• Journal for History of Mathematics
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• v.24 no.2
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• pp.47-59
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• 2011

Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

• School Mathematics
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• v.13 no.3
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• pp.423-446
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• 2011

In school mathematics, concepts of definite integral and integration by substitution have mathematical connection with introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. However, we have difficulty in finding mathematical connection between integration and continuous probability distribution in the curriculum manual, 13 kinds of 'Basic Calculus and Statistics' and 10 kinds of 'Integration and Statistics' authorized textbooks, and activity books applied to the revised curriculum. Therefore, the purpose of this study is to provide a teaching method connected with mathematical concepts of integral in regard to three concepts in continuous probability distribution chapter-introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. To find mathematical connection between these three concepts and integral, we analyze a survey of student, the revised curriculum manual, authorized textbooks, and activity books as well as 13 domestic and 22 international statistics (or probability) books. Developed teaching method was applied to actual classes after discussion with a professional group. Through these steps, we propose the result by making suggestions to revise curriculum or change the contents of textbook.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.305-321
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• 2019

Rapid demographic changes such as international marriages and immigration have led to the transition of Korea to a multicultural society, thereby causing the need for education for multicultural students. In particular, there is a growing need to support Korean Language Learners (KLLs) who learn in Korean in their classrooms and whose native language is a foreign language. This study aims to adapt some teaching strategies of the SIOP model developed in the U.S. for English Language Learners(ELLs) to fit classroom situations in Korea and apply them to the Korean language learners to analyze the features of mathematical communication and to examine the possibility of a change in mathematical errors. Specifically, three KLLs in 5th grade participated in seven geometry lessons adapting some characteristics of SIOP model and then, their mathematical communication and mathematical errors were analyzed. The results of this study are expected to provide didactical implications for identifying characteristics of KLLs and for setting direction for teaching them mathematics.

• Journal of the Korean School Mathematics Society
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• v.22 no.1
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• pp.23-45
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• 2019

The purpose of this research is to analyze the effect of storytelling teaching on the mathematical attitudes of Mathematics underachieved third-grade middle school students. 5 students with lower than 20% of math grades were selected and they were provided 36 hours of the storytelling teaching program in 18 weeks. The participant students took the mathematical attitudes questionnaires both before and after the storytelling teaching classes. As a result of the study, the mean score of the before and after questionnaires was increased, and t-test also had statistically significant results. In particular, the various details of mathematical attitudes revealed the greatest positive change in 'the application of learning technology', followed by 'interest' and 'self-study'. Therefore, we found that the storytelling teaching program has a positive effect on the mathematical attitudes of underachieved students.

• The Mathematical Education
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• v.57 no.3
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• pp.231-246
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• 2018

In this paper, we applied Sfard's reification theory to analyze the secondary students' level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget's theory as a criterion of content judgement in order to grasp students' conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the $9^{th}$ and $10^{th}$ graders. The main results are as follows. First, approximately 45% of $9^{th}$ graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of $10^{th}$ graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of $9^{th}$ graders, and there was no change in $10^{th}$ graders.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2000.05a
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• pp.28-35
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• 2000

For the merit of a container in transportation and cargo handling the amount of container freight has been continuously on the increase. On the other hand container crane had got the bottle neck in cargo handling due to low productivity so that freight congestion had been often occurred at ports. in this paper A mathematical model for container crane system is represented a method for designing a fuzzy controller of container crane system for high productivity in cargo handling is presented. The fuzzy controller is compared with other optimal controller at the same condition. in the computer simulation the fuzzy controller obtained an excellent response to reference change better than the optimal controller. For disturbance such as a strong storm and parameter change due to change of cargo weight the result was also stable and robust than the optimal controller.

• Proceedings of the KIEE Conference
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• 2000.07a
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• pp.376-378
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• 2000

The current worldwide electricity market introduced competition, which is breaking up the monopoly structure and also enforcing phased structural reform in South Korea. The change of the electricity charge from cost base to price base due to the introduction of the electricity market competition causes consumer to choose a variety of charge schemes and a portion of loads to be affected by this change. Therefore, in order to find a mathematical model of the sensitively-responding-to-price loads and reflect this to the DSM demand management, the price-sensitive load model is needed. Thus, this paper first proposes the composite price-sensitive load model that is expressed as a function of price, presents the methodology to estimate price-sensitive load model at each bus by bus load compositions.

• Journal of Mechanical Science and Technology
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• v.19 no.4
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• pp.958-967
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• 2005

The mathematical model for tension behaviors of a moving web by Shin (2000) is extended to the tension model considering the thermal strain due to temperature variation in furnace. The extended model includes the terms that take into account the effect of the change of the Young's Modulus, the thermal coefficient, and the thermal strain on the variation of strip tension. Computer simulation study proved that the extended tension model could be used to analyze tension behaviors even when the strip goes through temperature variation. By using the extended tension model, a new tension control method is suggested in this paper. The key factors of suggested tension control method include that the thermal strain of strip could be compensated by using the velocity adjustment of the helper-rollers. The computer simulation was carried out to confirm the performance of the suggested tension control method. Simulation results show that the suggested tension control logic not only overcomes the problem of the traditional tension control logic, but also improves the performance of tension control in a furnace of the CAL (Continuous Annealing Line).

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.47-64
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• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.