• 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.

• 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.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.237-260
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• 2018

This study investigated the models of four countries' elementary mathematics textbooks in Ratio and Rate and identified how multiplicative perspectives on proportional relationships and the structure of proportion situations are reflected in the textbooks. For this, textbooks of 5th and 6th grade textbooks in Korea Japan, Singapore and U.S. are compared and analyzed. As a result, we can find multiplicative perspectives on proportional relationships and the structure of proportion situations on pictorial models, ratio tables, double number lines and double tape diagrams. Also, the development of Japanese textbooks from multiple batches perspectives to variable parts perspectives and the examples of the use with two models together implied the connection and union of two multiplicative perspectives. Based on these results, careful verification and discussion for the next textbook is needed to develop students' proportional reasoning and teach some effective reasoning strategies. And this study will provide the implication for what kinds of and how visual models are presented in the next textbook.

• Archives of design research
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• v.13 no.2
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• pp.25-32
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• 2000

The body proportion of a passenger car has been changed by the demand of consumer and the market. Now the interior space proportion on a passenger car become to have the importance as the passenger space and this proportion has been changed as the new models have been developed. It didn't seems to had a unified direction or strategy in the dimensions of the domestic passenger cars on the early models, but they had a specific changes in dimensions on the later models. The proportion of the wheelbase and greenhouse can be calculated into as about 58% and 57% on the compact and sub-compact passenger cars while it is about 56% on mid-size sedan type passenger cars for thier 3-box structure body concept. The overrall proportion of the interior space is bigger on the compact and the sub-compact passenger cars than the mid-size passenger cars as the calculation shows. It can be concluded that the interior space proportion on the compact passenger cars would become larger, which is closed to 60%. And this trend would be appear on the mid-size passenger cars.

• Archives of design research
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• v.14 no.4
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• pp.47-56
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• 2001

It is doubtless that product aesthetics and design are very important keys determining the success and failure in today's market environment in spite of the lack of academic model and positive research results. However, surprisingly the research of such an aesthetic has not been active. Therefore the conceptual frame of product aesthetics should be examined centering around the research of product aesthetes in other to understand consumers'aesthetic requirement and desire in the research of aesthetics of product design and the design process by analyzing that how product aesthetics anon the consumers'response and product selection, what roles the aesthetic factor of product design play in product design and what aesthetic dimension of product design is related to design product should be established.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.279-291
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• 2012

When fitting a Cox proportional hazards model with missing covariates, it is inefficient to exclude observations with missing values in the analysis. Furthermore, if the missing-data mechanism is not Missing Completely At Random(MCAR), it may lead to biased parameter estimation. Many approaches have been suggested to handle the Cox proportional hazards model when covariates are sometimes missing, but they are based on the selection model. This paper suggest an approach to handle Cox proportional hazards model with missing covariates by using the pattern-mixture model (Little, 1993). The pattern-mixture model is expressed by the joint distribution of survival time and the missing-data mechanism. In the pattern-mixture model, many models can be considered by setting up various restrictions, and different results under various restrictions indicate the sensitivity of the model due to missing covariates. A simulation study was conducted to show the sensitivity of parameter estimation under different restrictions in a pattern-mixture model. The proposed approach was also applied to mouse leukemia data.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.235-241
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• 2000

가스기기 안전장치 및 조리기구에 중요한 안전장치인 Gas Sensor를 가속시험을 이용하여 신뢰성을 분석하였다. 시험을 실시한 결과 GAS SENSOR의 Heater는 인가전압에 따른 특성 변화가 아레니우스 모델과 어링모델이 잘 일치함을 보여주었다. 즉, Heater선의 전압은 발열온도에 비례하고 있음을 알 수 있었다. 이번 실험을 통하여 STRESS에 비례적으로 특성이 변하는 제품은 설계단계에서 수명에 영향을 주는 잠재적 취약부를 단시간에 효과적으로 끌어내어 개선할 수 있는 기술임을 입증하였으나 다양한 STRESS의 복합적인 인자에 의하여 변화되는 특성을 분석하여 실질적으로 현장실무에 활용을 위해서는 많은 기술적 보안이 필요할 것으로 판단된다.

• Journal of the Korea Concrete Institute
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• v.15 no.3
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• pp.433-442
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• 2003

This paper presents a hypoplastic model for three-dimensional analysis of concrete structures under monotonic, cyclic, proportional and non-proportional loading. The constitutive model is based on the concept of equivalent uniaxial strains that allows the assumed orthotropic model to be described via three equivalent uniaxial stress-strain curves. The characteristics of these curves are obtained from the ultimate strength surface in the principal stress space based on the Willam-Warnke curve. A cap model is added to consider loading along or near the hydrostatic axis. The equivalent uniaxial curve is based on the Popovics and Saenz models. The post-peak behavior is adjusted to account for the effects of confinement and to describe the change in response from brittle to ductile as the lateral confinement increases. Correlation studies with available experimental tests are presented to demonstrate the model performance. Tests with monotonic loading on specimens under constant lateral confinement are considered first, followed by biaxial and triaxial tests with cyclic loads. The triaxial test example considers non-proportional loading.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.305-321
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• 2015

This study started with wondering whether the nonproportional model used in unit assessment for 2nd graders is appropriate or not for them. This study aims to explore the applicability of the nonproportional model to 2nd graders when they learn about numbers. To achieve this goal, we analyzed elementary mathematics textbooks, applied two kinds of tests to 2nd graders who have learned three-digit numbers by using the proportional model, and investigated their cognitive characteristics by interview. The results show that using the nonproportional model in the initial stages of 2nd grade can cause some didactical problems. Firstly, the nonproportional models were presented only in unit assessment without any learning activity with them in the 2nd grade textbook. Secondly, the size of each nonproportional model wasn't written on itself when it was presented. Thirdly, it was the most difficult type of nonproportional models that was introduced in the initial stages related to the nonproportional models. Fourthly, 2nd graders tend to have a great difficulty understanding the relationship of nonproportional models and to recognize the nonproportional model on the basis of the concept of place value. Finally, the question about the relationship between nonproportional models sticks to the context of multiplication, without considering the context of addition which is familiar to the students.