• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.127-136
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• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• School Mathematics
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• v.15 no.4
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• pp.723-742
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• 2013

The purpose of this study was to analyze children's proportional reasoning process on an ill-structured "architectural drawing" problem solving and to investigate their level and characteristics of proportional reasoning. As results, they showed various perspective and several level of proportional reasoning such as illogical, additive, multiplicative, and functional approach. Furthermore, they showed their expanded proportional reasoning from the early stage of perception of various types of quantities and their proportional relation in the problem to application stage of their expanded and generalized relation. Students should be encouraged to develop proportional reasoning by experiencing various quantity in ration and proportion situations.

• Proceedings of the KIPE Conference
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• 2016.11a
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• pp.95-96
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• 2016

본 논문은 독립 운전 모드에서 전압 고조파 보상을 위한 비례 다중 공진 제어 기반의 전압 제어에 대해 다루고 있다. 독립 운전 모드에서 인버터는 계통과의 연계 없이 전체 지역적 부하의 수요를 담당해야 하기 때문에 전압원으로서 정의된다. 그런데 이때 부하가 불평형 또는 비선형 부하인 경우 역상차, 영상차 또는 특정 고조파 전류가 발생하며 이로 인해 출력 전압이 왜곡된다. 본 논문에서는 앞서 언급한대로 전압 고조파 보상을 위해 흔히 사용되는 비례적분 제어기 대신 고조파 보상 제어의 단순화를 위해 비례 공진 제어기를 사용하였다. 하지만 이와 같은 비례 공진 제어를 실용적인 텀으로서 추가될 경우 전압 매그니튜드 추종 에러가 발생하게 되므로 본 논문에서는 추가적으로 실용적인 비례 공진 제어기가 갖는 단점을 극복하고자 비례 적분 기반의 간단한 전압 회복 기법에 대해 제안하며 제안된 제어 방식은 PSiM 시뮬레이션과 실험을 통해 입증되었다.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.247-265
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• 2003

The purpose of this study is to analyze the essence of ratio concept from educational viewpoint. For this purpose, it was tried to examine contents and organizations of the recent teaching of ratio concept in elementary school text of Korea from ‘Syllabus Period’ to ‘the 7th Curriculum Period’ In these text most ratio problems were numerically and algorithmically approached. So the Wiskobas programme was introduced, in which the focal point was not on mathematics as a closed system but on the activity, on the process of mathematization and the subject ‘ratio’ was assigned an important place. There are some educational implications of this study which needs to be mentioned. First, the programme for developing proportional reasoning should be introduced early Many students have a substantial amount of prior knowledge of proportional reasoning. Second, conventional symbol and algorithmic method should be introduced after students have had the opportunity to go through many experiences in intuitive and conceptual way. Third, context problems and real-life situations should be required both to constitute and to apply ratio concept. While working on contort problems the students can develop proportional reasoning and understanding. Fourth, In order to assist student's learning process of ratio concept, visual models have to recommend to use.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.165-173
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• 2010

In this paper, the dynamic stiffness of scaled boundary finite element method(SBFEM) was analytically derived to represent the non-homogeneous space. The non-homogeneous parameters were introduced as an expotential value of power function which denoted the non-homogeneous properties of analysis domain. The dynamic stiffness of analysis domain was asymptotically expanded in frequency domain, and the coefficients of polynomial series were determined to satify the radiational condition. To verify the derived dynamic stiffness of domain, the numerical analysis of the typical problems which have the analytical solution were performed as various non-homogeneous parameters. As results, the derived dynamic stiffness adequatlly represent the features of the non-homogeneous space.

• School Mathematics
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• v.16 no.4
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• pp.659-675
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• 2014

The purpose of this study is to investigate the effects of scheme based strategy Instruction on problem solving of word problems of ratio and proportion for students with under achievement or at risk for learning disabilities. Three $7^{th}$ graders of underachieving or at risk LD were participated in this study. Three steps of instructional experiment-testing baseline, intervention with schematic-based strategy, testing for the abilities of problem solving, generalization, & sustainability. The results showed that the schema-based strategy, FOPS was effective method for all three students enhancing problem solving abilities and for generalizing and sustaining the problem solving.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.273-288
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• 2019

This study focuses on understanding proportionality, in particular, what constitutes relational understanding of a:b=c:d, which is called proportional expression. The meanings of a:b=c:d are analyzed and some suggestions are offered for improving the teaching and learning of it. The equation a:b=c:d has three different meanings. First, it represents two different structures in one proportional situation. Second, it represents a common structure in two different proportional situations. Finally, it represents a number or a quantity underlying in different proportional situations. It is important to choose and use a unit flexibly to understand the first and the second meanings of a:b=c:d, Double strip diagram and double number line are useful to visualize the meanings of a:b=c:d. In addition, what a number or a quantity in the third meaning of a:b=c:d refers to in proportional situations should be emphasized in teaching and learning of a:b=c:d.

• Korean Journal of Legislative Studies
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• v.25 no.3
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• pp.5-31
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• 2019

In the process of changing the Korean electoral system, various terms such as representation, majority, minority, plurality, and proportionality are not used correctly, making normative judgment on its desirable electoral system difficult. This paper clarifies the concepts and terminology related to the electoral system in order to enable proper normative discussion. First, the misuse of the names of the electoral system is reviewed. This includes the majority representative system versus the minority representative system, the single-member constituency versus the multi-member constituency, the absolute majority system versus the relative majority system, and the majority representative system versus the proportional representative system. Next, the principles of representation, proportionality, democracy, direct ballot, and equal ballot are discussed to evaluate the decisions made by the Constitutional Court of Korea. In the current electoral system of the National Assembly, the equivalence between its constituency member and its proportional representation member is very low in terms of proportionality between votes received and seats allotted. Finally, the coherence between proportional representation and other political institutions is examined. Strengthening the proportionality of parliamentary elections alone does not necessarily increase the proportionality of the entire power structure.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.4
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• pp.367-371
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• 2009

Analysis on optimality of the proportional navigation guidance(PNG) law is presented in this paper. While most of previous studies on optimality of PNG were relied on the linear formulation, this paper is based on the nonlinear formulation. The analysis shows that PNG is an optimal solution minimizing a range-weighted control energy, where the weighting function is an inverse of $\alpha$ power of the distance-to-target. We show that the navigation constant N is related to $\alpha$ directly. And also the conditions required to ensure the analysis result are investigated.