• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.141-161
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• 2009

Mathematical Communication ability can be more developed through sharing thoughts with others. Therefore when we instruct students in math, it is very important for teachers to provide them with opportunity to communicate mathematically. So this study provided open-ended problems in small-group collaborative learning. And we analyzed students' mathematical communication focused on the student's level of understanding. Furthermore, to improve students' mathematical communication ability, this study tries to attract the factors that we should consider the exact date for inserting the open-ended problems into a course of math and the student's level of understanding for selecting suitable open-ended problems.

• East Asian mathematical journal
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• v.32 no.4
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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.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.10a
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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.

• Journal of the Korean Chemical Society
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• v.50 no.5
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• pp.385-393
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• 2006

In this study, we analyzed the effects of science inquiry learning that applies open-ended hypothesis-testing learning model in a high school chemistry class of grade 11 in respect of science process skills, science-related attitude, and appreciation towards science class by cognitive level. Open-ended science inquiry learning activities on Metals and their applications unit in Chemistry I were developed and applied to the treatment groups while the conventional science activities were applied to the control groups. Four classes of 92 students in a high school located in Seoul were assigned into the treatment and control groups, respectively. According to the results in the test of science process skills, the students treated with the alternative experiments emphasizing open-ended hypothesis-testing obtained higher scores in experimental design, data conversion and description, and hypothesis test than those with conventional experiments but not in problem cognition and definition and hypothesis fixing'. There was negative effect on science-related attitude due to increased roles and tasks in the open-ended science inquiry learning activities.

• Journal of Elementary Mathematics Education in Korea
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• v.7 no.1
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• pp.23-44
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• 2003

The purpose of the study is to examine the phenomenon presented the process of problem solving activities of students with the mathematical context information accompanied problem based on Freudenthal's mathematizing theory and Realistic Mathematics Educations about cognitive and emotional aspects. In conclusion, taking a look at the results of study, open-ended contextual problem was had to offer in order to pull out various solutions. Teachers should help students develop their own methods, discuss their methods with others' and reinvent formal mathematics and its constructive process under the guidance of the teachers.

• Research in Mathematical Education
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• v.5 no.2
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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.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.10a
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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.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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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.

• Research in Mathematical Education
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• v.8 no.2
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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.

• Proceedings of the KIEE Conference
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• 1987.07a
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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.