• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.81-96
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• 2006

This paper aims to review Leibniz's analytic ideas in his philosophy, logics, and mathematics. History of analysis in mathematics ascend its origin to Greek period. Analysis was used to prove geometrical theorems since Pythagoras. Pappus took foundation in analysis more systematically. Descartes tried to find the value of analysis as a heuristics and found analytic geometry. And Descartes and Leibniz thought that analysis was played most important role in investigating studies and inventing new truths including mathematics. Among these discussions about analysis, this paper investigate Leibniz's analysis focusing to his ideas over the whole of his studies.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.347-366
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• 2004

Recently, there have been many assessment researches in Korea. The aim of this study is to reflect on framework for mathematics assessment in RME which is based on Jan de Lange's assessment theory and to induce desirable directions for our mathematics assessment in nation-level and class-level. In order to attain these purposes, the present paper reflects the philosophy of RME, Jan de Lange's framework for mathematics assessment, assessment framework of the unit 'Side Seeing', one of Mathematics in Context textbook series, as an exemplar to which Jan de Lange's framework is applied. Based on these reflections, it is discussed that it needs to specify achievement standards presented in mathematics curriculum more particularly in order to have framework including mathematical abilities of level 2 and level 3 in Jan de Lange's framework appropriate to our situations, to apply the framework to nation-level and class-level consistently, and to enhance abilities of teachers and student teachers for mathematics assessment.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.111-122
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• 1983

지금까지 H. Aebli, A. Fricke, R.W. Copeland, G. Steiner, E. Wittmann, R.R.Skemp, Z.P. Dienes등에 의해 Piaget이론의 수학교육적 연구가 상당한 정도로 이루어져 왔다. 그러나 Centre International D'epistemologie Genetique를 중심으로 한 집단사고와 방대한 연구결과를 집약한 소위 'Piaget이론'은 타에 그 종례를 찾아볼 수 없는 포괄적인 것인 바, 지금까지 이루어진 Piaget이론의 수학교육적 접근은 Piaget이론의 한정된 부분의 단편적인 응용에 불과하며, Piaget의 발생적 수학인식론 및 심리학의 중심원리와 연구결과를 반영한 보다 철저한 연구가 요망되고 있다. 본 고는 그 이론적 기초에 관한 연구의 일환으로 1969년에 출판된 Psychologie et pedagogie에 실린 'La didactique des mathematiques'와 1972년 ICMI의 제2차 수학교육국제회의에 기고한 논문 'Comments on mathematical education'에 나타난 수학교육에 대한 Piaget자신의 견해를 그의 수학인식론의 분석적 고찰을 통해 양세화하고, 그 실제적 구현방안을 제시해 본 것이다.

• The Mathematical Education
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• v.59 no.3
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• pp.237-254
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• 2020

The current study investigated the relationships between mathematical knowledge for teaching and the mathematical quality in instruction in order to gain insight about teacher education for secondary teachers in South Korea. We collected and analyzed twelve high school teachers' scores of the multiple-choice assessment for mathematical knowledge for teaching developed by the Measures of Effective Teaching project. Their instruction was video recorded and analyzed with the mathematical quality in instruction developed by the Learning Mathematics for Teaching project. We also interviewed the teachers about how they planned and assessed their instruction by themselves in order to gain information about their intention and interpretation about instruction. There was a statistically significant and positive association between the levels of mathematical knowledge for teaching and the mathematical quality in instruction. Among three dimensions of the mathematical quality in instruction, mathematical richness seemed most relevant to mathematical knowledge for teaching because subject matter knowledge plays an important role in mathematical knowledge for teaching. Furthermore, working with students and mathematics as well as students participation were critical to decide the quality of instruction. Based on these findings, the current study discussed offering opportunities to learn mathematical knowledge for teaching and philosophy about how teachers need to consider students in high schools particularly in terms of constructivism.

• The Mathematical Education
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• v.24 no.2
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• pp.48-73
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• 1986

Though the tradition of Korean mathematics since the ancient time up to the 'Enlightenment Period' in the late 19th century had been under the influence of the Chinese mathematics, it strove to develop its own independent of Chinese. However, the fact that it couldn't succeed to form the independent Korean mathematics in spite of many chances under the reign of Kings Sejong, Youngjo, and Joungjo was mainly due to the use of Chinese characters by Koreans. Han-gul (Korean characters) invented by King Sejong had not been used widely as it was called and despised Un-mun and Koreans still used Chinese characters as the only 'true letters' (Jin-suh). The correlation between characters and culture was such that, if Koreans used Han-gul as their official letters, we may have different picture of Korean mathematics. It is quite interesting to note that the mathematics in the 'Enlightenment Period' changed rather smoothly into the Western mathematics at the time when Han-gul was used officially with Chinese characters. In Koryo, the mathematics existed only as a part of the Confucian refinement, not as the object of sincere study. The mathematics in Koryo inherited that of the Unified Shilla without any remarkable development of its own, and the mathematicians were the Inner Officials isolated from the outside world who maintained their positions as specialists amid the turbulence of political changes. They formed a kind of Guild, their posts becoming patrimony. The mathematics in Koryo significant in that they paved the way for that of Chosun through a few books of mathematics such as 'Sanhak-Kyemong', 'Yanghwi-Sanpup' and 'Sangmyung-Sanpup'. King Sejong was quite phenomenal in his policy of promotion of mathematics. King himself was deeply interested in the study, createing an atmosphere in which all the high ranking officials and scholars highly valued mathematics. The sudden development of mathematic culture was mainly due to the personality and capacity of king who took anyone with the mathematic talent into government service regardless of his birth and against the strong opposition of the conservative officials. However, King's view of mathematics never resulted in the true development of mathematics perse and he used it only as an official technique in the tradition way. Korean mathematics in King Sejong's reign was based upon both the natural philosophy in China and the unique geo-political reality of Korean peninsula. The reason why the mathematic culture failed to develop continually against those social background was that the mathematicians were not allowed to play the vital role in that culture, they being only the instrument for the personality or politics of the king. While the learned scholar class sometimes played the important role for the development of the mathematic culture, they often as not became an adamant barrier to it. As the society in Chosun needed the function of mathematics acutely, the mathematicians formed the settled class called Jung-in (Middle-Man). Jung-in was a unique class in Chosun and we can't find its equivalent in China or Japan. These Jung-in mathematician officials lacked tendency to publish their study, since their society was strictly exclusive and their knowledge was very limited. Though they were relatively low class, these mathematicians played very important role in Chosun society. In 'Sil-Hak (the Practical Learning) period' which began in the late 16th century, especially in the reigns of Kings Youngjo and Jungjo, which was called the Renaissance of Chosun, the ambitious policy for the development of science and technology called for. the rapid increase of he number of such technocrats as mathematics, astronomy and medicine. Amid these social changes, the Jung-in mathematicians inevitably became quite ambitious and proud. They tried to explore deeply into mathematics perse beyond the narrow limit of knowledge required for their office. Thus, in this period the mathematics developed rapidly, undergoing very important changes. The characteristic features of the mathematics in this period were: Jung-in mathematicians' active study an publication, the mathematic studies by the renowned scholars of Sil-Hak, joint works by these two classes, their approach to the Western mathematics and their effort to develop Korean mathematics. Toward the 'Enlightenment Period' in the late 19th century, the Western mathematics experienced great difficulty to take its roots in the Peninsula which had been under the strong influence of Confucian ideology and traditional Korean mathematic system. However, with King Kojong's ordinance in 1895, the traditional Korean mathematics influenced by Chinese disappeared from the history of Korean mathematics, as the school system was hanged into the Western style and the Western mathematics was adopted as the only mathematics to be taught at the Schools of various levels. Thus the 'Enlightenment Period' is the period in which Korean mathematics shifted from Chinese into European.

• Korean Journal of Logic
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• v.15 no.1
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• pp.155-190
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• 2012

As far as Hilbert's Program is concerned, there seems to be important differences in the development of Wittgenstein's thoughts. Wittgenstein's main claims on this theme in his middle period writings, such as Wittgenstein and the Vienna Circle, Philosophical Remarks and Philosophical Grammar seem to be different from the later writings such as Wittgenstein's Lectures on the Foundations of Mathematics (Cambridge 1939) and Remarks on the Foundations of Mathematics. To show that differences, I will first briefly survey Hilbert's program and his philosophy of mathematics, that is to say, formalism. Next, I will illuminate in what respects Wittgenstein was influenced by and criticized Hilbert's formalism. Surprisingly enough, Wittgenstein claims in his middle period that there is neither metamathematics nor proof of consistency. But later, he withdraws his such radical claims. Furthermore, we cannot find out any evidences, I think, that he maintained his formerly claims. I will illuminate why Wittgenstein does not raise such claims any more.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.313-330
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• 2015

The classification is an important activity that is directly related to concept formation. Thus it will need to be made meaningful learning to classification through learner-centered teaching. But we doubts weather teaching and learning to the classification are reflected in the constructivist philosophy of 'learner-centered' well or not. The purpose of this study was to analyze critically the content of elementary textbooks and guidebook for teachers relating to the classification of angles and triangles in terms of constructivism. As a result, there is a problem in the classification of angles that are not provided a reasonable chance to set criteria by agreement of the communities. There is a problem in the classification of triangles that has the characteristics of radical development in terms of diversity. In addition, response of students was predicted like anyone who already acquired knowledge. And it has the shortcomings that the opportunity to have a choice and a discussion to hierarchical and partition classification are not provided. The followings are proposed based on such features; faithful reflection of 'Learner-centered' principle, careful prediction of student response, teaching that focus on process than results.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

• Journal of Engineering Education Research
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• v.8 no.1
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• pp.84-98
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• 2005

This study is on improving the general engineering education for enhancing the quality of engineers at a local engineering school in which the students are not highly qualified for engineering education. Based on the analysis on the current engineering education by asking questions to professors, students and alumni of Hongik College of Science and Engineering, we have set the basic educational philosophy as educating practical engineers and have decided the goals of basic engineering education as changing to student oriented education, enhancing the field adaptation capability, improving the problem solving ability and introducing engineering design courses. For achieving the foregoing goals, we have changed several basic engineering courses. Mathematics, science courses, computer related courses, English, communication skill related courses are strengthened, but general college education courses are reduced. We also have encouraged students to participate the classes actively and study efficiently, think logically and creatively. For the operational details, we have tried to impose less courses to freshmen and sophomores, to impose the prerequisite courses, to activate summer and winter schools. Finally, we have tried to find the ways to support continuous improvement on the basic engineering education.