• 한국컴퓨터정보학회논문지
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• 제20권9호
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• pp.21-29
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• 2015

The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.

• 대한산업공학회지
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• 제40권4호
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• pp.396-403
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• 2014

The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).

• 한국수학사학회지
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• 제32권6호
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• pp.281-299
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• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• 한국과학교육학회지
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• 제14권2호
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• pp.143-158
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• 1994

This study aims to identify the characteristics of gas phase problem solving of college freshmen. Four students were participated in this study and solved the problem by using think-aloud method. The thinking processes were recorded and transferred into protocols. Problem solving stage, the ratio spended in each solving stage, solving strategy, misconceptions, and errors were identified and discussed. The relationships between students' belief system about chemistry problem solving and problem solving characteristics were also investigated. The results were as follows: 1. Students felt that chemical equation problem was easier than word problem or pictorial problem. 2. When students had declarative knowledge and procedural knowledge required by given problem, their confidence level and formula selection were not changed by redundunt information in the problem. 3. When the problem seemed to be difficult, students tended to use the Means-End or Random strategy. 4. In complicated problems, students spent longer time for problem apprehension and planning. In familiar problems, students spent rather short time for planning. 5. Students spent more time for overall problem solving process in case of using Means-End or Random strategy than using Knowledge-Development strategy.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권1호
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• pp.1-31
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• 2007

Recent research has documented that there is a close relationship between problem posing and problem solving in arithmetic. However, most studies investigated the relationship between problem posing and problem solving only by means of standard problem situations. In order to overcome that shortcoming, a pilot study with Chinese fourth-graders was done to investigate this relationship using a non-standard, realistic problem situation. The results revealed a significant positive relationship between students' problem posing and solving abilities. Based on that pilot study, a more extensive and systematic ascertaining study was carried out to confirm the observed relationship between problem posing and problem solving among Chinese elementary school children. Results confirmed that there was indeed a close relationship between both skills.

• 가정과삶의질연구
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• 제17권1호
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• pp.155-166
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• 1999

The purpose of this study was to analyze a causal relationship of children's behavior problem and the related variables(socio-economic status mother's psychological problem mother's affective parenting behavior children's negative emotionality and children's self-control). The major findings of this study were as follows: 1) Socio-economic status had indirect in influence to children's behavior problem via mother's psychological problem and mother's affective parenting behavior. 2) Mother's psychological problem had direct influence and also indirect influence to hildren's behavior problem via mother's affective parenting behavior and children's negative emotionality. 3) Mother's affective parenting behavior and children's negative emotionality had a direct effect on children's behavior problem and affected indirectly via children's self-control. 4) Children's self-control had direct influence to children's behavior problem. 5) Mother's psychological problem was the most signi icant variable affecting children's behavior problem.

• 대한지구과학교육학회지
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• 제7권1호
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• pp.133-143
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• 2014

The purpose of this study was to examine the effect of scientific discussion classes focusing problem finding on the primary school students' scientific creative problem solving ability, science process skills and attitude toward science class. To verify this research problem, the subject of this study was fifth-grade students selected from four classes of M elementary school located in Busan city. For four months, the experimental group of 51 students was taught using the "scientific discussion classes focusing problem finding". The control group also of 53 students was taught in normal classes which used a text-book. All students were given pre and post test to verify the effects of scientific discussion classes focusing problem finding on the primary school students' scientific creative problem solving ability, science process skills and attitude toward science class. The results from this study are as the following. First, the scientific discussion classes focusing problem finding were effective in scientific creative problem solving ability among the primary school students. It is possibly because in the process where one student compare his/her own thoughts with the others' ones and discuss them. Second, the scientific discussion classes focusing problem finding were effective in science process skills among the primary school students. Third, the scientific discussion classes focusing problem finding were effective in attitude toward science class. In conclusion, the scientific discussion classes focusing problem finding had positive effects on improvement of primary school students' scientific creative problem solving ability, science process skills and also could lead to a change in students' cognition about science class to a positive way. Therefore, the scientific discussion class focusing problem finding is hopefully to be provided as an effective instructive strategy of science class in school in the future.

• 한국학교수학회논문집
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• 제21권1호
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• pp.63-89
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• 2018

본 연구에서는 예비수학교사들의 수학적 문제제기 교육에 대한 전문성 신장을 위하여 예비수학교사 교육에 적용할 수 있는 문제제기 수업을 개발하여 적용한 후 연구에 참여한 예비수학교사들의 문제제기에 대한 인식의 변화 및 문제제기 수업 경험에 대한 의견을 살펴보았다. 본 연구에서 개발한 문제제기 수업은 문제제기 이론에 대한 교육, 문제제기 활동 체험, 문제제기 수업 지도안 작성 및 수업 수행의 3단계로 구성되었다. 설문 조사, 면담, 수업 일지 분석 결과를 종합하여 보면, 본 연구를 통해 수행된 문제제기 수업은 예비수학교사들의 문제제기 활동 및 문제제기 전략에 대한 이해도와 문제제기 교육의 효과에 대한 이해도를 향상시키는데 매우 효과적인 것으로 나타났고, 이와 더불어 예비교사들의 문제제기 활동에 대한 긍정적인 태도의 함양에도 효과적인 것으로 나타났다. 특히, 문제제기 수업에서 이루어진 다양한 문제제기 활동에 대한 직접적인 체험과 문제제기 수업 수행 경험이 예비교사들의 문제제기에 대한 이해 및 교수학적 내용 지식의 함양에 핵심적인 역할을 한 것으로 나타났다.

• 대한수학교육학회지:학교수학
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• 제3권1호
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• pp.1-23
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• 2001

In this paper, contents related to problem solving in 7th elementary mathematics curriculum analyzed in five aspects: problem solving stages, problem solving strategies, problems, problem posing, and assessment on problem solving abilities. From the results and processes of analysis, following conclusions are obtained: First, it is difficult to say the contents related to problem solving in 7th elementary mathematics curriculum are prepared organically. Second, it is difficult to say that contents related to problem solving in 7th elementary mathematics curriculum reflect results of recent researches.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.673-687
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• 2022

In this study, we solve the Cayley inclusion problem and the fixed point problem in real Hilbert space using Tseng's technique with inertial extrapolation in order to obtain more efficient results. We provide a strong convergence theorem to approximate a common solution to the Cayley inclusion problem and the fixed point problem under some appropriate assumptions. Finally, we present a numerical example that satisfies the problem and shows the computational performance of our suggested technique.