• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.617-636
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• 1999

This study was executed with the intention of guiding ‘open education’ toward a desirable school innovation. The basic two directions of curriculum reconstruction essential for implementing ‘open education’ are one toward intra-subject (within a subject) and inter-subject (among subjects). This study showed an example of intra-subject curriculum reconstruction with a problem solving area included in elementary mathematics curriculum. In the curriculum, diverse strategies to enhance ability to solve problems are included at each grade level. In every elementary math textbook, those strategies are suggested in two chapters called ‘diverse problem solving’, in which problems only dealing with several strategies are introduced. Through this method, students begin to learn problem solving strategies not as something related to mathematical knowledge or contents but only as a skill or method for solving problems. Therefore, problems of ‘diverse problem solving’ chapter should not be dealt with separatedly but while students are learning the mathematical contents connected to those problems. Namely, students must have a chance to solve those problems while learning the contents related to the problem content(subject). By this reasoning, in the name of curriculum reconstruction toward intra-subject, this study showed such case with two ‘diverse problem solving’ chapters of the 4th grade second semester's math textbook.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.397-414
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• 2005

In the existing literature, most of the purchasing models were developed only for retailers problem ignoring the constraint of storage capacity of retailers shop/showroom. In this paper, we have developed a deterministic model of wholesaler-retailers' problem of single product. The storage capacity of wholesaler's warehouse/showroom and retailers' showroom/shop are assumed to be finite. The items are transported from wholesaler's warehouse to retailers' Own Warehouse (OW) in a lot. The customer's demand is assumed to be displayed inventory level dependent. Demands are met from OW and that spaces of OW will immediately be filled by shifting the same amount from the Rented Warehouse (RW) till the RW is empty. The time duration between selling from OW and filling up its space by new ones from RW is negligible. According to relative size of the retailers' existing (own) warehouse capacity and the demand factors, different scenarios are identified. Our objectives are to optimize the cost functions of wholesaler and two retailers separately. To solve this problem, a real coded Genetic Algorithm (GA) with roulette wheel selection/reproduction, whole arithmetic crossover and non-uniform mutation is developed. Finally a numerical example is presented to illustrate the results for different scenarios. To compare the results of GA, Generalised Reduced Gradient Method has been used for the problem. Also, a sensitivity analysis has been performed to study the variations of the optimal average cost with respect to the different parameters.

• 컴퓨터교육학회논문지
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• 제13권5호
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• pp.71-80
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• 2010

지식정보화시대에 로봇은 현 시대가 요구하는 창의성 신장, 문제해결력 그리고 긍정적인 학습동기유발에 효과적인 도구라는 국내외의 다양한 연구결과가 발표되고 있다. 본 연구는 교수 학습 환경 개선측면으로 수학교과 학습에 로봇을 학습교구로 활용함으로써 교육적 효과를 검증하는데 목적이 있다. 초등학교 수학과 교육과정 및 로봇 프로그래밍 내용을 분석한 후 로봇통합 수학프로그램을 개발하였으며 초등학교 5학년 수학과 학습에 총 16차시에 걸쳐 투입하였다. 연구결과 전통적인 방식의 비교집단보다 로봇을 활용한 실험집단에서 학습태도 및 문제해결력이 높게 나타났다. 이것은 로봇 프로그래밍을 활용한 수학 학습이 문제해결력을 향상시켰으며, 긍정적 수학 학습경험을 제공한 것으로 보인다.

• 한국학교수학회논문집
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• 제9권1호
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• pp.1-17
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• 2006

현재 학교수학이 추구하는 목표는 수학의 기본적인 지식과 기능을 습득하고 수학적으로 사고하는 능력을 길러 실생활의 여러 가지 문제를 합리적으로 해결할 수 있는 능력과 태도를 기르는 것이다. 이에 부합하기 위해서 본 연구는 협동학습 모델 중 개별화 학습프로그램이 큰 장점인 TAI 모델과 특별한 소집단 성적 산출로 인해 모든 소집단 구성원이 소집단 성공에 기여할 수 있다는 장점을 가지고 있는 STAD 모델을 혼합하여 새로운 모델을 제시하였다. 이 새로운 혼합모델을 학교 현장에 적용하여 학습자의 문제해결능력 및 정의적 영역에 있어서 어떤 영향을 주는지 알아보았다.

• 한국학교수학회논문집
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• 제15권4호
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• pp.699-718
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• 2012

학생들이 문장으로 이루어진 문제를 해결과정에서 발생하는 오류의 유형을 분류하고, 각각의 오류 유형을 보인 학생들의 면담(인터뷰)을 통하여 오류를 범하게 된 요인을 분석하였다. 연구결과에 따라 나타난 대표적인 오류 유형은 '문항 이해의 부족', '풀이과정의 오류', '정리나 정의에 대한 왜곡된 이해', '이기과정의 오류', '기술적 오류', '풀이과정 생략' 등으로 나타났다. 또한 일부 학생들은 문장제에 대한 부담감으로 문제를 해결하기보다는 포기하는 현상이 나타났으며, 학생들은 문장으로 이루어진 문제를 해결을 하기 위해서 무엇보다 문제에 대한 이해가 필요한데, 이 부분이 절대적으로 부족하여 문제에서 주어진 자료를 자의적으로 판단하고 활용하는 경향이 짙게 보였다. 교사는 학생들이 문장제 문제 해결과정에서 발생하는 오류를 미리 파악하고 이를 보안할 수 있는 교수-학습방법으로 학생들을 지도한다면 오류를 사전에 예방하여 발생빈도를 줄일 수 있고, 학생들로 하여금 효과적인 학습이 이루어 질 수 있을 것이다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.231-242
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• 2006

National curriculum is very important for the future of nation. So, continuous efforts are needed to improve the national curriculum. This study examined the issues and the problems related with the 7th optional mathematics curriculum, and gave the message about th: methods of implementation. For this, we analyzed the result of the questionnaire survey which consisted in the question about the 7th optional mathematics curriculum. 264 high school mathematics teachers are participated in this survey. We found the result that the 7th optional mathematics curriculum has the problem in contents and management. So, this study gave not only the problem but also the various concrete methods for management of the 7th optional mathematics curriculum. We hope that mathematics education members research and argue about the optional mathematics curriculum for next curriculum.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.363-381
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• 2012

Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ${\psi}$ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.283-290
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• 2008

This paper is motivated by the problem of fitting a group of cuboids into a simplified rotating vessel of the artificial satellite. Here we introduce a combinatorial optimization model which reduces the three-dimensional layout problem with behavioral constraints to a finite enumeration scheme. Moreover, a global combinatorial optimization algorithm is described in detail, which is an improved graph-theoretic heuristic.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1533-1539
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• 2011

In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.