching practices:Exploring a complex relationship", pp.2008
- Christou, C., "Proofs through exploration in dynamic geometry environments", International Journalof Science and Mathematics Education, 2(3), pp.339~352 (2004)
- Cole, M., "Cultural psychology: a once and future discipline" (1996), Harvard
- Cortazzi, M., "Narrative analysis" (1993), Falmer Press
- Davis, B., "Listening for differences : An evolving conception of mathematics teaching", Journal for Research in Mathematics Education, 28(3), pp.355~376 (1997)
- Dewey, J., "Experience and education" (1938), Collier Macmillan
- Drijvers, P., "The teacher and the tool : Instrumental orchestrations in the technology-rich mathematics classroom", Educational Studies in Mathematics, 75(2), pp.213~234 (2010)
- Duranti, A., "Rethinking context: language as an interactive phenomenon" (1992), Cambridge University Press
- Edwards, D., "Common knowledge:the development of understanding in the classroom" (1987), Routledge
- Erbas, A. K., "The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons", Computers & Education, 57(4), pp.2462~2475 (2011)
- Fennema, E., "A longitudinal study of learning to use children’s thinking in mathematics instruction", Journal for Research in Mathematics Education, 27(4), pp.403~434 (1996)
- Ferrara, F., "Handbook of research on the psychology of mathematics education: past, present and future", pp.237~273 (2006), Sense
- Freudenthal, H., "Revisiting mathematics education: China lectures" (1991), Kluwer
- Gee, J. P., "Units in the production of narrative discourse", Discourse Processes, 9, pp.391~422 (1986)
- Gee, J. P., "Discourse analysis, learning, and social practice : a methodological study", Review of Research in Education, 23, pp.119~169 (1998)
- Glazer, N., "Challenges with graph interpretation : A review of the literature", Studies in Science Education, 47(2), pp.183~210 (2011)
- Goos, M., "Perspectives on technology mediated learning in secondary school mathematics classrooms", Journal of Mathematical Behavior, 22(1), pp.73~89 (2003)
- Hall, J., "Teaching algebra and geometry with GeoGebra: Preparing pre-service teachers for middle grades", secondary mathematics classrooms, 2013, pp.30(1–2), 12~29
- Healy, L., "Software tools for geometrical problem solving : Potentials and pitfalls", International Journal of Computers for Mathematical Learning, 6, pp.235~256 (2001)
- Hill, H., "Mathematical knowledge for teaching and the mathematical quality of instruction : An exploratory study", Cognition and Instruction, 26, pp.430~511 (2008)
- Hoffkamp, A., "The use of interactive visualizations to foster the understanding of concepts of calculus : Design principles and empirical results", ZDM Mathematics Education, 43(3), pp.359~372 (2011)
- Hohenwarter, M., "BSRLM Geometry Working Group : Ways of linking geometry and algebra, the case of GeoGebra", Proceedings of the British Society for Research into Learning Mathematics, 27(3), pp.126~131 (2007)
- 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, pp.164~192 (2007)
- Holt, J., "How children fail" (1982), Dell
- Jaworski, B., "Theory and practice in mathematics teaching development : Critical inquiry as a mode of learning in teaching", Journal of Mathematics Teacher Education, 9, pp.187~211 (2006)
- Johnson, E., "Teachers’ mathematical activity in inquiry-oriented instruction", Journal of Mathematical Behavior, 32, pp.761~775 (2013)
- Johnson, E. M. S., "Teacher listening : The role of knowledge of content and students", Journal of Mathematical Behavior, 31, pp.117~129 (2012)
- Jones, K., "Research on the use of dynamic geometry software : Implications for the classroom", MicroMath, 18(3), pp.44~45 (2002)
- King, A., "Cognitive perspectives on peer learning", pp.87~115 (1999), Erlbaum
- King, A., "Facilitating elaborative learning through guided student-generated questions", Educational Psychologist, 27, pp.111~126 (1992)
- Larsen, S., "Proofs and refutations in the undergraduate mathematics classroom", Educational Studies in Mathematics, 67(3), pp.205~216 (2007)
- Manouchehri, A., "Increasing access to shared knowledge", Paper presented at the 84th Annual Meeting of the American Educational Research Association (2003)
- Mevarech, Z. R., "Interaction between knowledge and contexts on understanding abstract mathematical concepts", Journal of Experimental Child Psychology, 65(1), pp.68~95 (1997)
- Moss, J., "Knowledge building in mathematics : Supporting collaborative learning in pattern problems", International Journal of Computer-Supported Collaborative Learning, 1(4), pp.441~465 (2006)
- National Council of Teachers of Mathematics, "Principles and standards for school mathematics" (2000), National Council of Teachers of Mathematics
- National Council of Teachers of Mathematics, "Professional standards for teaching mathematics" (1992), National Council of Teachers of Mathematics
- National Council of Teachers of Mathematics, "Curriculum and evaluation standards for school mathematics" (1989), National Council of Teachers of Mathematics
- National Research Council, "Standards for teaching and learning mathematics and sciences" (2000), National Research Council
- National Research Council, "Inquiry and the national science education standards: A guide for teaching and learning" (2000), National Academy Press
- Northedge, A., "Issues in Access to Higher Education", pp.145~151 (1994), University of Southern Maine
- Nussbaum, M., "Technology as small group face-to-face collaborative scaffolding", Computers & Education, 52(1), pp.147~153 (2009)
- Pea, R. D., "Distributed cognitions: psychological and educational considerations", pp.47~87 (1993), Cambridge University Press
- Phelps, E., "Problem solving with equals : peer collaboration as a context for learning mathematics and spatial concepts", Journal of Educational Psychology, 81, pp.639~646 (1989)
- Ploetzner, R., "Students’ difficulties in learning from dynamic visualizations and how they maybe overcome", Computers in Human Behavior, 25, pp.56~65 (2009)
- Rakes, C. R., "Methods of instructional improvement in algebra : A systematic review and meta-analysis", Review of Educational Research, 80(3), pp.372~400 (2010)
- Rasmussen, C., "Advancing mathematical activity : A practice-oriented view of advanced mathematical thinking", Mathematical Thinking and Learning, 7(1), pp.51~73 (2005)
- Reynolds, R. E., "Views of knowledge acquisition and representation : a continuum from experience centered to mind centered", Educational Psychologist, 21, pp.93~104 (1996)
- Saxe, G. B., "Culture and cognitive development:studies in mathematical understanding" (1991), Lawrence Erlbaum
- Selden, A., "Making the connection: Research and teaching in undergraduate mathematics education", pp.95~110 (2008), MAA
- Sinclair, M. P., "Peer interactions in a computer lab : Reflections on results of a case study involving web-based dynamic geometry sketches", The Journal of Mathematical Behavior, 24(1), pp.89~107 (2005)
- Stein, M., "Orchestrating productive mathematical discussions : Five practices for helping teachers move beyond show and tell", Mathematical Thinking and Learning, 10, pp.313~340 (2008)
- Weber, K., "Expanding participation in problem solving in a diverse middle school mathematics classroom", Mathematics Education Research Journal, 22(1), pp.91~118 (2010)
- Weber, K., "Semantic and syntactic proof productions", Educational Studies in Mathematics, 56, pp.209~234 (2004)
- Wood, T., "Deepening the analysis : Longitudinal assessment of a problem-centered mathematics program", Journal for Research in Mathematics Education, 28(2), pp.163~186 (1997)
- Yackel, E., "Didactising : Continuing the work of Leen Streefland", Educational Studies in Mathematics, 54, pp.101~126 (2003)
