연결성 관점에서 본 수학과 교육과정 국제 비교·분석 연구: 한국, 싱가포르, 홍콩을 중심으로 = Comparative Study of Mathematics Curriculum from the Perspective of Connection: Focused on Korea, Singapore, and Hong Kong

다국어 초록 (Multilingual Abstract)

The purpose of this study This study aimed to analyze the curricula of Korea, Singapore, and Hong Kong from the perspective of connection — one of the competences of the 2022 national revised mathematics curriculum — and to suggest theoretical ideas for the Korean curriculum. The curricula were divided into three categories, and the criteria for the classification of connection were set into four categories: horizontal and vertical connections in terms of mathematical internal connection, connection through other subjects, and real life in terms of mathematical external connection. The analysis showed that none of the three countries revealed horizontal connections in goals and characteristics. Regarding achievement standards, horizontal connections did not appear in Korea; moreover, this was the case for vertical connections in Singapore as well as vertical connections and connections through other subjects in Hong Kong. All types of connections were reflected in teaching, learning, and assessment, with the exception of Hong Kong’s horizontal connection. Therefore, Korea needs to stipulate internal connections in goals and characteristics, reflect horizontal connections in achievement standards, and specify vertical connections in teaching, learning, and assessment. Moreover, specific methods were discussed for Singapore and Hong Kong.

국문 초록 (Abstract)

본 연구의 목적은 연결성 관점에서 한국, 싱가포르, 홍콩의 초,중학교 교육과정을 비교 분석하여 향후 교육과정에 대한 이론적 아이디어를 제시하는 것이다. 서로 다른 체제를 지닌 세 교육과정을 통일성 있게 분석하기 위해 목표 및 성격, 성취기준, 교수·학습 및 평가의 3개 범주로 나누고, 연결성 분류기준으로 수학 내적 연결성 관점에서의 수평적 연결, 수직적 연결과 수학 외적 연결성 관점에서의 타 교과와의 연결, 실생활과의 연결을 설정하였다. 분석 결과, 목표 및 성격에서는 세 국가 모두 수평적 연결이 드러나지 않았다. 성취기준에서는 우리나라에는 수평적 연결이, 싱가포르에는 수직적 연결이, 홍콩에는 수직적 연결과타 교과와의 연결이 나타나지 않았다. 교수·학습 및 평가에는 홍콩의 수평적 연결을 제외하고 연결성이 모두 반영되어 있었다. 따라서, 교육과정의 목표 및 성격에서 내적 연결성을 구체화하고, 성취기준에 수평적 연결을 반영하며 수학 외적 연결성 요소를 다양화하고, 교수·학습 및 평가에서 수직적 연결을 구체적으로 다룰 필요가 있다는 결론을 내릴 수 있었고, 그 구체적인 방안에 대해 싱가포르와 홍콩의 사례로부터 함의되는 바를 논의하였다.

참고문헌 (Reference)

• 1 김왕준, "홍콩, 싱가포르, 핀란드, 아일랜드의 교육개혁의 비전과 주요 정책" 한국초등교육학회 23 (23): 321-340, 2010
• 2 권석일, "초등학교 수학과 교육과정 기하 영역 국제 비교: 우리나라, 싱가포르, 홍콩을 중심으로" 학습자중심교과교육학회 16 (16): 693-712, 2016
• 3 김유경 ; 방정숙, "초등학교 수학 수업에 나타난 수학적 연결의 대상과 방법 분석" 한국수학교육학회 51 (51): 455-469, 2012
• 4 문교부, "중학교 교과과정"
• 5 교육부, "수학과 교육과정"
• 6 이예진 ; 최혜령, "수학 내적 연결성의 관점에서 본 CMP 교과서와 2015 개정 수학 교과서의 비교 분석" 한국초등수학교육학회 26 (26): 257-281, 2022
• 7 이송희 ; 임웅, "부등식의 영역 교육과정 분석: 고교-대학수학의 연계 및 수학적 연결성을 중심으로" 한국수학교육학회 59 (59): 1-15, 2020
• 8 반은섭 ; 류희찬 ; 신재홍, "대수와 기하의 연결에 관한 Descartes의 관점 재조명 연구" 대한수학교육학회 26 (26): 715-730, 2016
• 9 문교부, "국민학교 교과과정"
• 10 Willy, M., "Understanding connections in the school mathematics curriculum" 28 (28): 189-202, 2008
• 11 Gueudet, G., "Transitions in mathematics education" Springer International Publishing AG 2016
• 12 Department of Education and Early Childhood Development, "Transitioning from primary to secondary school. 5-7"
• 13 Noss, R., "The construction of mathematical meanings: Connecting the visual with the symbolic" 33 (33): 203-233, 1997
• 14 Masyita Dini Islami, "The Mathematical Connections Process of Junior High School Students with High and Low Logical Mathematical Intelligence in Solving Geometry Problems" AI Publications 5 (5): 10-18, 2018
• 15 Denisse, R. T., "The Korean mathematics curriculum characteristics and challenges" Information Age Publishing 211-227, 2017
• 16 Mullis, I. V. S., "TIMSS 2019 international results in mathematics and science. Retrieved from Boston College"
• 17 Mullis, I. V. S., "TIMSS 2015 Encyclopedia: Education Policy and Curriculum in Mathematics and Science"
• 18 Vivi Rachmatul Hidayati, "Students’ Mathematical Connection Error in Solving PISA Circle Problem" Universitas PGRI Madiun 8 (8): 76-, 2020
• 19 Smith, J. S., "Student and stakeholder perceptions of the transition to high School" 91 (91): 32-42, 2008
• 20 Skemp, R. R., "Relational understanding and instrumental understanding" 77 : 20-26, 1976
• 21 Gökhan Karakoç, "Real World Connections in High School Mathematics Curriculum and Teaching" Auricle Technologies, Pvt., Ltd. 6 (6): 31-, 2015
• 22 Foster, J. K., "Prospective teachers’ pedagogical considerations of mathematical connections : A framework to motivate attention to and awareness of connections" 23 (23): 95-118, 2021
• 23 National Council of Teachers of Mathematics, "Principles and standards for school mathematics" National Council of Teachers of Mathematics 2000
• 24 Ministry of Education, Singapore, "Mathematics syllabus secondary one to four"
• 25 Ministry of Education, Singapore, "Mathematics syllabus primary one to six"
• 26 Ministry of Education, Singapore, "Mathematics syllabus primary one to six"
• 27 Curriculum Development Council, the Government of the Hong Kong Special Administrative Region, "Mathematics education, key learning area curriculum guide (primary 1–secondary 6)" Curriculum Development Council, the Government of the Hong Kong Special Administrative Region 2017
• 28 Singletary, L. M., "Mathematical connections made in practice: an examination of teachers’ beliefs and practices" University of Georgia 2012
• 29 Jennifer A. Eli, "Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry" Wiley 113 (113): 120-134, 2013
• 30 Baiduri*, Octavina, "Mathematical Connection Process of Students with High Mathematics Ability in Solving PISA Problems" Eurasian Society of Educational Research 9 (9): 1527-1537, 2020
• 31 Hiebert, J., "Making sense : Teaching and learning mathematics with understanding" Heinemann 1997
• 32 Menanti, H., "Improve mathematical connections skills with realistic mathematics education based learning" Atlantis Press 200 : 2018
• 33 Hiebert, J., "Handbook of research on mathematics teaching and learning" Macmillan 65-97, 1992
• 34 Cuoco, A., "Habits of mind : An organizing principle for mathematics curricula" 15 : 375-402, 1996
• 35 Boaler, J., "Exploring the nature of mathematical activity : Using theory, research and ‘working hypotheses’ to broaden conceptions of mathematics knowing" 51 : 3-21, 2002
• 36 Businskas, A. M., "Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections" Simon Fraser University 2008
• 37 Online Etymology Dictionary, "Connection"
• 38 Hodgson, T. R., "Connecting mathematics across the curriculum" National Council for Teaching Mathematics 13-21, 1995
• 39 Coxford, A. F., "Connecting mathematics across the curriculum" National Council for Teaching Mathematics 3-12, 1995
• 40 Georgia Department of Education, "Common core Georgia performance standards frameworks of mathematics, CCGPS coordinate algebra unit 6: Connecting algebra and geometry through coordinates. U.S.A"
• 41 D S Ayunani, "Analyzing mathematical connection skill in solving a contextual problem" IOP Publishing 1511 (1511): 012095-, 2020
• 42 Langenkamp, A. G., "Academic vulnerability and resilience during the transition to high school : The role of social relationships and district context" 83 (83): 1-19, 2010
• 43 Erhan Bingölbali, "A Proposed Conceptual Framework For Enhancing The Use Of Making Connections Skill In Mathematics Teaching" Turkish Education Association 41 (41): 2016
• 44 Mesture Kayhan Altay, "8th Grade Student’s Skill of Connecting Mathematics to Real Life" Redfame Publishing 5 (5): 158-, 2017