• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.677-690
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• 2006

We show that a group of three closure properties including the selectively Pytkeev property coincide on $C_k$(X) for a locally compact X. We also introduce a new game characterization of these properties for such spaces.

• CELLMED
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• v.5 no.2
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• pp.9.1-9.14
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• 2015

The so-called "Needham's Grand Question" (NGQ) can be formulated as why modern science was developed in Europe despite the earlier successes of science and technology in ancient China. Numerous answers have been proposed. In this review, it will be pointed out that traditional Chinese natural philosophy (TCNP) and traditional Chinese medicine (TCM) are in fact dealing with problems of highly complex dynamical systems of Nature and human beings. Due to the lack of mathematical machinery in dealing with such complex phenomena, a holistic approach was taken by ancient Chinese instead. It was very successful for the first eighteen centuries. In the recent three centuries, however, the reductionist and mechanistic viewpoints of Western natural philosophy, sciences, and medicine have been prevalent all over the world up to now. The main obstacle in preventing the advancement of TCM, TCNP and its sciences is actually the lacking of proper mathematical tools in dealing with complex dynamical systems. Fortunately, the tools are now available and a "chaotic wave theory of fractal continuum" has been proposed recently. To give the theory an operational meaning, three basic laws of TCNP are outlined. These three laws of wave/field interactions contrast readily with those of Newton's particle collisions. Via the proposed three laws, TCM, TCNP and its sciences can be unified under the same principles. Finally, an answer to NGQ can be accurately given. It is hoped that this review will help promoting a genuine understanding of natural philosophy, sciences, and medicine in an ecumenical way.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.10a
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• pp.185-187
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• 2022

Because of the rapid change in the educational paradigm in the Fourth Industrial Revolution Era, Artificial Intelligence (AI) Education is becoming increasingly important today. The 2022 Revised Curriculum focuses on AI Education that can cultivate the fundamental skills and competencies needed in the future society. The following are the directions presented in this study for improving computational thinking and mathematical thinking in AI Education in elementary and secondary schools. First, studying teaching principles that allow students to understand AI concepts and principles and develop their ability to solve real-life problems is necessary in terms of computational thinking skills education. Second, an educational program is required for students to acquire algorithms using formulas and learn principles in the process of computers thinking like humans as part of their mathematical thinking ability to understand AI. A study on expectations through the analysis of competent learning effects that may arise from the relationship between instructors and learners was proposed as a future research project.

• 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.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.151-163
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• 1998

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

• Korean Journal of Geomatics
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• v.1 no.1
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• pp.69-74
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• 2001

In conventional photogrammetry, three-dimensional coordinates are obtained from two consecutive images of a stationary object photographed from two exposure stations, separated by a certain distance. However, it is impossible to photograph moving objects from two stations with one camera at the same time. Various methods to overcome this obstacle were devised e. g. taking the left and right scenes simultaneously with one camera using a beam splitter attached to the front, thus creating a stereo scene in one image. A beam splitter consists of two outer mirrors and two inner mirrors. This paper deals with research where the optical principles of the beam splitter were evaluated based on light path phenomena between the outer mirrors and the inner mirrors. A mathematical model of the geometric configuration was derived for the beam splitter. This allows us to design and control a beam splitter to obtain maximum scale and maximum base-height ratio by stepwise application of the mathematical model. The results show that the beam splitter is a very useful tool for stereophotography with one camera. The optimum geometric configurations ensuring maximum scale and base-height ratio are closely related to inner and outer reflector sizes, their inclination angles and the offsets between the outer mirrors.

• Research in Mathematical Education
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• v.26 no.1
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• pp.39-43
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• 2023

Choosing to See: A Framework for Equity in the Math Classroom is a book intended to be a practical tool for teachers to build empowering mathematics classrooms for their students from marginalized groups. Pamela Seda and Kyndall Brown provide concrete guidance using seven key principles, the ICUCARE (pronounced "I See You Care") Equity Framework, to provide a pathway for teachers for how to meaningfully make their classrooms a more equitable space for all students.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.55-66
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• 1999

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, ′the process of the length of curve being equal to the sum of the vectors when intervals get smaller′ and ′the process of calculating volume of spinning curve by using definite integral.′ Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Also it can help students with solving mathematical problems intuitively. Consequently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the application of definite integral", which exists in mathematical curriculum the second and third grade of high school. When this study is used for students as assisting materials, it is expected the following educational effect. 1. Students will have precise concepts because they can understand what they learn intuitively. 2. Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 3. It is possible to change the teacher-centered instruction into the student-centered instruction. 4. Students will understand the relation between velocity and distance correctly because they can see the process of getting the length of curve by vector through the monitor. For the purpose of increasing the efficiencies and qualities of mathematics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, teachers have to use the CIA program carefully.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.27-32
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• 2001

The paper describes some principles how we design the mathematics curriculum through mathematical Modelling. since the motivation for modelling is that it give us a cheap and rapid method of answering illposed problem concerning the real world situations. The experiment was focussed on the possibility that they can involved in modelling problem sets and carry modelling process. The main principles could be described as follows. principle 1. we as a teacher should introduce the modelling problems which have many constraints at the begining situation, but later eliminate those constraints possibly. principle 2. we should avoid the modelling real situations which contain the huge data collection in the classroom, but those could be involved in the mathematics club and job oriented problem solving. principle 3. Analysis of modelling situations should be much emphasized in those process of mathematics curriculum principle 4. As a matter of decision, the teachers should have their own activities that do mathematics curriculum free. principle 5. New strategies appropriate in solving modelling problem could be developed, so that these could contain those of polya's heusistics

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.425-437
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• 1998

The difference between "open" mathematics education and education of "open mathematics" arises from the difference of tearcher's understanding on the meaning of "teaching and learning mathematics" in the paper. Discusses the agreements and the worries of the researchers, the teachers, the students in korea, about open educationism, firstly, Three practical cases in mathematics lesson in korea are reviewed and analyzed in the respect of learning principles, secondly. Thirdly, the paper examines how to be modified two main learning principles, individualised learning and self-regulation of learning by teachers in the process of instruction. Finally, open mathematics advocated by Fisher(1984) and closed mathematics are compared especially in the probability unit. It concludes that the open approaches in mathematics lessons in korea need to improve with respect to teacher's attitude for didactic contents or mathematical knowledge. It is argued that teacher's open or flexible understanding of mathematical knowledge is no less important than that of their pupils.ant than that of their pupils.