• Journal of the Korea Society of Computer and Information
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• v.20 no.9
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.4
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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).

• Journal for History of Mathematics
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• v.32 no.6
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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.

• Journal of The Korean Association For Science Education
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• v.14 no.2
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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.

• Research in Mathematical Education
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• v.11 no.1
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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.

• Journal of Families and Better Life
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• v.17 no.1
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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.

• Journal of the Korean Society of Earth Science Education
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• v.7 no.1
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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.

• Journal of the Korean School Mathematics Society
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• v.21 no.1
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• pp.63-89
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• 2018

In this study, the researcher developed a course integrated mathematical problem posing activities in order to enhance pre-service mathematics teachers' ability to carry out problem posing activities in mathematics classroom, and examined the changes of pre-service mathematics teachers' perceptions about problem posing through the course. The problem posing course developed in this study consisted of three stages: education on the theories regarding problem posing; activities with problem posing; development and implementation of problem posing tasks. According to the results of the questionnaires, interviews, and class journals data analysis, the problem posing experiences provided in this study were very effective in improving pre-service mathematics teachers' understanding of the problem posing strategies and the benefit of problem posing activities to student learning. Particularly, the experience in various problem posing activities and the implementation experience of problem posing provided in the course played a key role in the improvement of pre-service mathematics teachers' understanding of problem posing and PCK.

• School Mathematics
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• v.3 no.1
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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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• v.62 no.4
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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.