• 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.

• 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.

• 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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2006.11a
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• pp.21-21
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• 2006

21세기 정보통신 및 관련 소재의 연구방향은 새로운 기능성 확보, 극한적 제어성, 복합 및 융합이라는 경향으로 발전해 가고 있다. 반도체 기술 분야에서 현재의 공정적 한계를 극복하고 새로운 기능성을 부여하기 위해 나노 합성과 배열을 기본으로 하여 bottom-up 방식의 나노소자 구현이 큰 주목을 받고 있다. 나노선의 경우 나노 스케일의 dimension, 양자 제한 효과, 우수한 결정성, self-assembly, internal stress 등 기존 벌크형 소재에서 발견할 수 없는 새로운 기능성이 나타나고 있어 바이오, 에너지, 구조, 전자, 센서 등의 분야에서의 활용이 가능하다. 현재 국내외적으로 반도체 나노선으로 널리 연구되고 있는 재료는 ZnO, $SnO_2$, SiC 등이 중심이 되고 있다. 이중 ZnO 나 노선의 합성을 위해서는 thermal CVD, MOCVD, PLD, wet-chemical 등 다양한 방법이 사용되고 있다. 특히 MOCVD 방법에 의해 수직 정렬된 ZnO 나노막대를 성장할 수 있다. 이러한 나노막대는 MO 원료 및 산소 공급량을 적절히 제어함으로서 수직 배향 및 나노선의 구경 제어가 가능하며, 나노 막대의 크기 제어와 관련해서는 반응 관내의 DEZn 와 $O_2$의 양을 변화시켜 구조체의 크기를 수 십 ~ 수 백 나노미터의 크기로 제어할 수 있다. 본 연구는 이러한 ZnO 나노선의 성장과정에서 $210^{\circ}C$ 이하의 저온에서 성장한 ZnO 버퍼층을 이용해 나노구조의 형상을 제어하고자 하였다. 특히 ZnO 저온 버퍼층의 두께에 따라 나노막대의 직경변화, 수직배향성, 형상변화의 제어가 가능하였다. 나노막대의 특성 평가는 TEM, SEM, PL, XRD 등을 이용하여 구조적, 결정학적, 광학적 특성을 분석하였다.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.9
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• pp.800-807
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• 2016

In this paper, we study the characteristics of dual band microstip antenna with modified inset feeder and a single slot. The modified inset feeder consists of the vertical inset feeder placed in x direction and the horizontal one in y direction for shortening the total length of inset feeder. The optimun feeding position for good impedance matching at two resonant frequencies can be easily found by adjusting the horizontal inset distance. And Various frequency ratios can be simply obtained by the parameters of slot. The measurements for fabricated antenna prototypes are carried out for validation. The measured results show a tunable frequency ratio from 1.25 to 1.88 with the variation of slot parameters. It is worthwhile to point out that the radiation patterns are similar at both bands. and below -20.0 dB of cross polarization level at the E plane.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.8 no.1
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• pp.36-41
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• 1998

Intercalation compounds of alkyl sulfonates into layered double hydroxides (LDH) have been directly synthesized. From the X-ray diffraction data and the alkyl sulfonates size, the orientation of the intercalated alkyl sulfonate into the layered double hydroxide was determined. The intercalated alkyl sulfonate is arranged with molecular chain perpendicular to the hydroxide layer with an antiparallel pattern.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.7B
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• pp.895-900
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• 2001

본 논문에서는 하나의 급전선을 갖는 원형 섹터 마이크로스트립 안테나를 사용하여 서로 수직한 편파 특성을 갖는 이중주파수 안테나를 설계하였다. 여기되는 모드 및 주파수를 공진기 모델을 사용하여 계산하였으며, 반경과 섹터 각도를 파라미터로 하여 여기되는 두 주파수를 설계할 수 있었다. 약 2GHz 대역에서 동작하는 안테나를 제작하여 안테나의 특성을 측정하였다. 안테나의 반경을 고정하고 섹터 각도를 75$^{\circ}$에서 120$^{\circ}$까지 변화시켜, 여기되는 두 주파수의 비가 1.08에서 1.518까지 변하는 것을 볼 수 있었다.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.40 no.11
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• pp.77-84
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• 2003

This paper presents a multi-functional microstrip spital antenna that operates in dual frequency bands. Several types of beam shape can be selected by controlling the phase difference of two spiral arms with the phase shifters located on each feed line. It has a normal beam at the lower frequency band, and four different patterns at the higher frequency band: normal beam, conical beam and two types of tilted beam. The antenna exhibits more than 10% of bandwidth at each band. The antenna is fabricated with conductor backed electromagnetic absorber in order to attain unidirectional radiation pattern and confirmed the multi-functionality by measurements.