• Research in Mathematical Education
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• v.12 no.3
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• pp.179-191
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• 2008

Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.263-285
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• 2002

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev's basis functions $R_{bf}$ based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Numerical results obtained by $R_{bf}$ functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.

• Korean Management Science Review
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• v.20 no.2
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• pp.81-93
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• 2003

These days we come across many wicked problems whose solutions are beyond individuals intellectual ability. These problems can be resolved through collaborative group interaction. We developed an internet-based asynchronous group interaction support system, after looking into the collaborative problem solving process and the IBIS (Issue-Based Information System) argumentation model. It has the following characteristics ; 1) it is developed based on the modified IBIS model which is a model for group interaction to resolve wicked problems ; 2) it supports both processes of seeking and comparing solutions, while most similar systems do not have a feature to support the latter process ; 3) different structures can be defined dynamically according to the purpose of group interaction, so that it could be used for collaborative problem solving in a specific domain. To show the usability of the system, we carried out an experiment, whose result is shown at the end.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.169.5-169
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• 2001

This study proposes a neural network for solving optimization problems such as the TSP (Travelling Salesman Problem), scheduling, and line balancing. The Hopfield network has been used for solving such problems, but it frequently gives abnormal solutions or non-optimal ones. Moreover, the Hopfield network takes much time especially in solving large size problems. To overcome such disadvantages, this study adopts nodes whose outputs changes with a fixed value at every evolution. The proposed network is applied to solving a TSP, finding the shortest path for visiting all the cities, each of which is visted only once. Here, the travelling path is reflected to the energy function of the network. The proposed network evolves to globally minimize the energy function, and a ...

• Journal of Korean Society for Quality Management
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• v.37 no.2
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• pp.68-77
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• 2009

There are many quality control(QC) tools useful for solving quality problems. In this paper, QC 7 tools, new QC 7 tools, and other quality tools are first compared with respect to their frequency of use. We suggest an integrated problem-solving procedure to systematically deal with various quality problems. For each step a streamlined flow chart is presented to help the practitioners to adopt relevant tools depending on certain situations they face. The procedure will help quality practitioners solve field quality problems.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.571-591
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• 2012

To the best of our knowledge, there is no method, in the literature, to find the fuzzy optimal solution of fully fuzzy shortest path (FFSP) problems i.e., shortest path (SP) problems in which all the parameters are represented by fuzzy numbers. In this paper, a new method is proposed to find the fuzzy optimal solution of FFSP problems. Kumar and Kaur [Methods for solving unbalanced fuzzy transportation problems, Operational Research-An International Journal, 2010 (DOI 10.1007/s 12351-010-0101-3)] proposed a new method with new representation, named as JMD representation, of trapezoidal fuzzy numbers for solving fully fuzzy transportation problems and shown that it is better to solve fully fuzzy transportation problems by using proposed method with JMD representation as compare to proposed method with the existing representation. On the same direction in this paper a new method is proposed to find the solution of FFSP problems and it is shown that it is also better to solve FFSP problems with JMD representation as compare to existing representation. To show the advantages of proposed method with this representation over proposed method with other existing representations. A FFSP problem solved by using proposed method with JMD representation as well as proposed method with other existing representations and the obtained results are compared.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.

• Journal of The Korean Association For Science Education
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• v.14 no.1
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• pp.85-102
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• 1994

The purpose of this study was to analyze students' physics problem solving processes and to find the patterns of their problem spaces when high school and university students solved the physics problems. A total of 51 students in a high school and in two universities participated in this study. Their thinking processes in solving 5 physics problems on electric circuit were recorded by using 'thinking aloud' method and were transferal into protocols. 'The protocols were analyzed by the coding system of problem solving process. One of the major theoretical contributions of the computer simulation approach to problem solving is the idea of problem space. Such a concept of problem space was applied to physics problems on electric circuit in this study, and students' protocols were analyzed by the basic problem spaces which were made up from the item analysis by the researcher. The results are as follows: 1) On the average 4.0 test items among 5 ones were solved successfully by all subjects, and all of the items were solved correctly by only 19 persons among all of them. 2) In regard to the general steps of problem solving process, there was little difference for each item between the good solvers and the poor ones. But according to the degree of difficulty of task there was a good deal of difference. For a complex problem all of 4 steps were used by most of students, but for a simple one only 3 steps except evaluating step were used by most of them. 3) It was found in this study that most of students used mainly the microscopic approach, that is, a method of applying Ohm's law on electric circuit simply and immediately, not using the properties of electric circuits. And also it was observed that most of students used the soloing tom below, that is, a solving path in which they were the first to calculate physical Quantities of circuit elements, before they caught hold of the meaning of the given problem regardless of the degree of difficulty.

• The Mathematical Education
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• v.55 no.1
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• pp.21-39
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• 2016

This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.129-136
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• 2001

We introduce and discuss a new numerical method for solving system of second order boundary value problems, where the solution is required to satisfy some extra continuity conditions on the subintervals in addition to the usual boundary conditions. We show that the present method gives approximations which are better than that produced by other collocation, finite difference and spline methods. Numerical example is presented to illustrate the applicability of the new method. AMS Mathematics Subject Classification : 65L12, 49J40.