• Journal of Computing Science and Engineering
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• v.7 no.2
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• pp.99-111
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• 2013

Approximating a divergence between two probability distributions from their samples is a fundamental challenge in statistics, information theory, and machine learning. A divergence approximator can be used for various purposes, such as two-sample homogeneity testing, change-point detection, and class-balance estimation. Furthermore, an approximator of a divergence between the joint distribution and the product of marginals can be used for independence testing, which has a wide range of applications, including feature selection and extraction, clustering, object matching, independent component analysis, and causal direction estimation. In this paper, we review recent advances in divergence approximation. Our emphasis is that directly approximating the divergence without estimating probability distributions is more sensible than a naive two-step approach of first estimating probability distributions and then approximating the divergence. Furthermore, despite the overwhelming popularity of the Kullback-Leibler divergence as a divergence measure, we argue that alternatives such as the Pearson divergence, the relative Pearson divergence, and the $L^2$-distance are more useful in practice because of their computationally efficient approximability, high numerical stability, and superior robustness against outliers.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.383-404
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• 1999

This study began with an epistemological question about the nature of mathematical cognition in relation to the learner's activity. Therefore, by examining Piaget's 'reflective abstraction' theory which can be an answer to the question, we tried to get suggestions which can be given to the mathematical education in practice. 'Reflective abstraction' is formed through the coordination of the epistmmic subject's action while 'empirical abstraction' is formed by the characters of observable concrete object. The reason Piaget distinguished these two kinds of abstraction is that the foundation for the peculiar objectivity and inevitability can be taken from the coordination of the action which is shared by all the epistemic subjects. Moreover, because the mechanism of reflective abstraction, unlike empirical abstraction, does not construct a new operation by simply changing the result of the previous construction, but is forming re-construction which includes the structure previously constructed as a special case, the system which is developed by this mechanism is able to have reasonability constantly. The mechanism of the re-construction of the intellectual system through the reflective abstraction can be explained as continuous spiral alternance between the two complementary processes, 'reflechissement' and 'reflexion'; reflechissement is that the action moves to the higher level through the process of 'int riorisation' and 'thematisation'; reflexion is a process of 'equilibration'between the assimilation and the accomodation of the unbalance caused by the movement of the level. The operational learning principle of the theorists like Aebli who intended to embody Piaget's operational constructivism, attempts to explain the construction of the operation through 'internalization' of the action, but does not sufficiently emphasize the integration of the structure through the 'coordination' of the action and the ensuing discontinuous evolvement of learning level. Thus, based on the examination on the essential characteristic of the reflective abstraction and the mechanism, this study presents the principles of teaching and learning as following; $\circled1$ the principle of the operational interpretation of knowledge, $\circled2$ the principle of the structural interpretation of the operation, $\circled3$ the principle of int riorisation, $\circled4$ the principle of th matisation, $\circled5$ the principle of coordination, reflexion, and integration, $\circled6$ the principle of the discontinuous evolvement of learning level.

• The Mathematical Education
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• v.56 no.1
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• pp.119-130
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• 2017

The purpose of this study is to explain the long term growth and development of elementary teachers' Professional Learning Communities(PLC) about mathematics implemented on an institutional basis. Especially, it is meaningful to analyze and present the development process and characteristics of PLC, which was started by the basis on the collaboration of a National University of Education and its affiliated elementary school. In this study, PLC activities during three years were analyzed according to the capacities and dimensions of a professional learning community. The developmental capacity of the PLC analyzed in this study can be summarized as follows. In the first year, development of organizational competence in terms of capacity, resources, structure, and system of exchanges was the main factor in personal competence, and the development of individual competence began to share collective learning and practice. In the second year, personal exchanges were active in all the topics of activities, and personal level competence was activated such that more activities of critical knowledge formation were performed on an individual level. On the basis of the development of the individual level formed in the second, individual competence and organizational capacity developed. Factors that have influenced the development of capacities of PLC include: disclosure of activities outside the community, participation in outsiders, provision of procedures to share equal participation and leadership, voluntary and critical participation of teachers, improvement of mathematics teaching methods, sharing themes and visions.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.57-76
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• 2006

In this paper, we generalized number partion problems in elementary situations to number partition models that provide some mathematical problem situations for experiencing mathematising of secondary pre-service teachers. We designed substantial teaching units entitled 'the inquiry intof number partition models' through 4 steps: (1) key problems, (2) integration from the view of partition, (3) defining partition (4) a real practice of inquiry into models. This teaching unit can contribute to secondary pre-service teacher education as follows: first, This teaching unit have pre-service teachers experience mathemtising. second, This teaching unit have pre-service teachers see the connection between school mathematics and academic mathematics. third, This teaching unit have pre-service teachers foster their mathematical creativity.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.261-279
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• 2009

Permutation and combination are the subjects that most teachers feel difficult to teach in Mathematics. This paper investigated evaluation items and factors of anxiety of students for permutation and combination, and further examined the way to lessen the factors of anxiety. Two high school students participated for over a year from December 2007 to February 2008. Also, two teachers joined for the analysis of evaluation items. We found that the ill-structured problems and word problems are the main factors to bring about the anxiety, whereas cooperative learning with high intelligent peers, practice to read word problems and write the process of problems solving are helpful in lessening the mathematical anxieties. Further we propose that the study of appropriate teaching and learning method for permutation and combination should be performed in the future.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.161-177
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• 2020

This study constructed an experiment group and a comparative group, composed of high school students preparing for "Na" type math exam and provided one-to-many tutoring cooperative learning. This study tested the differences between group and between pre- and post-treatment scores by group using non-parametric statistics techniques. Moreover, this study conducted an open-type survey twice and had individual interviews to examine the affective domains of students. The difference in scores between the experimental group and the comparative group was not significant. However, the difference between pre- and post-treatment math scores was only significant in the experiment group among the three groups. Additionally, the student-teacher could reflect on him or her and improve self-efficacy while teaching other ordinary students. The ordinary students were more interested and motivated in the lessons and became more confident. In terms of mathematics competency, we could see that communication, problem-solving, reasoning, and attitude & practice were improved.

• Journal of Engineering Education Research
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• v.5 no.1
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• pp.77-84
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• 2002

The 18th century Joseon(朝鮮) science philosopher Hong Dae-Yong(洪大容, 1731-83) tried to create his own scientific system, while partially keeping the Eastern view of nature and accepting Western science and technology. Most of all, he confirmed that Western science and technology was based on mathematical principles and accurate observation and wrote a math book, [Juhaesuyong(籌解需用)]. Therefore, we have good reason to call him a mathematician. He produced so many achievements that he can be considered a natural scientist in the late Joseon era; he accepted the Eastern view of nature critically and sometimes refused it. He also suggested new and various scientific thoughts, including an infinite universe theory, on the basis of Western scientific thought. Hong Dae-Yong emphasized the importance of practice. He understood the principle of the Western Honcheonui(渾天儀) and manufactured an alarm clock with a craftsman's help. He was an excellent engineer and he set a personal observatory. Considering the level of scientific technology at that time, it is reasonable to regard Hong Dae-Yong as a 'scientific technologist in the 18th century Joseonera', well equipped as a mathematician, a natural scientist, and an engineer. In conclusion, it is with 'mathematical thinking, creative conception, and practical activities' that Hong Dae-Yong maintained throughout his life that we can set a guide to produce excellent Korean scientific technologists and engineers in the 21st century.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.349-368
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• 2008

The purpose of this study was to investigate the small-group instruction of mathematics in elementary schools. For this, a sample of 742 teachers of elementary schools completed the survey. As a result, about 27.8% of the teachers reported using small group instruction while they worked with one group or they assigned to other groups worked alone. Only 2% of the teachers reported using small group in which students were encouraged to participated cooperatively. This study discusses the five issues about small group instruction in elementary school. The five issues were investigated in this survey. First, major teaching method in mathematics classroom and using of small group instruction were described. Second, frequency and period of small-group instruction were reported. Third, grouping method in small-group instruction was described. And Fourth, effect grouping practices of small-group instruction were described. Fifth, the model of small group instruction and assessment in small-group instruction were reported.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.525-541
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• 2010

The purpose of this thesis is to investigate the effects of the topics in basic mathematics on academic achievement in order to improve the problem-solving abilities of low achievement students in university general mathematics. This program has been conducted from P University as a part of Education Capacity Enhancing Project. The goals of this program are to make students who have fear to mathematics feel confident for mathematics, and make easier to study general mathematics and major field without any difficulties for the students. The topics in basic mathematics was enforced with solving problem based on comprehension of the basic concept and computer-based learning. The classes were organized as Algebra-Geometry, Calculus, and General mathematics class by students' applications for classes and basic academic ability. As a result, the topics in basic mathematics has been evaluated as positive way to effect satisfaction and learning effect for the students who have low-level in basic academic ability. And also, according to the survey, the result shows that assignment through Webwork system and Mathematica program practice are helpful for learning basic mathematics. But several measures are asked for participation in the class and prevention for quitter of participants.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.221-229
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• 2023

Urbanization and industrialization have significantly increased the amount of solid waste produced in recent decades, posing considerable disposal problems and environmental burdens. The practice of waste utilization in concrete has gained popularity among construction practitioners and researchers for the efficient use of resources and the transition to the circular economy in construction. This study employed Lytag aggregate, an environmentally friendly pulverized fuel ash-based lightweight aggregate, as a substitute for natural coarse aggregate. At the same time, fly ash, an industrial by-product, was used as a partial substitute for cement. Concrete mix M20 was experimented with using fly ash and Lytag lightweight aggregate. The percentages of fly ash that make up the replacements were 5%, 10%, 15%, 20%, and 25%. The Compressive Strength (CS), Split Tensile Strength (STS), and deflection were discovered at these percentages after 56 days of testing. The concrete cube, cylinder, and beam specimens were examined in the explorations, as mentioned earlier. The results indicate that a 10% substitution of cement with fly ash and a replacement of coarse aggregate with Lytag lightweight aggregate produced concrete that performed well in terms of mechanical properties and deflection. The cementitious composites have varying characteristics as the environment changes. Therefore, understanding their mechanical properties are crucial for safety reasons. CS, STS, and deflection are the essential property of concrete. Machine learning (ML) approaches have been necessary to predict the CS of concrete. The Artificial Fish Swarm Optimization (AFSO), Particle Swarm Optimization (PSO), and Harmony Search (HS) algorithms were investigated for the prediction of outcomes. This work deftly explains the tremendous AFSO technique, which achieves the precise ideal values of the weights in the model to crown the mathematical modeling technique. This has been proved by the minimum, maximum, and sample median, and the first and third quartiles were used as the basis for a boxplot through the standardized method of showing the dataset. It graphically displays the quantitative value distribution of a field. The correlation matrix and confidence interval were represented graphically using the corrupt method.