• 한국초등수학교육학회지
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• 제13권2호
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• pp.141-161
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• 2009

본 연구에서는 소집단 협동학습 형태에서 개방형 문제를 활용하여 학생들의 학습 수준에 따라 나타나는 수학적 의사소통의 특징을 말하기와 쓰기를 중심으로 조사하였다. 본 연구의 결과는 개방형 문제 유형과 학생들의 학습 수준을 고려한 수학적 의사소통 능력 신장 방안에 대한 추후의 연구에 기초 자료로서 활용될 수 있을 것이다. 본 연구의 결과로써 개방형 문제를 활용한 소집단 협동학습 상황에서 학생들의 의사소통 형태가 시간이 지날수록 보다 구체화되고 정련되는 모습을 관찰할 수 있었다. 또한, 본 연구에서는 학생들의 학습 수준에 따라 말하기와 쓰기 부분에서 서로 다른 특징이 나타난다는 사실과 학습 수준에 따른 개방형 문제 유형의 선호도가 다르다는 사실을 확인하였다.

• East Asian mathematical journal
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• 제32권4호
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• pp.545-563
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• 2016

The aim of this study was to observe processes and implication to a given program for the 20 gifted children grade 5 by making the number from 1 to 100 with natural numbers 4,4,9 and 9. Revelation of creativity, mathematical tendency of students and meaningful responses were observed by the qualitative records of this game activity and the analysis of result. The major result of a study is as follows: The mathematical creativities of students were revealed and developed by this activity. And the mathematical attitude were changed and developed, so student could actively participate. And students could experience collaborative and social composition learning by presentations and discussion, competition with a permissive atmosphere and open-game rule. It was meaningful that mathematical ideas (negative number, square root, factorial, [x]: the largest integer not greater than x, absolute value, percent, exponent, logarithm etc.) were suggested and motivated by students themselves.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2006년도 제37회 전국수학교육연구대회 프로시딩
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• pp.45-62
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• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U.S. researchers. We examine the approach by illustrating its three aspects: open process (there is more than one way to arrive at the solution to a problem; 2) open-ended problems (a problem can have several of many correct answers), and 3) what the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U.S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• 대한화학회지
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• 제50권5호
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• pp.385-393
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• 2006

연구에서는 고등학교 화학 수업에서 개방적 가설검증 학습모형을 적용한 과학 탐구학습을 실시하고, 학생들의 인지 수준에 따른 과학 탐구능력, 과학 수업에 대한 태도에 미치는 효과와 수업에 대한 인식을 알아보았다. 서울에 소재한 남자 고등학교 2학년 4개 학급의 학생들(92명)을 대상으로 개방적 가설검증 학습모형을 적용한 과학 탐구학습을 실시한 처치집단과 실험과정이 모두 제시된 실험 수업을 실시한 통제집단으로 배치한 후, 화학의 ‘금속과 그 이용' 단원에 대해서 수업을 실시하였다. 연구 결과에 의하면, 개방적 가설검증 학습모형을 적용한 과학 탐구학습은 과학 탐구능력 향상에 관해서 실험설계, 자료 변환 및 해석, 가설검증의 영역에서 유의미한 효과가 있었으며 문제 파악 및 정의, 가설설정의 영역에서는 효과가 없었다. 한편, 개방적 과학 탐구학습에서 학생들의 역할 및 수행할 과제의 증가로 인해 과학 수업에 대한 태도는 처치집단에 부정적인 효과가 나타났다.

• 한국초등수학교육학회지
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• 제7권1호
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• pp.23-44
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• 2003

수학적 맥락 정보를 이용한 문제가 주어졌을 때, 학생들의 문제 해결 활동을 관찰하고 인지적 측면과 정서적 측면에서 분석하였다. 수학적 맥락 문제들은 Freudenthal의 수학 교육 이론과 RME에 따라 구성하였다. 그 결과, 개방된 형태의 맥락 문제가 보다 다양한 풀이를 산출해냄을 알 수 있었다. 따라서 교사는 스스로 형식적 수학을 재발명하고, 학생들로 하여금 그에 걸맞은 인지적 활동이 이루어지도록 나름대로의 교수 학습 방법을 개발하여야 한다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제5권2호
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• pp.87-98
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• 2001

The Center for Science Gifted Education (CSGE) of Chongju National University of Education was established in 1998 with the financial support of the Korea. Science & Engineering Foundation (KOSEF). In fact, we had prepared mathematics and science gifted education program beginning in 1997. It was possible due to the commitment of faculty members with an interest in gifted education. Now we have 5 classes in Mathematics, two of which are fundamental, one of which is a strengthened second-grade class gifted elementary school students, and one a fundamental class, and one a strengthened class for gifted middle school students in Chungbuk province. Each class consists of 16 students selected by a rigorous examination and filtering process. Also we have a mentoring system for particularly gifted students in mathematics. We have a number of programs for Super-Saturday, Summer School, Winter School, and Mathematics and Science Gifted Camp. Each program is suitable for 90 or 180 minutes of class time. The types of tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving tasks. Levels of the tasks developed for talented elementary students in mathematics can be further divided into grade 5 and under, grade 6, and grade 7 and over. Types of the tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving task. Also levels of the tasks developed for talented elementary students in mathematics can be divided into the level of lower than grade 5, level of grade 6, and level of more than grade 7. Three tasks developed and practiced are reported in this article.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2006년도 제37회 전국수학교육연구대회 프로시딩
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• pp.63-78
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• 2006

미국에서 학교 수학 수업에서의 개방적 접근은 일본과 미국 연구자들의 공동연구의 결과물이다. 우리는 그것에 대한 세 가지의 측면을 실례로 살펴보면 접근을 시도하겠다. : 1) 개방된 과정(open process)(문제의 해답에 이르는 방법이 여러 가지이다: 2) 개방형 문제(open-ended problems)(문제에 대한 정답이 여러 가지가 될 수 있는 문제), 3) 일본에서 '문제로부터 문제(from problem to problem)'라고 불리는 것 혹은 문제고안(problem formulating)하기(학생들이 새로운 문제를 명확하게 나타내기 위해 자신의 생각을 써 내려 가는 것)수학 지도에서 일본의 개방적 접근에 대한 우리의 이해를 바탕으로, 우리는 미국에서 보다 효과적인 수학 지도를 위한 몇 가지 방법을 선택 적용해 보았다. 이러한 접근의 대부분은 학습 계획안을 만들 때 여러 교사가 함께 참여하고 일련의 토론과 수정과정을 거친 뒤, 많은 부분이 개선되고 효과적인 계획안을 만들어 낸다는 점에서 미국의 수학교사들에게 새로운 것이다. 또한 이 접근법에서는 교사가 문제를 해결하는 과정에서 학생 개개인이나 그룹을 활동적으로 관찰하여 그들의 활동을 비교하고 토론한다.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.405-423
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• 1998

This study aims to reflect the origin and the meaning of open education and to derive pedagogical principles for open mathematics education. Open education originates from Socrates who was the founder of discovery learning and has been developed by Locke, Rousseau, Froebel, Montessori, Dewey, Piaget, and so on. Thus open education is based on Humanism and Piaget's psychology. The aim of open education consists in developing potentials of children. The characteristics of open education can be summarized as follows: open curriculum, individualized instruction, diverse group organization and various instruction models, rich educational environment, and cooperative interaction based on open human relations. After considering the aims and the characteristics of open education, this study tries to suggest the aims and the directions for open mathematics education according to the philosophy of open education. The aim of open mathematics education is to develop mathematical potentials of children and to foster their mathematical appreciative view. In order to realize the aim, this study suggests five pedagogical principles. Firstly, the mathematical knowledge of children should be integrated by structurizing. Secondly, exploration activities for all kinds of real and concrete situations should be starting points of mathematics learning for the children. Thirdly, open-ended problem approach can facilitate children's diverse ways of thinking. Fourthly, the mathematics educators should emphasize the social interaction through small-group cooperation. Finally, rich educational environment should be provided by offering concrete and diverse material. In order to make open mathematics education effective, some considerations are required in terms of open mathematics curriculum, integrated construction of textbooks, autonomy of teachers and inquiry into children's mathematical capability.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제8권2호
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• pp.81-93
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• 2004

This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.105-109
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• 1987

A solution which combines ray and aperture integration(AI) techniques is presented for the problem of electromagnetic plane wave scattering by an open-ended, perfectly-conducting, semi-infinite parallel plate waveguide with a thin, uniform layer of lossy or absorbing material on its inner walls, and with a simple planar termination inside. Numerical results are given for the fields outside the waveguide.