[논문]초등학생들의 비구조화된 문제 해결 과정에서 나타나는 공간 추론 능력과 문제 해결 능력

최주연; 김민경

doi:10.7468/mathedu.2021.60.1.133

초등학생들의 비구조화된 문제 해결 과정에서 나타나는 공간 추론 능력과 문제 해결 능력
An analysis of spatial reasoning ability and problem solving ability of elementary school students while solving ill-structured problems 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.2, 2021년, pp.133 - 157

최주연 (이화여자대학교 대학원) , 김민경 (이화여자대학교)

초록
AI-Helper

본 연구에서는 학생들의 생활과 밀접한 공간을 기반으로 한 비구조화된 문제를 개발하고 수업에 적용하였다. 이 과정에서 6학년 학생들의 공간 추론 능력으로는 외적 추론에 비해 내적 추론에서 어려움을 표했으며, 공간 추론이 수와 연산, 측정 등의 영역과 연계되어 활용될 때 그 수준이 더 높게 나타났다. 문제 해결 능력에서는 반성 요소가 미흡하게 나타났으며 초등 현장에서 온라인 환경에서의 협력과 수학적 모델링 학습이 적용 가능하다는 결과를 얻었다. 이를 통해 수학 교육 현장에 공간 학습과 실생활 문제 해결에 관한 의미 있는 시사점을 도출할 것으로 기대된다.

Abstract ▼ AI-Helper

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

주제어

표/그림 (12)

표 [Table 1] Types of spatial reasoning by Ramey et al. (2020)
표 [Table 2] Lesson plan of ill-structured problem
표 [Table 3] Lesson plan of ill-structured problem
표 [Table 4] The score of spatial reasoning ability
그림 [Fig. 1] PPT presentation of Group 1 on task
그림 [Fig. 2] Worksheets of Group 1 and 4 on task
그림 [Fig. 3] Worksheets of Group 3 and 4 on task
그림 [Fig. 4] Worksheet of group 3 on task
표 [Table 5] The score of problem-solving ability
그림 [Fig. 5] Places where students decided to set cameras.
그림 [Fig. 6] Worksheet and photos of group 2 on task
그림 [Fig. 7] Worksheets of group 1 and 4 on task

참고문헌 (32)

Battista, M. T., & Clements, D. H. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York, NY: National Council of Teachers of Mathematics, Macmillan Publishing Co.
Burte, H., Gardony, A. L., Hutton, A., & Taylor, H. A. (2017). Think 3d!: Improving mathematics learning through embodied spatial training. Cognitive Research, 2(13), 1-18.
Chang, H. S., Hong, J. A., & Lee, B. (2020). An analysis on middle school students' space geometrical thinking based on cylinder. The Mathematical Education, 59(2), 113-130.
Cho, H. J. (2008). An analysis of face-to-face and web-based collaborative problem solving process on ill-structured problem. The Korean Journal of Educational Methodology Studies, 20(1). 173-195.
Cho, M. K. (2016). A study on ill-structured mathematical problem-solving and peer interactions according to teacher's scaffolding (Doctoral dissertation). Ewha Womans University. Seoul.
Choi, J. (2021). A study on spatial reasoning ability and problem solving ability of elementary school student while solving ill-structured problems - Based on the unit of 6th grade 'Three dimensional space'- (Master's thesis). Ewha Womans University. Seoul.
Chong, Y. (2004). On the teaching of building with blocks in primary school mathematics. The Journal of Curriculum & Evaluation, 7(2), 75-101.

상세보기
Clements, D. H. (1999). Geometric and spatial thinking in young children. In V. C. Juanita (Ed.), Mathematics in the early years (pp. 66-79). Reston, VA: National Council of Teachers of Mathematics.
de Moor, E. (1990). Geometry instruction in the Netherlands (ages 4-14): The realistic approach. In L. Streefland (Ed.), Realistic mathematics education in primary school (pp. 119-138). Culembog: Technipress.
Do, J., & Paik, S. (2019). Analysis of characteristics from meta-affect viewpoint on problem-solving activities of mathematically gifted children. The Mathematical Education, 58(4), 519-530.
Gagne, E. D. (1985). The cognitive psychology of school learning. Boston, MA: Little, Brown Company.
Ge, X., & Land, S. M. (2004). A conceptual framework for scaffolding ill-structured problem-solving process using question prompts and peer interactions. Educational Technology Research and Development, 52(2), 5-22. The Pennsylvania State University.
Hong, J. Y. (2013). A study on the mathematical abstraction and proportional reasoning of elementary school students in the process of solving an ill-structured problem (Doctoral dissertation). Ewha Womans University. Seoul.
Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65-94.
Kim, A. R. (2019). The effects of the discussion using errors on mathematical problem solving abilities and mathematical dispositions (Master's thesis). Seoul National University of Education. Seoul.
Kim, D., & Kim, M. K. (2016). A study on creativity.integrated thinking and problem solving of elementary school students in ill-structured mathematics problems. School Mathematics, 18(3), 541-569.
Kim, M. K., Kim, H. W., Min, S. H., Park, E. J., Lee. J., Cho, M. K., ..., Hong, J. Y. (2014). Elementary mathematics problem solving enhancing thinking ability - ill-structured problem and problem soving-. Seoul: Kyungmoonsa.
Kim, M. K., Heo, J. Y., & Park, E. J. (2014). Design, application, and its educational implication of ill-structured problem solving in elementary mathematics education. Journal of Elementary Mathematics Education in Korea, 18(2), 189-209.
Kim, Y. K., & Pang, J. S. (2007). An investigation on 6th grade students' spatial sense and spatial reasoning. School Mathematics, 9(3), 353-373.
Koo, M. J. (2007). An analysis of the spatial reasoning ability of middle and senior grade students in elementary school (Master's thesis). Korea National University of Education. Chung-buk.
Lee, H. (2014). Comparative analysis of elementary mathematics textbooks of Korea, USA, Japan and Finland on the mathematical connections (Master's thesis). Seoul National University of Education. Seoul.
Lee, H. J. (2016). The effects of the collaborative problem solving on scholastic achievement and character strengths in sixth grade elementary students in mathematics (Master's thesis). Gyeongin National University of Education. Gyeong-gi.
Ministry of Education (2018a). Korean national elementary mathematics 6-2. Seoul: Chunjae Education.
Ministry of Education (2018b). Korean national elementary mathematics 6-2 teachers' guide. Seoul: Chunjae Education.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Oh, Y. Y., & Park, J. K. (2019). Exploring the task types of mathematical modeling applied to elementary school. The Journal of Korea Elementary Education, 30(1), 87-99.

상세보기
Park, K., Lee, H., Park, S., Kwon, J. R., Yoon, S., Kang, H., ..., Jeon, I. (2015). Study on development of mathematics curriculum according to 2015 revised curriculum II. Korea Foundation for the Advancement of Science and Creativity BD15120005.
Polya, G. (1957). How to solve it?. Princeton, NJ: Princeton University Press.
Ramey, K. E., Stevens, R., & Uttal, D. H. (2020). In-FUSE-ing STEAM learning with spatial reasoning: Distributed spatial sensemaking in school-based making activities. Journal of Educational Psychology, 112(3), 466-493.

상세보기
Shin, K. M., & Shin, H. K. (2010). The effect of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. Journal of Elementary Mathematics Education in Korea, 14(2), 401-420.
Spiro, R. J., Vispoel, W. P., Schmitz, J. G., Ala, S., & Boerger, A. E. (1987). Knowledge acquisition for application: Cognitive flexibility and transfer in complex content domains (Tech. Rep. No. 409). Champaign, IL: University of Illinois, Center for the Study of Reading.
Sung, C., & Park, S. (2012). Analysis on analogical transfer between mathematical isomorphic problems with different level of structuredness. Education of Primary School Mathematics, 15(2), 59-75.

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