[논문]전개도 과제에서 지오픽스와 Cabri 3D를 활용한 학습의 효과 비교

서화진; 이광호

doi:10.7468/mathedu.2021.60.1.159

[국내논문] 전개도 과제에서 지오픽스와 Cabri 3D를 활용한 학습의 효과 비교
Comparative study of the effects in using geofix and cabri 3D on folding nets' activities 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.2, 2021년, pp.159 - 172

서화진 (전주송원초등학교) , 이광호 (한국교원대학교)

초록
AI-Helper

본 연구의 목적은 조작 교구와 탐구형 기하 소프트웨어를 활용한 전개도 학습이 초등학교 5학년 학생들의 공간 감각에 주는 영향을 비교·분석하는 것이다. 이를 위해 한 실험집단은 조작 교구인 지오픽스를 한 실험집단은 탐구형 기하 소프트웨어인 Cabri 3D를 활용하여 전개도를 학습하였다. 비교 집단은 교구나 소프트웨어의 사용 없이 학습지만으로 학습을 진행하였다. 사전과 사후에 공간 감각 검사를 실시하여 그 수준을 파악하였고, 시선 추적 검사를 실시하여 전개도 과제를 해결하는 학생들의 전략을 분석하였다. 그 결과 조작 교구인 지오픽스를 활용한 전개도 학습이 공간 감각에 가장 효과적이었으며, Cabri 3D 또한 전개도를 학습하기 위한 좋은 도구가 될 수 있음을 확인할 수 있었다. 또한, 전개도 학습 이후 학생들의 해결 전략은 가장 효율적인 전략이었던 분석적 전략이 증가하였으며, 이러한 과정에서 시선 추적은 학생들의 전략을 탐색하는 매우 유용한 도구가 됨을 알 수 있었다.

Abstract ▼ AI-Helper

The purpose of this study is to compare and analyze the effects of physical manipulative and exploratory geometry software on the spatial sense for 5th grade elementary school students in learning nets. For this purpose, ton experimental group used Geofix, an operational learning tool, and the experimental group used Cabri 3D, an exploratory geometry software to learn the nets of solids. The comparison group was learned by worksheet only without any manipulative or software. Spatial sense tests were conducted before and after to determine the level, and eye tracking were used to analyze the strategies of students in solving nets problems. As a result, it was confirmed that the using Geofix group was the most effective for the spatial sense, and Cabri 3D could also be a good tool for learning the nets of solids. In addition, after learning the nets of solids, the analytical strategy, which was the most effective strategy for students' solving strategies, increased. In the process of solving spatial tasks such as the spatial sense tasks, eye tracking technology become a very useful tool for exploring students' strategies, so it is expected that objective and useful data will be collected through more active use in the future.

Keyword

표/그림 (15)

그림 [Fig. 1] An example of Tartre's spatial factor classification and its tasks (Tartre, 1990b, p.30)
그림 [Fig. 2] The framework for the spatial test
표 [Table 1] The schedule of the course activities
표 [Table 2] Contents of spatial sense test
표 [Table 3] Sample questions in eye tracking tasks
표 [Table 4] Strategy division of the development tasks
표 [Table 5] Descriptive statistics of the three groups in pre and post tests
표 [Table 6] Descriptive statistics of the data from eye tracking tests
표 [Table 7] The results of Bonferroni between three groups
표 [Table 8] An example of holistic strategy on a gaze plot(students G20(left) and P04(right))
표 [Table 9] An example of analytic strategy on a gaze plot(students C05(left) and P03(right))
표 [Table 10] Gaze plot of a participant G20
그림 [Fig. 3] Accuracy and response time for the strategy in eye tracking tests
표 [Table 11] Accuracy and response time for the strategy in eye tracking tests
표 [Table 12] Percentages used the strategy in pre-test and post-test (%)

참고문헌 (48)

Accascina, G., & Rogora, E. (2006). Using cabri 3D diagrams for teaching geometry. International Journal for Technology in Mathematics Education, 13(1), 11-22.
Alias, M., Black, T. R. & Gray, D. E. (2002). Effect of instructions on spatial visualisation ability in civil engineering students. International Education Journal, 3(1), 1-12.
Arici, S., & Aslan-Tutak, F. (2015). The effect of origami-based instruction on spatial visualization, geometry achievement, and geometric reasoning. International Journal of Science and Mathematics, 13, 179-200.
Baki, A., Kosa, T., & Guven, B. (2011). A Comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualisation skills of pre-service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310.

상세보기
Battista, M. T., Wheatley, G. H., & Talsma, G. (1982). The importance of spatial visualization and cognitive development for geometry learning of preservice elementary teachers. Journal for Research in Mathematics Education, 13, 332-340.
Burin, D. I., Delgado, A. R., & Prieto, G. (2000). Solution strategies and gender differences in sptatial visualization tasks. Psicologica, 21, 275-286.
Chaim, D. B., Lappan, G., & Houang, R. T. (1988). The Effect of Instruction on Spatial Visualization Skills of Middle School Boys and Girls. American Educational Research Journal, 25(1), 51-71.

상세보기
Cho, Y. S. & Chong, Y. O. (2012). Survey on the Spatial Sense Ability of Elementary School Students. Journal of Elementary Mathematics Education in Korea, 16(3), 359-388.
Chong, Y. O. (2017). Teaching Spatial Sense of Solid Figures in Elementary School Mathematics. Journal of Elementary Mathematics Education in Korea, 21(1), 161-194.
Chung, Y. W, & Kim, B. Y. (2014). Didactical Contemplation on the Development Figure. School Mathematics, 16(2), 285-301.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: Macmillan.
Cohen, N. (2003). Curved solids nets. In N. Pateman, B. J. Dougherty, & J. Zillox (Eds.), Proceedings of the 27th PME International Conference, 2, 229-236.
Cochran, K. F., & Wheatley, G. H. (2002). The Journal of General Psychology, 116(1), 43-55.
Del Grande, J. J. (1987). Spatial perception and primary geometry. In M. M. Lindquist & A. P. Shulte (Eds ), Learning and teaching geometry K-12 (pp. 126-135). Reston, VA: National Council of Teachers of Mathematics.
Ekstrom, R. B., French, J. W., Harman, H. H., & Dermen, D. (1976). Manual for kit of factor-referenced cognitive test. Princeton, NJ: Educational Testing Service.
Fennema, E., & Romberg, T. A. (Eds.) (1999). Mathematics Classrooms that Promote Understanding. Mahwah, NJ: Erlbaum., 이광호, 이현숙, 이경미, 윤혜영, 정미혜, 하수현 (역) (2011). 이해를 촉진하는 수학교실. 서울: 경문사.
Gilligan, K. A., Flouri, E. & Farran, E. K.(2017). The contribution of spatial ability to mathematics achievement in middle childhood. Journal of Experimental Child Psychology, 163, 107-125.

상세보기
Gluck, J., & Fitting, S. (2003). Spatial strategy selection: Interesting incremental information. International Journal of Testing, 3(3), 293-308.

상세보기
Guven, B., & Kosa, T. (2008). The effect of dynamic geometry software on student mathematics' spatial visualization skills. The Turkish Online Journal of Educational Technology, 7(4), Article 11.
Hong, G. J. & Yi, H. S. (2015). A Study on Sketch Maps and Planar Figures in Elementary School-In Consideration of Successive Korean Curriculums and Foreign Textbooks. School Mathematics, 17(4), 531-553.
Jeong, H. R., Lee, S. J. & Cho, H. H. (2016). Educational Application of Turtle Representation System for Linking Cube Mathematics Class. School Mathematics. 18(2). 323-348.
Karakus, F., & Peker, M. (2015). The effects of dynamic geometry software and physical manipulatives on pre-service primary teachers' van hilel elvels and spatial abilities. Turkish Journal of Computer and Mathematics Education, 6(3), 338-365.
Kell, H. J., & Lubinski, D. (2013). Spatial ability: A neglected talent in educational and occupational settings. Roeper Review, 35(4), 219-230.

상세보기
Kim, Y. K. & Pang, J. S. (2007). An Investigation on 6th Grade Students' Spatial Sense and Spatial Reasoning. School Mathematics, 9(3), 353-373.
Kosa, T. (2016). The effect of using dynamic mathematics software: cross section and visualization. International Journal of Technology in Mathematics Education, 23(4), 121-128.
Kozhevnikov, M., & Hegarty, M. (2001). A dissociation between object manipulation spatial ability and spatial orientation ability. Memory & Cognition, 29(5), 745-756.

상세보기
Kurtulus, A. (2013). The effects of web-based interactive virtual tours on the development of prospective mathematics teachers' spatial skills. Computers & Education, 63, 141-150.

상세보기
Kurtulus, A., & Uygan, C. (2010). The effects of Google Sketchup based geometry activities and projects on spatial visualization ability of student mathematics teachers. World Conference on Learning, Teaching and Administration (pp. 384-389). Cairo, Egypt: Elsevier Ltd.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of gender differences in spatial abilities: a meta-analysis. Child Development, 56(6), 1479-1498.
Lohman, D. F. (1979). Spatial ability: A review and re-analysis of the correlational literature (Technical Report No. 8). Stanford CA: Stanford University, School of Education, Aptitude Research Project.
Mcgee, M. G. (1979). Human spatial abilities: sources of sex differences. New York: Praeger.
Ministry of Education(2015a). Mathematics curriculum. Proclamation of the Ministry of Education #2015-74 [Annex 8].
Ministry of Education(2015b). Mathematics 5-1. Seoul: Chunjae)
Ministry of Education(2015c). Mathematics 6-1. Seoul: Chunjae.
National Council of Teachers of Mathematics. (2000). Principles and stadards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. 류희찬, 조완영, 이경화, 나귀수, 김남균, 방정숙 (역) (2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
Pavlovicova, G., & Svecova, V. (2015). The development of spatial skills through discovering in the geometrical education at primary school. Social and Behavioral Sciences, 186, 990-997.
Risma, D. A., Putri, R. I., & Hartono, Y. (2013). On developing students' spatial visualisation ability. International Educational Studies, 6(9), 1-12.
Risto, L., Marjatta, K., Merja, S., Ann, M., S., & Tuula, U. L. (2012a). LASKUTAITO in English 4A. WSOY pro., Ltd. 양재욱, 도영(역) (2012). 핀란드 초등수학교과서 Laskutaito 4-1 Korean edition. 서울: 솔빛길출판사.
Risto, L., Marjatta, K., Merja, S., Ann, M., S., & Tuula, U. L. (2012b). LASKUTAITO in English 6A. WSOY pro., Ltd. 오수현, 도영(역) (2012). 핀란드 초등수학교과서 Laskutaito 6-1 Korean edition. 서울: 솔빛길출판사.
Seo, H. J. & Lee, K. H. (2018). An International Comparison of Nets of Solids Presented in Elementary Mathematics Textbooks. Journal of Elementary Mathematics Education in Korea, 22(2), 199-220.
Shepard, R. N., & Metzler, J. (1971). Mental rotation of three dimensional objects. Science, 171, 701-703.

상세보기
Sukumar, K., Zhou, Z., & Mohler, J. L. (2016). Strategy variability in solving spatial visualization tasks: Rethinking the purdue spatial visualization test - developments. Paper presented at the annual meeting of the American Society for Engineering Education.
Tartre, L. A. (1990a). Spatial orientation skill and mathematics problem solving. Journal for Research in Mathematics Education, 21(3), 216-229.
Tartre, L. A. (1990b). Spatial skills, gender, and mathematics. In Fennema, E. & Leder, G. (Eds.), Mathematics and gender: Influences on teachers and students (pp.27-59). New York: Teachers College Press, Columbia University.
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychological Bulletin, 139, 352-402.

상세보기
Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835.

상세보기
Wright V., Smith K. (2017). Children's schemes for anticipating the validity of nets for solids. Mathematics Education Research Journal, 29(3), 369-394.

상세보기
Yurt, E., & Sunbul, A. M. (2012). Effect of modeling-based activities developed using virtual environments and concrete objects on spatial thinking ad mental rotation skills. Educational Science: Theory & Practice, 12, 1987-1992.

저자의 다른 논문 :

표제어: PCR

동의어: Packet Collision Rate

용어 설명 출처 목록 (6)

용어 설명: PCR은 세균 특이성이 있는 primer를 이용하여 적은 수의 세균이 있을지라도 쉽게 검출할 수 있는 유용한 방법이며, 이를 이용하여 구강 내 치면세균막이나 타액에서 직접 세균을 검출할 수 있게 되었다[8].

내보내기 구분	파일저장 인쇄 메일전송
구성항목	기본정보 상세정보 관리번호, 논문명, 저널/프로시딩명, 저자 , 발행년, 권, 호, 시작페이지, 끝페이지, 발행기관 관리번호, 논문명, 대등논문명, 저자 , 저널/프로시딩명, 발행기관, 발행년, 발행언어, 권, 호, 시작페이지, 끝페이지, ISBN, ISSN, 주제분야, 키워드, 초록(한글), 초록(영문), 저자(소속기관)
저장형식	Text(ASCII format) Excel format RefWorks Direct Export RIS format (for Reference Manager, ProCite, EndNote), Scholar's Aids, Mendeley
메일정보	받는사람 (필수) @ 보내는사람 (선택) @ 제목 내용 KISTI 검색결과 이메일 서비스
안내	총 건의 자료가 검색되었습니다. 다운받으실 자료의 인덱스를 입력하세요. (1-10,000) 검색결과의 순서대로 최대 10,000건 까지 다운로드가 가능합니다. 데이타가 많을 경우 속도가 느려질 수 있습니다.(최대 2~3분 소요) 다운로드 파일은 UTF-8 형태로 저장됩니다. 파일의 내용이 제대로 보이지 않을실 때는 웹브라우저 상단의 보기 -> 인코딩 -> 자동선택 여부를 확인하십시오. ~ Text(ASCII format) Excel format

연합인증