• The Mathematical Education
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• v.24 no.2
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• pp.105-116
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• 1986

For any thought and knowledge, its growth and development has close relation with the society where it is developed and grow. As Feuerbach says, the birth of spirit needs an existence of two human beings, i. e. the social background, as well as the birth of body does. But, at the educational viewpoint, the spread and the growth of such a thought or knowledge that influence favorably the development of a society must be also considered. We would discuss the goal and the function of mathematics education in relation with the prosperity of a technological civilization. But, the goal and the function are not unrelated with the spiritual culture which is basis of the technological civilization. Most societies of today can be called open democratic societies or societies which are at least standing such. The concept of rationality in such societies is a methodological principle which completes the democratic society. At the same time, it is asserted as an educational value concept which explains comprehensively the standpoint and the attitude of one who is educated in such a society. Especially, we can considered the cultivation of a mathematical thinking or a logical thinking in the goal of mathematics education as a concept which is included in such an educational value concept. The use of the concept of rationality depends on various viewpoints and criterions. We can analyze the concept of rationality at two aspects, one is the aspect of human behavior and the other is that of human belief or knowledge. Generally speaking, the rationality in human behavior means a problem solving power or a reasoning power as an instrument, i. e. the human economical cast of mind. But, the conceptual condition like this cannot include value concept. On the other hand, the rationality in human knowledge is related with the problem of rationality in human belief. For any statement which represents a certain sort of knowledge, its universal validity cannot be assured. The statements of value judgment which represent the philosophical knowledge cannot but relate to the argument on the rationality in human belief, because their finality do not easily turn out to be true or false. The positive statements in science also relate to the argument on the rationality in human belief, because there are no necessary relations between the proposition which states the all-pervasive rule and the proposition which is induced from the results of observation. Especially, the logical statement in logic or mathematics resolves itself into a question of the rationality in human belief after all, because all the logical proposition have their logical propriety in a certain deductive system which must start from some axioms, and the selection and construction of an axiomatic system cannot but depend on the belief of a man himself. Thus, we can conclude that a question of the rationality in knowledge or belief is a question of the rationality both in the content of belief or knowledge and in the process where one holds his own belief. And the rationality of both the content and the process is namely an deal form of a human ability and attitude in one's rational behavior. Considering the advancement of mathematical knowledge, we can say that mathematics is a good example which reflects such a human rationality, i. e. the human ability and attitude. By this property of mathematics itself, mathematics is deeply rooted as a good. subject which as needed in moulding the ability and attitude of a rational person who contributes to the development of the open democratic society he belongs to. But, it is needed to analyze the practicing and pursuing the rationality especially in mathematics education. Mathematics teacher must aim the rationality of process where the mathematical belief is maintained. In fact, there is no problem in the rationality of content as long the mathematics teacher does not draw mathematical conclusions without bases. But, in the mathematical activities he presents in his class, mathematics teacher must be able to show hem together with what even his own belief on the efficiency and propriety of mathematical activites can be altered and advanced by a new thinking or new experiences.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.17-48
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• 2017

This case study examined mathematics anxiety of a public high school sophomore who was unable to perform well in mathematics but later overcame his fear of mathematics. In this study, he showed high levels of mathematics anxiety in the assessment tools that evaluate mathematical anxiety factors. Cognitive and behavior treatments were carried out to alleviate his anxiety. First, cognitive treatments that were implemented include: understanding his own problems, writing down his thoughts on a record sheet, and changing intermediate and core beliefs. This paper explored cognitive and affective changes and reactions during the treatment process. Second, behavioral treatments that were conducted include: the divided-page method and peer tutoring. The divided-page technique involves the test subject to write down and solve his problems on a note to see what kind of cognitive and affective changes occur during the process. This paper also explored how Su-chul, an overly competitive student, changed and reacted cognitively and affectively through peer tutoring. The results revealed that Su-chul's exam anxiety, as well as other factors, has decreased. Moreover, he regained his self-confidence by solving math problems that he had felt difficult. His competitive attitude also has turned into a cooperative and thoughtful one.

• The Mathematical Education
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• v.49 no.1
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• pp.15-37
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• 2010

In this study, we investigated the application of oriental history of mathematics in school mathematics teaching. We set up three study problems to achieve this purpose. First, we analyze the middle and high school mathematics textbooks and auxiliary books. Second, we survey the mathematics teacher's knowledge and degree of application on history of mathematics. Third, we develop the teaching and learning materials on oriental history of mathematics. We performed three study-methods to settle above study problem. First, we analyzed 24 textbooks and auxiliary books for study problem 1. There were 6 middle school mathematics textbooks and 6 auxiliary books and also 6 high school mathematics textbooks and 6 auxiliary books. We categorized the contents into "anecdote", "systematization", "application of problem", "expansibility of thought", and "comparative of the contents". Second, we surveyed the 78 mathematics teachers's knowledge and degree of application using questionnaire about knowledge and application on history of mathematics. The questionnaire was made up of four types of question; the effect of material about history of mathematics, the understanding of western history of mathematics, the understanding of oriental history of mathematics; the direction of development of teaching material. Third, we exemplified the teaching and learning materials about three categories: "anecdote", "comparative of the contents".

• Geomechanics and Engineering
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• v.22 no.6
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• pp.519-528
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• 2020

A mathematical wetting model is usually used to predict the deformation of core wall rockfill dams induced by the wetting effect. In this paper, a series of wetting triaxial tests on a rockfill was conducted using a large-sized triaxial apparatus, and the wetting deformation behavior of the rockfill was studied. The wetting strains were found to be related to the confining pressure and shear stress levels, and two empirical equations, which are regarded as the proposed mathematical wetting model, were proposed to express these properties. The stress and deformation of a core wall rockfill dam was studied by using finite element analysis and the proposed wetting model. On the one hand, the simulations of the wetting model can estimate well the observed wetting strains of the upstream rockfill of the dam, which demonstrated that the proposed wetting model is applicable to express the wetting deformation behavior of the rockfill specimen. On the other hand, the simulated additional deformation of the dam induced by the wetting effect is thought to be reasonable according to practical engineering experience, which indicates the potential of the model in dam engineering.

• East Asian mathematical journal
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• v.24 no.5
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• pp.547-564
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• 2008

The purpose of this study was to investigate 5th graders' performance for mixed operational problem. For this purpose. two kinds of studies were conducted: a descriptive study by pencil and paper tests(32 problems) and a clinical study by interviews. The conclusions drawn from the results obtained in this study were as follows: First, students were highly scored in pencil and paper tests(M=85.25%). But that score is not up to scratch. Because the problem was composed of simple calculations and if students calculate problems from only let side, they gel 75% right answer, etc. Second, most of students solved mixed operational problems by text-based way, but some students solved flexibly. There are several error types. The main error type is students' following the wrong order of calculations. Some students have obstacles to express their thought with numerical expressions. So they make errors. Third, students solve mixed operational problems with various strategies. For examples, they solve problems by describing calculation procedures, drawing lines to indicate the order of calculations, carrying out two numerical expressions, etc.

• The Mathematical Education
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• v.47 no.4
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

• The Mathematical Education
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• v.48 no.3
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• pp.265-285
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• 2009

In this study, we investigate the science and mathematics articles in Hansungsunbo and Hansungjubo which are the first modernistic newspapers in Korea. Hansungsunbo was published from October 31, 1883 to December 4, 1884 and Hansungjubo was issued from January 25, 1886 to July, 1888. While these papers were published, Korea had concluded a treaty with America(1882), England(1883), Germany(1883), Russia, and France(1884). Therefore, Korea had a lot of problems with commercial relations, the civilization and enlightenment of the Korean society. In this situation, some leaders who had the enlightenment thought published these two papers in order to inform the Korean people of the worldwide news on the politics, economy, history, science and technology, and so on. In this paper, we bring up the title and the contents on the science articles and the mathematics test problems of 'Dongmoonguan' and 'Chunjinmoobi School'.

• Research in Mathematical Education
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• v.22 no.1
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• pp.19-33
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• 2019

While the field of mathematics education strives to promote equitable mathematics learning and identifies it as a core instructional practice, less is known about its effective enactment. As teachers' teaching practices are dependent on their views and beliefs, this study investigated 133 elementary pre-service teachers' (PSTs') interpretations of diverse learners' learning experiences and proposed accommodations for them as reflected in their lesson planning process. Findings showed that PSTs came up with some strategies that are often suggested in teacher education literature, such as using multiple modes of representation and various grouping strategies. However, their responses were generic in nature rather than specific to diverse learners. Also, it was noted that many PSTs' interchangeably referred to the English Language Learners (ELLs), struggling learners, and culturally diverse learners, inferring that they thought that culturally diverse students must have been ELLs and that ELLs or culturally diverse students must have been weaker students in math. We found that the PSTs used their own frames while filtering and discarding information about diverse student populations to develop instructional plans, rather than based on the results of assessments of learning. We suggest that it is the critical first step to unwrap PSTs' unproven assumptions to better equip them for working with all of their future students.

• Journal of Elementary Mathematics Education in Korea
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• v.4 no.1
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• pp.39-55
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• 2000

The purpose of this research is to analyse Korean elementary mathematics curriculum taking a philosophical view of mathematics education. In this research, 1 will analyze not only the current elementary mathematics curriculum but also the past ones. There have been intermittently quantitative and external analysis so far to comprehend the elementary mathematics curriculum. But, I thought we also need qualitative and internal comprehension and examined the curriculums through a philosophical analysis. Generally, mathematics curriculums at every period have their own mathematical philosophy consciously or tacitly. And, the school mathematics is the practice of mathematics curriculum based on that mathematical philosophy. Mathematical curriculum reflects both the philosophical aspect in mathematical philosophy that forms the background of the mathematical curriculum and the sociological aspect in real-class that is the output of the curriculum. With this view, the logic of social constructivism can be an appropriate way that leads mathematical philosophical analysis and sociological analysis in mathematics education. So, I comprehend the tendency of the Korean elementary mathematics curriculum from the first to the seventh through the philosophical views. In view of the results so far achieved, after the second half of the 20th century, the Korean mathematical curriculums mainly have the tendency from the Ideology of progressive educator (the first) to of technological pragmatist (the second), from that of old humanist (the third and forth) to progressive educator (the fifth and sixth), and lastly that of social constructivism (the seventh).