• School Mathematics
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• v.19 no.2
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• pp.229-248
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• 2017

This study investigated the factors that should be considered when teaching proportional expression and proportional distribution through literature review. Based on these results, we analyzed and compared Korean and foreign mathematics textbooks on proportional expression and proportional distribution longitudinally and horizontally to search for desirable methods of organizing the unit of proportional expression and proportional distribution in mathematics textbooks. For longitudinal analysis, we took the mathematics textbooks according to the national curriculum since the 5th one. For horizontal analysis, we selected the mathematics textbooks of Japan, Singapore, and China. In each textbook, the contents and the order in relation to proportional expression and proportional distribution, the definitions of terminology, and the contexts and the visual representations for introducing related concepts are selected as the analysis framework. The results of analysis revealed many characteristics and the differences in ways of dealing contents about proportional expression and proportional distribution. Based on these results, we suggested some implications for writing the unit of proportional expression and proportional distribution in elementary mathematics textbooks.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.73-75
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• 2002

컴퓨터 시스템의 성능이 발전하면서 동시에 실행되는 프로그램의 수도 증가하게 되었다. 이로 인해 자원을 두고 경쟁하는 프로세스들의 우선순위에 따라 분배되는 자원의 양을 세밀하게 조절하는 기능이 필요하게 된다. 우선순위에 따른 자원의 비례배분 알고리즘에 대한 연구가 많이 있었고, 이를 바탕으로 대부분의 자일을 관리하는 운영체계들도 개발되었다. 하지만 가상메모리 자일에 대해서는 자원의 할당량의 모호함과 프로세스가 사용할 메모리 필요량이 예측불가능하기 때문에 적은 연구가 이루어졌을 뿐이다. 본 논문에서는 프로세스가 단위 작업을 수행할 때 발생하는 페이지폴트의 양이 프로세스의 우선순위에 반비례하는 것으로 가상 메모리에 대한 비례배분 개념을 정의 하고, 프로세스 마다 메모리에 대한 요구 형태가 다른 환경에서 이를 가능하게 하는 페이지대치 알고리즘을 제안한다. 제안한 페이지대치 알고리즘을 리눅스 커널상에 구현한다. 구현된 페이지대치 알고리즘을 사용하면 우선순위가 높긴 프로세스가 우선순위가 낮은 프로세스에 비해서 페이지폰트를 적게 발생하고, 그 발생량은 반비례 관계에 있음을 보인다.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1155-1167
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• 2009

We made a new sample design for life and consciousness survey of Kyungpook people in 2007. We used the 10% sample survey data of 2005 population and housing census as a survey population. After stratification, we allocate proportionally samples within strata after examining various characteristics in previous survey, which includes economic activity state, an income level per year, and housing possession. And we calculated weight in a new sample design and derived estimators and a formula of standard error using the weights.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.445-459
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• 2018

The purpose of this study is to provide a method to help elementary school students learn ratio-related concepts effectively through visual representations. This study was conducted to identify the differences in the composition of ratio-related concepts between Korean and Singaporean textbooks, reconstruct a unit of proportional expressions and distributions by using visual representations and confirm the differences in performance between an experimental and a comparison group of 6th grade students. While the experimental group mathematics lessons is from the reconstructed textbook, the comparison group lessons is from an existing textbook that does not include any reconstructive representations. A t-test of mean was applied to determine the differences between the experimental and comparison group. Analysis revealed significant differences in the mean between the experimental group and the comparison group, and the intermediate level group showed more improvement compared to the higher and lower level groups. An implication of this study is that the application of visual representations can assist students' understanding of ratio-related concepts.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1443-1452
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• 2016

In this paper, we study a sample design for survey on goodwill in retail properties to provide a protecting policy for small traders and tenants, to use basic data for a dispute case related to goodwill. Since goodwill in retail properties is occurred by individual rent company, we use the census on establishments from the Statistics Korea as population. First of all, we consider preferentially seven metropolitan cities in which there are more than half of population. Total sample size is decided as 8,000. We allocate the sample size for markets as stratum in each city using proportional formula and the sample size for industrial classifications in each market using root proportional formula. Also we compute survey weights and calculate estimators, standard errors and interval of estimators for each characteristic such as type of establishments and market in seven metropolitan cities.

• The Korean Journal of Applied Statistics
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• v.26 no.2
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• pp.209-222
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• 2013

We apply stratified cluster sampling to a replicated systematic unrelated question model for a large scale survey in which the population is comprised of several strata developed by several clusters and with sensitive parameters. We first present a replicated systematic unrelated question model using an unrelated question model to procure sensitive information from the population of clusters and then develop a suggested model to an unrelated question by a stratified cluster replicated systematic sampling that can be used in large population of strata. We cover the proportional and optimum allocation for the suggested model. Finally, we compare and analyze the efficiency of the suggested model with the replicated systematic unrelated question model.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.791-810
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• 2017

This study explored the possibility of using visual models in teaching proportional reasoning based on the review of previous studies. Many studies on proportional reasoning emphasize that students tend to simply apply formal procedures without understanding the meaning behind them and that using visual models may be an alternative to help students develop informal strategies and proportional reasoning. Given these, we re-constructed and implemented the unit of a textbook to teach sixth graders proportional reasoning with ratio table, double number line, and double tape diagram. The results of this study showed that such visual models helped students understand the meaning of proportion, explore the properties of proportion, and solve proportional problems. However, several difficulties that students experienced in using the visual models led us to suggest cautionary notes when to teach proportional reasoning with visual models. As such, this study is expected to provide empirical information for textbook developers and teachers who teach proportional reasoning with visual models.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.27-38
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• 1995

In the surveys of sensitive issues of the population that is composed of several unknown-size stratum, we propose the unrelated question model with quantitative attribute by using stratified double sampling. And, we consider two types of sample allocations under the fixed cost, which are the proportional allocation, the optimum allocation. In efficiency, the proosed model is inferior to the unrelated question model with quantitative attribute by stratified sampling in case of the size of each stratum is known. But we find that efficiency of the proposed model is increased, when the selecting probability of sensitive question p is small and first stage sample size n' is large.