• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.431-456
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• 2016

The purpose of this study is to investigate the appropriate time of introduction and the usage of the number line, in order to suggest the right point of learning the number concept to the elementary school students. For the efficient achievement of this purpose, we investigated the mathematical models for constructing the number concept such as number line, empty number line and double number line, counting and development of number concept. Then, we conducted case study on the time of introduction and the usage of the number line. Finally, we analyzed the result. First, there is need for adjustment to conduct the introduction of the number line from the second year of elementary school, so to help the students understand the continuing number concept through the understanding on the metaphorical concept of the number line. Second, there is the need of positive introduction and the use on the mathematical models; empty number line which helps to draw various thinking strategy visually through the process of operations such as addition and subtraction; the division into equal part and division by equal part in which multiplicative comparative situation or division takes place; the double number line which helps to understand the rate or proportional distribution. Finally, when adopting the number line, the empty number line, or the double number line, we suggested the necessity of learning about elaborate guidance and the usage in order to fully understand the metaphorical concept of the number line.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.53.2-53.2
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles indicating the presence of a relativistic accretion disk model. Using a Monte Carlo technique, we compute the linear polarization of a double peaked broad emission line. A Keplerian accretion disk is adopted for the double peak emission line region and the Schwarzschild geometry is assumed in the emission region. Far from the accretion disk where flat Minkowski geometry is appropriate, we place a scattering region in the shape of a spherical shell sliced. We generate a line photon in the accretion disk in an arbitraray direction in the local rest frame and follow the geodesic of the photon until it hits the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the linear degree of polarization also shows a double peak structure. Under a favorable condition we show that up to 1% of linear degree of polarization may be obtained.

• 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.

• Journal of The Korean Astronomical Society
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• v.44 no.2
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• pp.59-65
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles that are well-fitted by a relativistic accretion disk model. We develop a Monte Carlo code to compute the linear polarization of a double peaked broad emission line arising from Thomson scattering. A Keplerian accretion disk is adopted for the double peak emission line region and the geometry is assumed to be Schwarzschild. Far from the accretion disk where flat Minkowski geometry is appropriate, we place an azimuthally symmetric scattering region in the shape of a spherical shell sliced with ${\Delta}{\mu}=0.1$. Adopting a Monte Carlo method we generate line photons in the accretion disk in arbitrary directions in the local rest frame and follow the geodesic paths of the photons until they hit the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the degree of linear polarization also shows a double peak structure. Under favorable conditions we show that up to 0.6% linear polarization may be obtained. We conclude that spectropolarimetry can be a powerful probe to reveal much information regarding the accretion disk geometry of these active galactic nuclei.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.85-101
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• 2017

The purpose of this study is to investigate how elementary school students understand and use the number line relating number concept and what is the main problem in the learning process. For the efficient achievement of this purpose, we investigated how the number line metaphor is related to the number concept and considered the role of the number line on Freudenthal's number concept teaching theory. The test conducted to find the degree of understanding and difficulty on using the number line by actual elementary school students consisted of two questions ; to find appropriate number corresponding to the given number on the number line and to identify contents of chapters about the use of number line on each grade. It was found that many students couldn't solve the problem represented by the number line though they could solve the problem represented by other ways such as number track and pictures. The only difference between the two problems was the way of representation, and they had same contents and structure. This study tried to figure out the meaning of this phenomenon. Also, by using various teaching-learning method (number track, pictures, empty number line, and double number line etc.), this study was aimed to provide the way to help learning 'related number concept' and to solve the difficulty on understanding the number line.

• Education of Primary School Mathematics
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• v.22 no.1
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• pp.29-48
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• 2019

Previous studies on double scale models, visual models with two different scales (Chong, 2015), have focused on double number line and little research has been conducted on how to employ double scale models in the elementary mathematics textbooks series. Given this, we analyzed the characteristics of double scale models in the Japanese elementary mathematics textbooks in the following aspects: (a) the contents of units where double scale models were used; (b) the purposes of using such models; (c) the types of such models tailored to the contents and grade levels; and (d) the characteristics of problem contexts dealing with the models. The results of this study showed that double scale models were effectively used to connect the contents related to multiplication, specifically for the contexts of ratio. Such models were addressed for students in a systematic and gradual way as the grade levels went up. Based on these results, this paper describes implications on how to use double scale models in mathematics textbooks.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.3
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• pp.193-199
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• 2009

Powerline communications (PLC) technology has been discussed and analyzed as a highly potential candidate of wireline access network solutions. In this paper, performance of double binary turbo coded orthogonal frequency division multiplexing (OFDM) system is analyzed and simulated in power line communications channel. In order to make power line channel environments, Bernoulli-Gaussian noise is considered. The performance is evaluated in terms of bit error probability. From the simulation results, it is demonstrated that the double binary turbo coding scheme offers considerable coding gain with reasonable encoding complexity. It is also shown that the system performance can be substantially improved by increasing the number of iterations.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2010.03b
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• pp.8-8
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• 2010

In this paper, the limiting characteristics of the fault current in a power system with a superconducting fault current limiter(SFCL) applied into neutral line of main transformer in a distribution power line were analyzed. The SFCL applied into the neutral line of main transformer power system can limit the unsymmetrical fault current from the single-line ground fault or the double-line ground fault. In addition, it could be decreased a number of SFCL and a load. This method could be expected to reduction of a power loss in the neutral line, because of a neutral line current is zero in ordinary times.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.2
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• pp.301-309
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• 1996

This paper estimates the electric field effect near 765[kV] AC double transmission line with numerical data. The induced voltage and current of a human and car under who kinds of phase arrangement are calculated when each of two objects is insulated or grounded. When the calculated results of the low-reactance and superposition phase arrangement are compared, it is proved that the induced voltage and current of the former are about 30 [%] smaller than that of the latter. The induced current of a human and car are less than 0.5[mA] which is about 10[%] less than that of the American National Standard Code. Also the induced voltage and current of dead lines by other live lines are calculated. Finally the effective number and position of shield wires to reduce the field in ground level are considered. charge simulation method and surface charge method are used to simulate the 2 or 3 dimensional transmission line model respectively.