초등 수학교과서의 문제해결 역량 및 과제 유형 분석: 수와 연산 영역의 도전/생각 수학과 탐구 수학을 중심으로
Analysis of problem solving competency and types of tasks in elementary mathematics textbooks: Challenging/Thinking and inquiry mathematics in the domain of number and operation
0
조회
0
다운로드
9
인용
0
참고문헌
키워드
초록
본 연구는 초등학교 교과서가 반영하고 있는 문제해결 양상을 수와 연산 단원들을 중심으로 살펴보았다. 문제해결의하위요소를 중심으로 수학적 활동에 대해 코딩을 실시한 결과 실행이 강조되는 가운데 학년별로 강조되는 하위 요소들이 다르게 나타났고, 잠재집단분석을 통해서 과제의 유형을 분류해 보았다. 향후 교과서 개발과 교사지원에 대한 시사점을 제공하고자 한다.
Abstract
Elementary mathematics textbooks present contents for enhancing problem solving competency. Still, teachers find teaching problem solving to be challenging. To understand the supports textbooks are suggesting, this study examined tasks from the challenging/thinking and inquiry mathematics. We analyzed 288 mathematical activities based on an analytic framework from the 2015 revised mathematics curriculum. Then, we employed latent class analysis to classify 83 mathematical tasks as a new approach to categorize tasks. As a result, execution of the problem solving process was emphasized across grade levels but understanding of problems was varied by grade levels. In addition, higher grade levels had more opportunities to be engaged in collaborative problem solving and problem posing. We identified three task profiles: ‘execution focus’, ‘collaborative-solution focus’, ‘multifaceted-solution focus’. In Grade 3, about 80% of tasks were categorized as the execution profile. The multifaceted-solution was about 40% in the thinking/challenging mathematics and the execution profile was about 70% in Inquiry mathematics. The implications for developing mathematics textbooks and designing mathematical tasks are discussed.
참고문헌 (90)
- Anderson, J. R., "Discovering the structure of mathematical problem solving", NeuroImage, 97, pp.163~177 (2014)
- 배혜진, "통계적 문제해결 과정 관점에 따른 초등 수학교과서 통계 지도 방식 분석", 한국초등수학교육학회지, 20(1), pp.55~69 (2016), 한국초등수학교육학회
- 배준환, "반성적 문제 만들기 활동이 초등학생들의 문제해결력 및 수학적 태도에 미치는 영향", 한국초등수학교육학회지, 20(2), pp.311~331 (2016), 한국초등수학교육학회
- Ball, D. L, "Reform by the book : What is—or might be—the role of curriculum materials in teacher learning and instructional reform", Educational Researcher, 25(9), pp.6~14 (1996)
- Bonotto, C., "Artifacts as sources for problem-posing activities", Educational Studies in Mathematics, 83, pp.37~55 (2013)
- Brannick, M. T., "Team performance assessment and measurement: Theory methods and applications", pp.3~16 (1997), Lawrence Erlbaum Associates
- Cai, J., "Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design", International Journal of Educational Research, 102, pp.101404~ (2020)
- Cai, J., "Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing", Journal of Mathematical Behavior, 21(4), pp.401~421 (2002)
- Cai, J., "An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks", International Journal of Science and Mathematics Education, 15(8), pp.1521~1540 (2017)
- Charalambous, C. Y., "A comparative analysis of the addition and subtraction of fractions in textbooks from three countries", Mathematical Thinking and Learning, 12(2), pp.117~151 (2010)
- 최윤석, "초등 수학에서 문제 만들기를 적용한 수업이 수학적 문제 해결력 및 태도에 미치는 효과", 한국초등수학교육학회지, 8(1), pp.23~43 (2004), 한국초등수학교육학회
- 최혜진, "생활 소재를 활용한 수학 문제 만들기 활동", 한국초등수학교육학회지, 15(1), pp.121~139 (2011), 한국초등수학교육학회
- 최인영, "초등학교 수업에서 수학 교과 역량으로서의 문제 해결 능력을함양하기 위한 지도 방안 탐색", 초등수학교육, 21(3), pp.351~374 (2018), 한국수학교육학회[DOI]
- Collopy, R., "Curriculum materials as a professional development tool : How a mathematics textbook affected two teachers' learning", Elementary School Journal, 103(3), pp.287~311 (2003)
- Crespo, S., "Learning to pose mathematical problems : Exploring changes in preservice teachers’practices", Educational Studies in Mathematics, 52(3), pp.243~270 (2003)
- Darling-Hammond, L., "Effective teacher professional development" (2017), Learning Policy Institute
- Davis, E. A., "Educative curriculum materials : Uptake, Impact, and Implications for Research and Design", Educational Researcher, 46(6), pp.293~304 (2017)
- Dillenbourg, P., "Sharing solutions : Persistence and grounding in multi-modal collaborative problem solving", The Journal of the Learning Sciences, 15, pp.121~151 (2006)
- Drake, C., "Using educative curriculum materials to support the development of prospective teachers' knowledge", Educational Researcher, 43(3), pp.154~162 (2014)
- Fan, L., "Representation ofproblem-solving procedures : A comparative look at China, Singapore, and US mathematics textbooks", Educational Studies in Mathematics, 66(1), pp.61~75 (2007)
- Fiore, S. M., "Toward an understanding of macro cognition in teams : Predicting processes in complex collaborative contexts", Human Factors, 52, pp.203~224 (2010)
- Fiore, S., "Team cognition: Understanding the factors that drive process and performance", pp.133~152 (2004), American Psychological Association
- Gracin, D., "Requirements in mathematics textbooks : a five-dimensional analysis of textbook exercises and examples", International Journal of Mathematical Education in Science and Technology, 49(7), pp.1003~1024 (2018)
- Graesser, A. C., "Assessment and teaching 21st century skills", pp.75~91 (2018), Springer
- Griffin, P., "Assessment and teaching 21st century skills", pp.1~15 (2012), Springer
- Hagenaars, J. A., "Applied latent class analysis" (2002), Cambridge University Press
- 한혜숙, "예비수학교사의 수학적 문제제기에 대한 인식 및 문제제기 전략", 학습자중심교과교육연구, 17(22), pp.325~352 (2017), 학습자중심교과교육학회[DOI]
- "Draft: A Framework for teachable collaborative problem solving skills. ATC21S: Australia, Melbern" (2012)[URL]
- Hesse, F., "Assessment and teaching 21st century skills", pp.37~56 (2015), Springer
- Hildebrandt, M., "Profiling the European citizen", pp.17~45 (2008), Springer
- Jäder, J., "Mathematical problem solving in textbooks from twelve countries", International Journal of Mathematical Education in Science and Technology, 51(7), pp.1120~1136 (2020)
- Jay, E. S., "The creativity research handbook", pp.257~293 (1997), Hampton Press
- Jitendra, A. K., "Adherence to mathematics professional standards and instructional design criteria for problem-solving in mathematics", Exceptional Children, 71(3), pp.319~337 (2005)
- 정성건, "수학 문제만들기 활동이 문제해결력과 학습 태도에 미치는 효과", 한국초등수학교육학회지, 14(2), pp.315~335 (2010), 한국초등수학교육학회
- Kilpatrick, J., "Teaching and learning mathematical problem solving: Multiple research perspective", pp.1~15 (2009), Lawrence Erlbaum Associates, Inc
- Kim, J. S., "A study on the problems in the school textbooks from a problem solving point of view", The Journal of Curriculum Studies, 16(2), pp.205~223 (1998)
- 김수철, "수학교과역량의 초등학교 교과서 적용 실태 분석: 2015 개정 교육과정을 중심으로", 예술인문사회 융합 멀티미디어 논문지, 9(4), pp.55~67 (2019), 사단법인 인문사회과학기술융합학회[DOI]
- 김혜미, "수학 문제해결 역량 평가도구 개발", 학교수학, 20(1), pp.83~105 (2018), 대한수학교육학회[DOI]
- 김해윤, "수학과 교수・학습 과정에 핵심역량의 반영 정도와 그 가능성에 대한 교사들의 인식조사", 한국학교수학회논문집, 15(4), pp.605~625 (2012), 한국학교수학회
- 김슬비, "예비교사의 문제 생성과 재구성 활동에 관한 탐색", 수학교육 논문집, 29(3), pp.533~551 (2015), 한국수학교육학회
- Kim, J. H., "Future research topics in the filed of mathematical problems solving: Using delphi method", Journal of Elementary Mathematics Education in Korea, 14(2), pp.187~206 (2011)
- 김윤민, "고등학생의 수학적 신념체계 및 중심신념요인 분석", 학교수학, 16(1), pp.111~133 (2014), 대한수학교육학회
- 김준겸, "문제 상황 제시에 따른 문제만들기 활동이 문제해결력에 미치는 영향", 한국초등수학교육학회지, 5(1), pp.77~98 (2001), 한국초등수학교육학회
- 김정원, "초등학교 5-6학년군 수학 교과서에 제시된 교과 역량 분석", 수학교육, 59(2), pp.147~166 (2020), 한국수학교육학회[DOI]
- 김경옥, "상황제시형 수학 문제 만들기(WQA) 활동이 문제해결력 및 수학적 태도에 미치는 영향", 학교수학, 11(4), pp.665~683 (2009), 대한수학교육학회
- Klein, C., "International review of industrial and organisational psychology", pp.80~126 (2006), Wiley
- Kotsopoulos, D., "Investigating imagination as a cognitive space for learning mathematics", Educational Studies in Mathematics, 70, pp.259~274 (2009)
- 권점례, "수학과 교육과정의 역량 반영 양상에 대한 국제 비교: 프랑스, 호주, 캐나다 브리티시 콜롬비아 주를 중심으로", 수학교육 논문집, 34(2), pp.135~160 (2020), 한국수학교육학회
- 이동환, "초등 예비교사의 수학적 문제제기 사례 분석", 학교수학, 19(1), pp.1~18 (2017), 대한수학교육학회
- 이민희, "수학사를 활용한 협력적 문제해결과정에서 나타난 담화 분석", 학습자중심교과교육연구, 19(16), pp.311~333 (2019), 학습자중심교과교육학회[DOI]
- 이종희, "수학 교과에서 협력적 문제해결 역량과 협력적 메타인지 요소에 대한 델파이 조사", 학습자중심교과교육연구, 20(23), pp.693~719 (2020), 학습자중심교과교육학회[DOI]
- Leung, S. S., "Teachers implementing mathematical problem posing in the classroom : Challenges and strategies", Educational Studies in Mathematics, 83(1), pp.103~116 (2013)
- Li, X., "Learning to teach mathematics through problem posing : teachers’beliefs and performance on problem posing", Educational Studies in Mathematics, 107(1), pp.1~23 (2020)
- Lin, P. J., "Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning", Proceedings of the 28th annual meeting of the International Group for the Psychology of Mathematics Education, 3, pp.257~264 (2004), Bergen University College
- Linzer, D. A., "poLCA : An R package for polytomous variable latent class analysis", Journal of statistical software, 42(1), pp.1~29 (2011)
- Mayer, R. E., "Brief note : A comparison of how textbooks teach mathematical problem solving in Japan and the United States", American Educational Research Journal, 32(2), pp.443~460 (1995)
- , 2015
- , 2015
- Ministry of Education, "Korean national elementary mathematics 3-1" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics workbook 3-2" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics 4-1" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics workbook 4-2" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics 5-1" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics workbook 5-2" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics 6-1" (2019), Chunjae Education
- Ministry of Education, "Korean national elementary mathematics workbook 6-2" (2019), Chunjae Education
- National Council of Teachers of Mathematics, "Principles and standards for school mathematics", National Council of Teachers of Mathematics, ~ (2000)
- National Research Council, "Assessing 21st century skills" (2011), National Academies Press
- Nylund, K. L., "Deciding on the number of classes in latent class analysis and growth mixturemodeling : A Monte Carlo simulation study", Structural Equation Modeling, 14(4), pp.535~569 (2007)
- "PISA 2015 collaborative problem solving framework" (2013)[URL]
- PISA 2012 results: Creative problemsolving:Students’ skills in tackling real-life problems (Volume, V), "Organisation for Economic Cooperation and Development", OECD Publishing, ~ (2014)
- The future of education and skills: Education 2030, "Organisation for Economic Cooperation and Development", OECD, ~ (2018)
- 오영수, "문제제기 활동이 수학에 대한 정의적 영역에 미치는 영향", 한국콘텐츠학회 논문지, 18(2), pp.541~552 (2018), 한국콘텐츠학회[DOI]
- 오동근, "동화를 활용한 문제 만들기 활동이 수학적 태도와 학업성취에 미치는 영향", East Asian Mathematical Journal, 26(4), pp.509~533 (2010), 영남수학회
- 오영열, "초등수학에 적용된 수학적 모델링 과제 유형 탐색", 한국초등교육, 30(1), pp.87~99 (2019), 초등교육연구원[DOI]
- 방정숙, "문제해결과 관련된 제7차 초등학교 수학과 교육과정 및 교과용 도서 분석", 학교수학, 8(3), pp.341~364 (2006), 대한수학교육학회
- A study on the development of proposal of mathematics curriculum revision II, "Park, K.", Korea Foundation for the Advancement of Science and Creativity, ~, pp.Korea Foundation for the Advancement of Science and Creativity research report BD15120005 (2015)
- 박혜영, "협력적 문제해결력 교수·학습 및 평가를 위한 PISA와 ATC21S의 특징 비교 분석", 학습자중심교과교육연구, 14(9), pp.439~462 (2014), 학습자중심교과교육학회
- Pólya, G., "Problem solving in school mathematics", pp.1~2 (1980), NCTM
- Remillard, J. T., "Conceptualizing the curriculum enactment process in mathematics education", ZDM, 46(5), pp.705~718 (2014)
- Remillard, J., "A cross-cultural analysis of the voice of curriculum materials", Proceedings of the International Conference on Mathematics Textbook Research and Development, pp.395~400 (2014), University of South Hampton
- Salas, E., "On teams, teamwork, and team performance: Discoveries and developments", Human Factors: The Journal of the Human Factors and Ergonomics Society, 50, pp.540~547 (2008)
- Schoenfeld, A. H., "Mathematical problem solving" (1985), Academic Press, Inc
- Silver, E. A., "On mathematical problem posing", For the Learning of Mathematics, 14(1), pp.19~28 (1994)
- Silver, E. A., "Fostering creativity through instruction rich in mathematical problem solving and problem posing", ZDM, 97(3), pp.75~80 (1997)
- Silver, E. A., "An analysis of arithmetic problem posing by middle school students", Journal for Research in Mathematics Education, 27, pp.521~539 (1996)
- Silver, E. A., "Posing mathematical problems : An exploratory study", Journal for Research in Mathematics Education, 27(3), pp.293~309 (1996)
- 손태권, "2015개정교육과정 분수의 덧셈과 뺄셈에 관한 수학 교과서 및 익힘책 분석", 학교수학, 22(3), pp.489~508 (2020), 대한수학교육학회
- 송민정, "문제 만들기 프로그램 개발적용이 수학 학업 성취도 및 태도흥미도에 미치는 영향", 한국초등수학교육학회지, 9(1), pp.1~18 (2005), 한국초등수학교육학회
- Stein, M. K., "Mathematics teachers at work:Connecting curriculum materials and classroom instruction", pp.37~55 (2009), Routledge
