• Advances in nano research
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• v.16 no.6
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• pp.623-638
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• 2024

This study investigates the thermal post-buckling behavior of concrete eccentric annular sector plates reinforced with graphene oxide powders (GOPs). Employing the minimum total potential energy principle, the plates' stability and response under thermal loads are analyzed. The Haber-Schaim foundation model is utilized to account for the support conditions, while the transform differential quadrature method (TDQM) is applied to solve the governing differential equations efficiently. The integration of GOPs significantly enhances the mechanical properties and stability of the plates, making them suitable for advanced engineering applications. Numerical results demonstrate the critical thermal loads and post-buckling paths, providing valuable insights into the design and optimization of such reinforced structures. This study presents a machine learning algorithm designed to predict complex engineering phenomena using datasets derived from presented mathematical modeling. By leveraging advanced data analytics and machine learning techniques, the algorithm effectively captures and learns intricate patterns from the mathematical models, providing accurate and efficient predictions. The methodology involves generating comprehensive datasets from mathematical simulations, which are then used to train the machine learning model. The trained model is capable of predicting various engineering outcomes, such as stress, strain, and thermal responses, with high precision. This approach significantly reduces the computational time and resources required for traditional simulations, enabling rapid and reliable analysis. This comprehensive approach offers a robust framework for predicting the thermal post-buckling behavior of reinforced concrete plates, contributing to the development of resilient and efficient structural components in civil engineering.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• Korean Journal of Radiology
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• v.22 no.10
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• pp.1697-1707
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• 2021

The recent introduction of various high-dimensional modeling methods, such as radiomics and deep learning, has created a much greater diversity in modeling approaches for survival prediction (or, more generally, time-to-event prediction). The newness of the recent modeling approaches and unfamiliarity with the model outputs may confuse some researchers and practitioners about the evaluation of the performance of such models. Methodological literacy to critically appraise the performance evaluation of the models and, ideally, the ability to conduct such an evaluation would be needed for those who want to develop models or apply them in practice. This article intends to provide intuitive, conceptual, and practical explanations of the statistical methods for evaluating the performance of survival prediction models with minimal usage of mathematical descriptions. It covers from conventional to deep learning methods, and emphasis has been placed on recent modeling approaches. This review article includes straightforward explanations of C indices (Harrell's C index, etc.), time-dependent receiver operating characteristic curve analysis, calibration plot, other methods for evaluating the calibration performance, and Brier score.

• Journal of the Korea Society of Computer and Information
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• v.25 no.2
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• pp.241-250
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• 2020

In this paper, we propose a direction of teaching method for future generations. In order to suggest such the direction, teaching and learning materials that integrate coding activities and mathematical modeling were developed through top-down and bottom-up processes. Coding and engineering experts and mathematics education experts developed teaching and learning materials through councils (top-down courses) and applied them to 24 high school first graders based on student responses (bottom-up courses). Additionally, the developed curriculum helped students increase interest and motivation and realize conceptual understanding, problem posing, and problem solving in mathematics. On the basis of these results, it provided an idea about how to develop curriculum combining mathematical modeling with coding activities, needed for the fourth industrial revolution.

• Research in Mathematical Education
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• v.27 no.1
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• pp.129-150
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• 2024

This study utilized South Korean elementary and middle school student data to examine the longitudinal change trajectories of learning motivation types according to the longitudinal change trajectories of mathematics academic achievement. Growth mixture modeling, latent growth model, and multiple indicator latent growth model were used to examine various change trajectories for longitudinal data. As a result of the analysis, it was classified into 4 subgroups with similar longitudinal change trajectories of mathematics academic achievement, and the characteristics of the mathematics subject, which emphasize systematicity, appeared. Furthermore, higher mathematics academic achievement was associated with higher self-determination and higher academic motivation. And as the grade level increases, amotivation increases and self-determination decreases. This study suggests that teaching and learning support using this is necessary because the level of learning motivation according to self-determination is different depending on the level of mathematics academic achievement reflecting the characteristics of the student.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.233-241
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• 2005

Mathematics has developed dramatically in today's world and come to be increasingly put into practical use in various fields in society. However, many Japanese students dislike mathematics. We have to study mathematics education with this situation in our mind. When we consider a better educational material, we don't have to consider only within the framework of the current school mathematics. We can expect to find good mathematical materials in fields beyond the school mathematics. In this paper, we study how the inclusion of idea such as 'fuzzy theory' and 'graph theory' influences pupils' approaches to learning mathematics.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.133-152
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• 2004

In this paper, we discuss students' conceptual development of eigen value and eigen vector in differential equation course based on reformed differential equation using the mathematical model of mass spring according to historico-generic principle. Moreover, in setting of small group interactive learning, we investigate the students' development of mathematical attitude.

• Education of Primary School Mathematics
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• v.8 no.1
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• pp.33-50
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• 2004

This study is intended to investigate the effect on the development of multiplicative thinking and multiplicative ability by teaching repeated addition, rate, comparison, area-array, and combination problems. Two research questions are established: first, is there any difference of multiplicative thinking between the experimental group(the modeling of problem situation learning group) and the control group(the traditional learning group)\ulcorner Second, is there any difference of multiplicative ability between the experimental group and the control group\ulcorner The treatment process for the experimental group is based on modeling problem situations for nine lesson periods. In order to answer the research questions the chi-square analysis was used for the first research question and the t-test was used for the second one. The findings are summarized as follows: there is no significant difference of multiplicative thinking be1ween the experimental and the control group but there is significant difference of multiplicative ability.

• Research in Mathematical Education
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• v.6 no.2
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• pp.159-170
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• 2002

The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing developmental research effort to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the teaching and learning of differential equations at Ewha Womans University. The RME theory based on the design heuristic using context problems and modeling was developed for primary school mathematics. However, the analysis of this study indicates that a RME design for a differential equations course can be successfully adapted to the university level.