• 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 for History of Mathematics
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• v.27 no.6
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.211-229
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• 2009

The purpose of this study is analysis of to investigate relation proportion problem of mathematics textbooks of 7th curriculum to proportional reasoning(relative thinking, unitizing, partitioning, ratio sense, quantitative and change, rational number) of Lamon's proposal at sixth grade students. For this study, I develop two test papers; one is for proportion problem of mathematics textbooks test paper and the other is for proportional reasoning test paper which is devided in 6 by Lamon. I test it with 2 group of sixth graders who lived in different region. After that I analysis their correlation. The result of this study is following. At proportion problem of mathematics textbooks test, the mean score is 68.7 point and the score of this test is lower than that of another regular tests. The percentage of correct answers is high if the problem can be solved by proportional expression and the expression is in constant proportion. But the percentage of correct answers is low, if it is hard to student to know that the problem can be expressed with proportional expression and the expression is not in constant proportion. At proportion reasoning test, the highest percentage of correct answers is 73.7% at ratio sense province and the lowest percentage of that is 16.2% at quantitative and change province between 6 province. The Pearson correlation analysis shows that proportion problem of mathematics textbooks test and proportion reasoning test has correlation in 5% significance level between them. It means that if a student can solve more proportion problem of mathematics textbooks then he can solve more proportional reasoning problem, and he have same ability in reverse order. In detail, the problem solving ability level difference between students are small if they met similar problem in mathematics text book, and if they didn't met similar problem before then the differences are getting bigger.

• 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 Korea Multimedia Society Conference
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• 2002.05c
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• pp.308-314
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• 2002

본 논문은 2인용 보드게임의 정보에 대한 전략을 학습할 수 있는 방법을 유전자기반 역전파 신경회로망과 Temporal Difference학습알고리즘을 이용하여 제안하였다. 학습의 과정은 역전파에 의한 초기학습에 이어 국부해의 단점을 극복하기 위하여 미세학습으로 유전자알고리즘을 이용하였다. 시스템의 구성은 탐색을 담당하는 부분과 기물의 수를 발생하는 부분으로 구성되어 있다. 수의 발생부분은 보드의 상태에 따라서 갱신되고, 탐색커널은 αβ탐색을 기본으로 유전자알고리즘을 이용하여 가중치를 최적화하는 유전자기반 역전파 신경회로망과 TD학습을 결합하여 게임에 대해 양호한 평가함수를 학습하였다. 일반적으로 많은 학습을 통하여 평가함수의 정확도가 보장되면 승률이 학습의 양에 비례함을 알 수 있었다.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.6A
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• pp.643-651
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• 2008

In this paper, we analyze the performance of normalized SNR based proportional fair scheduling with partial feedback information for multiuser MIMO-OFDMA systems. The closed form expression on the downlink capacity of the selective partial CQI feedback scheme is derived and its asymptotic behavior is investigated. From the performance analysis and numerical results, it is found that the optimal growth rate of downlink capacity can be achieved with bounded average feedback overhead irrespective of the number of users.

• Korean journal of applied entomology
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• v.10 no.1
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• pp.13-22
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• 1971

This experiment was conducted to investigate the differences of the in vitro inhibitory effect of various organephobphorua insecticides on the chlinesterase from rice stem borer and those of the toxicity of them against the insect, with special references to the relationship between the cholinesterase inhibition and the toxicity. The results obtained were summarized as follows: Phosphate compounds shelved stronger inhibitory effect on the cholinesterase than thhiophosphate compounds, but was not stronger in toxicity than the latter. Diethoxy compounds were not always stronger than dimethoxy in cholinesterase inhibition and the toxicity of organophosphorus insecticides. The organophosphorus insecticides that inhibited strongly the cholinesterase were not always stronger in the toxicity.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.1-16
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• 2013

The primary purpose of this study is to survey multiplicative thinking levels and its characteristics of third graders in elementary school and to analyze how to use it when they solve the proportional problems. As results, the transition thinking ranked the highest among the four kinds of thinking levels when the $3^{rd}$ graders solved the multiplication problems. It means that the largest numbers of students still can not distinguish the additive and multiplicative situations completely and remain in the transition thinking, which thinks both additively and multiplicatively. In addition, the performance of solving proportional problems was distinguished from the levels of thinking. Through this study, we can give some implications of the importance of multiplicative thinking and instructional methods related to multiplication.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.4
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• pp.279-284
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• 2007

There ate various studies being conducted regarding efficient routing schemes to reduce energy consumption in the wireless sensor network, for which energy transformation is difficult. In terms of routing, many believe that the dynamic clustering technique is most efficient. The dynamic clustering technique consists of cluster construction and data transmission. Energy consumption for data transmission is proportional to $d^2$ and $d^4$ around the crossover area. This paper proposed algorithms for reducing energy consumption by improving efficiency of the cluster construction process that in the dynamic cluster mechanism and minimizing long-distance data transmission outside the crossover area. The proposed algorithms reduced energy consumption by implementing bridge clusters in the crossover area and decreasing the data transmission distance. The benefits of the proposed algorithms were confirmed through simulation experiments.