• The Mathematical Education
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• v.60 no.4
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• pp.409-429
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• 2021

This study investigated instructional methods for fractional division emphasizing algebraic thinking with sixth graders. Specifically, instructional elements for fractional division emphasizing algebraic thinking were derived from literature reviews, and the fractional division instruction was reorganized on the basis of key elements. The instructional elements were as follows: (a) exploring the relationship between a dividend and a divisor; (b) generalizing and representing solution methods; and (c) justifying solution methods. The instruction was analyzed in terms of how the key elements were implemented in the classroom. This paper focused on the fractional division instruction with problem contexts to calculate the quantity of a dividend corresponding to the divisor 1. The students in the study could explore the relationship between the two quantities that make the divisor 1 with different problem contexts: partitive division, determination of a unit rate, and inverse of multiplication. They also could generalize, represent, and justify the solution methods of dividing the dividend by the numerator of the divisor and multiplying it by the denominator. However, some students who did not explore the relationship between the two quantities and used only the algorithm of fraction division had difficulties in generalizing, representing, and justifying the solution methods. This study would provide detailed and substantive understandings in implementing the fractional division instruction emphasizing algebraic thinking and help promote the follow-up studies related to the instruction of fractional operations emphasizing algebraic thinking.

• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.1
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• pp.45-50
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• 1982

The present paper provides a method for solving a complementary programming problem with quadratic objective function subject to linear constraints. The procedure developed is based on the simplex method for quadratic programming problem. An example is added to illustrate the procedure.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.1
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• pp.87-95
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• 2004

We proposed the division algorithm that was aimed at dividing system models. It used a transitive matrix to express the relation between place and transition. And the division algorithm was applied to the scheduling problem, with the division-scheduling algorithm. The division-scheduling algorithm was able to calculate the divided subnet table. And it is able to reduce the analysis complexity. In this study, we applied the proposed division algorithm and division-scheduling algorithm to flexible manufacturing system models. We compared the efficiency and performance of the division-scheduling algorithm with the Hillion algorithm, Korbaa algorithm, and Unfolding algorithm proposed in previous researches.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1267-1286
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• 2020

We pay attention to a coupled problem by a penalty term which is induced from non-overlapping domain decomposition methods based on augmented Lagrangian methodology. The coupled problem is composed by two parts mainly; one is a problem associated with local problems in non-overlapping subdomains and the other is a coupled part over all subdomains due to the penalty term. For the speedup of iterative solvers for the coupled problem, we propose two different types of preconditioners: a block-diagonal preconditioner and an additive Schwarz preconditioner as overlapping domain decomposition methods. We analyze the coupled problem and the preconditioned problems in terms of their condition numbers. Finally we present numerical results which show the performance of the proposed methods.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• Journal of the Korean Society of Marine Environment & Safety
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• v.25 no.6
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• pp.743-748
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• 2019

This study suggested a process of redesigning and implementing problem based learning to enhance students' active and collaborative learning activities and learning outcomes. The results of this study are as follows. First, the ef ect of class participation, academic self-regulated learning, and academic self-efficacy were examined. As a result, first, the average of learning activity, class extension, and participation in class was high in the difference between before and after class. Second, the post average scores of all the factors except the 'evaluation' were higher than before. Third, academic self-efficacy showed a significant difference only in 'task preference'. Finally, students' satisfaction with the class was also high. The professor was also able to grasp the characteristics of individual students by designing and operating the classes using PBL, and it was confirmed that the interaction with students increased. Based on the results of this study, we discussed the limitations and educational implications of the problem based learning class and propose successful problem based learning design and operation of the classroom.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.10 s.352
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• pp.79-89
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• 2006

TCP is the most widely used transport protocol in Internet applications that guarantees a reliable data transfer. But, in the wireless multi-hop networks, TCP performance is degraded because it is designed for wired networks. The main reasons of TCP performance degradation are contention for wireless medium at the MAC layer, hidden terminal problem, exposed terminal problem, packet losses in the link layer, unfairness problem, reordering problem caused by path disconnection, bandwidth waste caused by exponential backoff of retransmission timer due to node's mobility and so on. Specially, in the mobile ad-hoc networks, discrepancy between a station's transmission range and interference range produces hidden terminal problem that decreases TCP performance greatly by limiting simultaneous transmission at a time. In this paper, we propose a new MAC algorithm for mobile ad-hoc networks to solve the problem that a node can not transmit and just increase CW by hidden terminal. In the IEEE 802.11 MAC DCF, a node increases CW exponentially when it fails to transmit, but the proposed algorithm, changes CW adaptively according to the reason of failure so we get a TCP performance enhancement. We show by ns-2 simulation that the proposed algorithm enhances the TCP performance by fairly distributing the transmission opportunity to the failed nodes by hidden terminal problems.

• Journal of The Korean Association of Information Education
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• v.16 no.1
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• pp.61-70
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• 2012

In this study, the newly designed course related to creative problem solving is introduced. According to the characteristics of multimedia engineering, the Alice, which is well known as an effective 3D interactive authoring tool, is adopted as the supporting tool to validate the accomplishment of study goals set up for software design. Each creative problem solving phase could be clearly implemented and its expected performance could be evaluated efficiently by using Alice. The result of curricular implementation and performance evaluation is shown.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.381-395
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• 2010

The purpose of this paper is to examine the competence and the methods of problem solving in four operations word problems based on the informal knowledges by five-year-old children. The numbers which are contained in problems consist of the numbers bigger than 5 and smaller than 10. The subjects were 21 five-year-old children who didn't learn four operations. The interview with observation was used in this research. Researcher gave the various materials to children and permitted to use them for problem solving. And researcher read the word problems to children and children solved the problems. The results are as follows: five-year-old children have the competence of problem solving in four operations word problems. They used mental computation or counting all materials strategy in addition problem. The methods of problem solving were similar to that of addition in subtraction, multiplication and division, but the rate of success was different. Children performed poor1y in division word problems. According to this research, we know that kindergarten educators should be interested in children's informal knowledges of four operations including shapes, patterns, statistics and probability. For this, it is needed to developed the curriculum and programs for informal mathematical experiences.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.473-484
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• 1998

We consider a finite difference approximation to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is proved that the rate of convergence is $O(h^2)$. To obtain the solution of the finite difference equation, an iterative scheme converging monotonically to the solution of the finite difference equation is introduced. And the numerical experiment of this method is given.