• Research in Mathematical Education
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• v.15 no.4
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• pp.311-325
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• 2011

In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.621-634
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• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.219-233
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• 2012

Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.59-72
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• 2005

The auxiliary principle is used to suggest and analyze some iterative methods for solving solving hemivariational inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. Since hemivariational in­equalities include variational inequalities and nonlinear optimization problems as special cases, our results continue to hold for these problems.

• Journal of the military operations research society of Korea
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• v.13 no.1
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• pp.91-100
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• 1987

This paper deals with an algorithm for solving nonlinear programming problems with equality constraints. Nonlinear programming problems are transformed into a square sums of nonlinear functions by the Lagrangian multiplier method. And an iteration method minimizing this square sums is suggested and then an algorithm is proposed. Also theoretical basis of the algorithm is presented.

• Journal of The Korean Association For Science Education
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• v.25 no.4
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• pp.526-532
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• 2005

The purpose of this study was to analyze physics problem solving processes to qualitative and quantitative problems in the area of 'Force and Motion' in high school science. The students who have already learned the area of 'Force and Motion' during the first semester of 10th grade have taken physics test to choose students who have basic knowledge of physics. Eight students were selected. After explaining the purpose and the procedure of this study, think-aloud method was instructed to the students, and the students practiced it. After that, the students solved three problems in each quantitative and qualitative type. Then, the questionnaire of belief system on physics and physics problem solving and the prerequisite knowledge test were administered. By recording the students' solving processes, protocol was made and analyzed. After solving problems, the students expressed their confidence, intimacy, and preference. Quantitative problems needed much time at planning step than qualitative problems did. Moreover, solving time was longer and repeating frequency was more than those of qualitative problems. It seemed because even though the students qualitatively knew the answer, they should determine the given quantitative conditions, consider formulae, and recall the specific numbers. Since the students usually got access to many quantitative items in their physics study, they were accustomed to solve problems by using formulae. In addition, they put confidence in formulae, so they tended to solve problems quantitatively. As the result, they preferred quantitative problems to qualitative problems.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.19-26
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• 2003

The purpose of this study is twofold: (i) to argue the importance of problem solving strategy in education and (m to propose an efficient way to use the problem-solving strategy, which is based on the survey to find out how well elementary school teachers recognize the importance of the strategy. Forty elementary school teachers participated in the survey. The result of the survey shows that they do not use various strategies when they solve problems. It also shows that the rate of wrong answers the teachers get when solving problems is pretty high because they adopt a wrong strategy. It is prerequisite that teachers recognize the importance of the strategy when solving problems and put into practice various strategies in order to help their students improve their problem-solving abilities.

• School Mathematics
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• v.5 no.3
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• pp.361-384
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• 2003

The purpose of this study was to investigate students' problem solving process based on the model of IDEAL if they learn to solve word problems of simultaneous linear equations through structure-representation instruction. The problem solving model of IDEAL is followed by stages; identifying problems(I), defining problems(D), exploring alternative approaches(E), acting on a plan(A). 160 second-grade students of middle schools participated in a study was classified into those of (a) a control group receiving no explicit instruction of structure-representation in word problem solving, and (b) a group receiving structure-representation instruction followed by IDEAL. As a result of this study, a structure-representation instruction improved word-problem solving performance and the students taught by the structure-representation approach discriminate more sharply equivalent problem, isomorphic problem and similar problem than the students of a control group. Also, students of the group instructed by structure-representation approach have less errors in understanding contexts and using data, in transferring mathematical symbol from internal learning relation of word problem and in setting up an equation than the students of a control group. Especially, this study shows that the model of direct transformation and the model of structure-schema in students' problem solving process of I and D stages.

• East Asian mathematical journal
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• v.35 no.2
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• pp.115-139
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• 2019

In problem solving education, sentence problems are a tool for comprehensive evaluation of mathematical ability. The sentence problems refer to the problem expressed in sentence form rather than simply a numerical representation of mathematical problems. In order to solve sentence problems with a mixture of mathematical terms and general language, problem-solving ability including the ability to understand the meaning of sentences as well as the mathematical computation ability is required. Therefore, it is important to analyze syntactic elements from the linguistic aspects in sentence problems. The purpose of this study is to investigate the complexity of sentence problems in the length of sentences and the grammatical complexity of the sentences in the depth of the sentences by analyzing the 51 sentence problems presented in the $4^{th}$ grade mathematics textbook(2015 revised curriculum). As a result, it was confirmed that it is necessary to examine the length and depth of the sentence more carefully in the teaching and learning of sentence problems. Especially in elementary mathematics, the sentence problems requires a linguistic understanding of the sentence, and therefore it is necessary to consider syntactic elements in the process of developing and teaching sentence problems in mathematics textbook.

• School Mathematics
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• v.6 no.2
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• pp.135-151
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• 2004

This study investigated children's realistic response on problematic word problems focused on number operations. Even though word problems and problem solving should be considered in terms of realistic context, results indicates that children's responses didn't show realistic consideration in solving problems. Also, children showed their tendency of mindless or mechanical operation in solving problems and modeling problems