미래학교 수학교실의 교육 방법론에 대한 탐색: 비구조화된 문제에서 학생들의 질문 만들기를 중심으로
Teaching Methodology for Future Mathematics Classroom : Focusing on Students' Generative Question in Ill-Structured Problem
0
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn’ or ‘study’ socially. In other words, we haven’t provided students with autonomous research and learning opportunities under ‘the dominant paradigm of visiting works’. As an alternative, he suggests that we should move on to a new didactic paradigm for ‘questioning the world a question’, and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students’ presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.
Abstract
This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn’ or ‘study’ socially. In other words, we haven’t provided students with autonomous research and learning opportunities under ‘the dominant paradigm of visiting works’. As an alternative, he suggests that we should move on to a new didactic paradigm for ‘questioning the world a question’, and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students’ presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.
참고문헌 (21)
- 권오남, "개방형 문제 중심의 프로그램이 수학적 창의력에 미치는 효과", 수학교육, 44(2), pp.307~323 (2005), 한국수학교육학회
- 김민경, "초등학교 4학년 학생들의 비구조화된 문제에서 나타난 해결 과정 및 추론 분석", 수학교육, 51(2), pp.95~114 (2012), 한국수학교육학회
- 김부윤, "ATD에 근거한 유리수의 대수학적 completion에 관한 연구", 수학교육, 50(2), pp.131~144 (2011), 한국수학교육학회
- 김혜진, "교수학의 인류학적 접근 이론(ATD)의 이해", 사회과교육, 54(4), pp.115~128 (2015), 한국사회과교육연구학회
- 윤나미, "교수학적 상황론의 이해와 측정 지도에의 적용", 수학교육학연구, 9(2), pp.473~491 (1999)
- 정제영, "지능정보사회 대비 미래 교육정책 방향과과제", 한국교육학회 교육정책포럼 자료집 (2016)
- Anderson, J., "Mathematics curriculum in school education", pp.209~230 (2014), Springer
- Chevallard, Y., "Proceedings of the 4th conference of the European Society for Research in Mathematics Education", pp.21~30 (2006), FUNDEMI IQS
- Chevallard, Y., "Teaching mathematics in tomorrow’s society: A case for an oncoming counter paradigm", 12th International Congress on Mathematical Education, pp.173~187 (2012)
- English, L. D., "Handbook of International research in mathematics education", pp.313~335 (2016), Routledge
- Jonassen, D. H., "Toward a design theory of problem solving", Educational Technology Research and Development, 48(4), pp.63~85 (2000)
- David H. Jonassen, "All Problems are Not Equal: Implications for Problem-Based Learning", Interdisciplinary Journal of Problem-Based Learning, 2(2) (2008), Purdue University (bepress)[DOI]
- Kapur, M., "Productive failure", Cognition and Instruction, 26(3), pp.379~424 (2008)
- Kapur, M., "Mathematical Problem Solving", pp.43~68 (2009), World Scientific
- Kapur, M., "Productive failure in mathematical problem solving", Instructional Science, 38(6), pp.523~550 (2010)
- Llanos, V. C., "The research and study paths in the secondary school : The case of the polynomial functions of the second degree", Problems of education in the 21st century, 52, pp.60~71 (2013)
- Reed, S. K., "The structure of ill-structured(and well-structured)problems revisited", Educational Psychology Review, 28(4), pp.691~716 (2016)
- Schwartz, D. L., "Inventing to prepare for future learning : the hidden efficiency of encouraging original student production in statistic instruction", Cognition and Instruction, 22(2), pp.129~184 (2004)
- Simon, H. A., "The structure of ill-structured problems", Artificial Intelligence, 4, pp.181~201 (1973)
- Winsløw C., "Un panorama de la TAD", pp.117~140 (2011), Centre de Recerca Mathemàtica
- Winsløw, C., "Study and research courses as an epistemological model for didactics", Educational Study Mathematics, 83, pp.267~284 (2013)