• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.343-352
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• 2022

We present the user-friendly graphical user interface design and implementation of Monte Carlo simulation (MCS) for computing option price of the four-underlying asset step-down equity linked securities (ELS) using the Android platform. The ELS has been one of the most important and influential financial products in South Korea. Most ELS products are based on one-, two-, and three-underlying assets. However, currently there is a demand for higher coupon payment from ELS products because of the increased interest rate in financial market. In order to allow the investors to have higher coupon payment, it is necessary to design a multi-asset ELS such as four-asset step-down ELS. We conduct the computational experiments to demonstrate the performance of the Android platform for pricing four-asset step-down ELS. Furthermore, we perform a comparison test with a three-asset step-down ELS.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.1-23
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• 2005

The decentralized static output feedback design problem is considered. A constrained trust region method is developed that solves this optimal control problem when a complete set of state variables is not available. The considered problem is interpreted as a non-linear (non-convex) constrained matrix optimization problem. Then, a decentralized constrained trust region method is developed for this problem class exploiting the diagonal structure of the problem and using inexact computations. Finally, numerical results are given for the proposed method.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.235-256
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• 2020

The purpose of this study was to investigate the experience of pre-service mathematics teachers who attended at a university course combined with teaching practicum based on design thinking process to identify the change of their awareness of its activities. For the research, 8 pre-service mathematics teachers participated in a mathematics major course, consisting of 5 phases of design thinking formed by Stanford d.school. In the end of the course, qualitative data were collected through individual and focus group interviews and the course activities. By data analysis, the results of this study were as follows. Firstly, the participants' perspectives of design thinking activities were changed from the difficulty and ambiguity of its activity in the beginning of the process to positiveness with competence of solving authentic problem in terms of teaching practicum over time. Secondly, the participating pre-service teachers emphasized that design thinking activities helped them prepare well teaching practicum and raise understanding of students they met in the school fields. Thirdly, some research participants went through the difficulty in utilizing their products drawn from 4th phase (prototyping) of design thinking process depending on the acceptance of their guidance teachers. Fourthly, the research participants also pointed out that the design thinking was a significant activity in that they learned how to understand and communicate with their students and how to collaborate with team members and it gave an insight about the preparation for a class. Through these results, this study identified the possibility of using the design thinking process for pre-service mathematics teachers' teaching practicum. In addition, the research put forward some implications for better use of design thinking in teacher education.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.167-178
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• 1997

In this paper we present an application to airfoil design of an optimum design method based on optimal control theory. The method used here transforms the design problem by way of a change of variable into an optimal control problem for a distributed system with Neumann boundary control. This results in a set of variational inequalities which is solved by adding a penalty term to the differential equation. This si inturn solved by a finite element method.

• Research in Mathematical Education
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• v.11 no.1
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• pp.65-74
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• 2007

The algorithmic idea has been a kind of necessary mathematics quality for modern people in this information society. In China the algorithm was represented fully as one of the new mathematics contents in the secondary level for the first time when The Standards of Mathematics Curriculum for the Senior High School was promulgated in 2003, so the research about the teaching algorithm undoubtedly has its practical implications for mathematics education. In this paper, with the conceptual framework of The Mathematics Task Framework as the research tool, an algorithmic teaching case based on LOGO software was introduced in detail, and data by ways of observations, interviews and worksheets were collected, then the case was analyzed. The results showed that the teaching of algorithm is feasible and effective in the LOGO environment. Some beneficial implications about the instructional design of algorithm were also discussed.

• The Mathematical Education
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• v.49 no.2
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• pp.175-198
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• 2010

To understand natural or social phenomena, we need various information, knowledge, and thought skills. In this context, mathematics and sciences provide us with excellent tools for that purpose. This explains the reasons why there is always significant emphasis on mathematics and sciences in school education; some of the general goals in school education today are to illustrate physical phenomena with mathematical tools based on scientific consideration, to encourage students understand the mathematical concepts implied in the phenomena, and provide them with ability to apply what they learned to the real world problems. For the mentioned goals, we extract six fundamental principles for the integrated mathematics and science education (IMSE) from literature review and suggest a instructional design model. This model forms a fundamental of a case study we performed to which the IMSE was applied and tested to collect insights for design and practice. The case study was done for 10 students (2 female students, 8 male ones) at a coeducational high school in Seoul, the first semester 2009. Educational tools including graphic calculator(Voyage200) and motion detector (CBR) were utilized in the class. The analysis result for the class show that the students have successfully developed various mathematical concepts including the rate of change, the instantaneous rate of change, and derivatives based on the physical concepts like velocity, accelerate, etc. In the class, they described the physical phenomena with mathematical expressions and understood the motion of objects based on the idea of derivatives. From this result, we conclude that the IMSE builds integrated knowledge for the students in a positive way.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1021-1035
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• 2008

In this paper, we analyze an N-design call center with skill-based routing, in which one pool of agents handles two types of calls and another pool of agents handles only one type of calls. The approximate analysis is motivated by a computational complexity that has been observed in the direct stochastic approach and numerical method for finding performance measures. The workforce staffing policy is very important to the successful management of call centers. So the allocation scheduling of the agents can be considered as the optimization problem of the corresponding queueing system to the call center. We use a decomposition algorithm which divides the state space of the queueing system into the subspaces for the approximate analysis of the N-design call center with two different types of agents. We also represent some numerical examples and show the impact of the system parameters on the performance measures.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.683-700
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• 2016

The traditional teaching-learning in mathematics, which pursue only one correct answer, should be reexamined to cope with an age of uncertainty. In this research, Perry's epistemological development scheme was noticed as a theoretical approach to diagnose problems of dualistic mathematics lessons and to search solutions of the problems. And Design-Based Research method was adopted, We developed the epistemological development scheme through considering Perry's theory and related studies, scaffoldings and teaching-learning to enhance students' epistemological positions in mathematics. Based on these discussions we designed teaching experiment about operations with negative numbers, and analyzed its didactic implications.

• Educational Technology International
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• v.14 no.1
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• pp.75-108
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• 2013

The purpose of this study is to find a way to improve digital textbooks for self-regulated learning by applying cognitive scaffolding designs to an elementary math digital textbook and examining the effectiveness of the system. Hence this study was conducted in two steps. First, a framework for scaffolding design was devised by examining the problems and difficulties students encounter when using a mathematics digital textbook. Second, after the digital textbook was revised by applying the scaffolding design frameworks, the effectiveness of the scaffolding framework was examined by comparing students' achievement levels in an experimental group and that of students in a control group. Seventy fifth-graders participated in this study. Students were divided into two groups: an experimental group and a control group. The students in the experimental group studied with the revised version of the digital textbook and the students in the control group studied with the original version of the digital textbook. The students received a pretest before the experiment. After the experiment, they took an achievement test and completed a usability questionnaire. The data were analyzed by ANCOVA with the SPSS Windows version. The results revealed that the students who used the revised program (to which design strategies for scaffolding were applied) showed higher levels of achievement than those who used the original version. In addition, students in the experimental group generally showed higher scores on the usability survey, which consisted of four sub-categories such as 'effectiveness', 'efficiency', 'satisfaction', and 'learnability'. There was a statistically significant effect on 'efficiency'. These results implied that scaffolding strategies were effective for mathematics learning through the use of an elementary digital textbook.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.13-20
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• 2001

Interaction through communication plays critical role in the mathematics learning in the sociocultural perspectives. The communication make the students construct shared knowledge, and also plays a role of mediation in making meaning. So, we have to consider sociocultural eprspectives in design of the mathematics leaning using computer. While Computer Assisted Instruction was the one-directional teaching program which proceed from computer to students, mathematics leaning using computer in the sociocultural perspectives have to consider two-directional instruction that proceed from computer to students as well as from students to computer. This interactional activity is the critical thing in the mathematics learning using computer.