• 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.

• 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.25 no.3
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• pp.213-232
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• 2022

With the importance of number line in learning fractions, this study investigated how 4th grade students understand fractions and its operations in number line. The questionnaire consisted 22 items which were related to representing fractions, comparing the size of fractions, and operating addition and subtraction of fractions. Both structured number line and sub-structured number line were presented in the items. As results of the study, the overall success rates were not high and even some items showed higher incorrect answer rates than the success rates. Also, the students showed a difficulty in solving non-structured number line tasks. It was also noticeable that students showed several types of incorrect answers, which means that students had incomplete understanding of both fractions and number line. This paper is expected to shed light on elementary students' understanding of fractions and number line and to provide implications of how to deal with number line in teaching and learning fractions in the elementary school.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.353-372
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• 2015

This study investigated how to utilize number line related number concept learning and analyzed problems related utilization of number line focused on natural number and rational number(fraction, decimal), in elementary school mathematics textbook. The purpose of this study is to identify desirable direction about the utilization of number line, based on analysis of the introduction of time, introduction contents and utilization method in elementary school mathematics textbook.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.135-152
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• 2013

The purpose of this study is to navigate to the desired direction for the figure of number line through the extensive analysis of number line in middle school textbooks and literatures. For the efficient achievement of this purpose, three research questions were posed as follows: First, we compare the figures of number line in textbooks of Korea and other countries. Korean math textbooks mark the arrow on both sides of number line. But, however, coordinate plane was marked with arrow on only positive direction of number line. In contrast, the majority of secondary school textbooks in several foreign countries has the arrow only on positive direction. Second, the change in the figure of number line has been analyzed historically from two perspectives. From the first to 2007-revised curriculum, math textbooks of Korea were analyzed. Since the 6th curriculum, the number of textbooks with arrows on both sides has increased sharply. That is, textbooks with one arrow almost have disappeared. It is strange that any explanation for this abrupt change can't be found. The following analysis was also performed on published foreign literatures since Descartes. There was no arrow in the early figures of number line. But after 19th century, number lines with one arrow have begun to appear. Third, based on the previous study, we propose a reasonable way for the figure of number line. In fact, we claim that, in terms of linguistic symbols, the number line should be with only one arrow on positive side.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.10
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• pp.1355-1360
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• 2020

In a map, placing the labels, corresponding to names or explanations of specific features, is called map labeling. In this paper, n points on a line are given, and placing rectangular labels for the points is considered. Particularly, the labels have a same height and their lower sides lie on a straight line in the upper of the line on which the given points are. The points and the labels are connected by polygonal lines, which are called leader lines. The leader lines are classified into straight leader lines and bended leader lines, where the straight leader line consists of only the vertical line and the bended leader line consists of vertical, horizontal, vertical lines. The problem is placing the labels to minimize the number of bended leader lines, and we propose an O(nlogn)-time algorithm, which improves the O(n2)-time algorithm previously provided in [13].

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.309_310
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• 2009

본 연구에서는 가공배전선로의 상하단 단락고장을 예방하기 위하여 현행 관련 기준의 적정성 여부를 검토하고자 한다. 이를 위하여 기준이도, 완철의 최소 이격거리, 미국 NESC(National Electric Safety Code)의 수직선간이격거리에 대하여 문헌적 고찰을 한 후, 이를 토대로 국내에 적용할 수직선간이격거리 및 지상고 검토 조건을 도출하였고, 기준이도 적용 시 가공배전선 종류별 75^{\circ}C$이도를 계산하여 그 결과들을 비교 검토하였다. 그 결과 상하단 선간단락 고장을 예방하기 위하여 나전선의 기준이도를 특고압전선과 동일하게 적용하여야 하며, 특고압 완철 간의 최소이격거리는 경간 100m 이상에서 수직이격거리가 부족하므로 0.1m 정도 증가 시키는 것이 바람직하다는 것을 발견하였다.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2009.06a
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• pp.48-48
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• 2009

최근 나노광전소자 응용에 큰 관심을 받는 물질인 산화물 나노선은 앞으로 불어 올 나노소재 시대를 여는 선두 물질이다. 이러한 산화물 나노선 가운데 가장 큰 관심을 받는 물질로는 산화아연 나노선을 들 수 있다. 삼화아연 나노선은 상온에서 큰 엑시톤 결합에너지 및 큰 밴드갭을 가지고 있으며 투명성 및 소자구동시 안정성을 지니고 있어 그 응용이 기대된다. 하지만 이러한 나노선을 이용한 광전소자 응용은 bottom-up 방식을 기초로 한 대면적 소자제작이 어렵다. 이러한 bottom-up 방식의 나노소자 제작에서 필요한 나노선 성장기술은 금속 catalyst 없이 대면적 성장, 나노선 수직어레이, 나노선의 고온성장, 기판 사이에 발생하는 자발적 계면층 제거 등으로 대표된다. 또한 나노선의 결정성 및 광특성 향상을 위해서는 고온성장이 불가피한데, 실리콘 기판과 같이 격자상수 불일치도가 큰 기판에서는 나노선 성장이 이루어지지 않고 다시 탈착되어 구조물이 성장되지 않는다. 본 연구에서는 선택적 삼원계 단결정 씨앗층을 이용하여 길이/직경 비가 매우 향상된 MgZnO 나노와이어를 interfacial layer 없이 수직으로 고온에서 성장하여 산화물 전계방출 에미터로서의 가능성을 확인하였다.

• The Mathematical Education
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• v.61 no.3
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• pp.375-396
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• 2022

With the importance for teachers of understanding students' strategies and providing appropriate feedback to their students, the purpose of this study is to analyze how prospective elementary teachers interpret and respond students' strategies for fraction tasks with number lines. The findings from analysis of 64 prospective teachers' responses were as follow. First, the prospective teachers in general could identify the students' understanding and errors based on their strategies, however, some prospective teachers overgeneralized students' mathematical thinking at a superficial level. Second, the prospective teachers could pose diverse tasks or activities for revising the students' errors, while some prospective teachers tried to correct students' errors by using only the area models. Based on these results, this study suggests for prospective teachers to have opportunities to understand elementary students' diverse problem strategies and to consider teaching methods with different fraction models.

• The Transactions of the Korea Information Processing Society
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• v.3 no.5
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• pp.1147-1159
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• 1996

In this paper. we develop an efficient algorithm which vectorize the table input for mixed document recognition system. It is necessary to separate character and line for recognizing the character in the table. For recognizing table, we have to recognize the character which is blocked by table line and develop the efficient rectorization method for table line. For vectorizing table, we develop several methods. The first method is to extract table line part using 8-dircction chaincodes. The second method is to extract horizontal and vertical lines using histogram of lines. The third one is to extract diagonal lines of table by using the cross points of horizontal and verticallines. Finally we also develop the table vectorization method which finds the regularity characteristics of horizontal and vertical lines composing table, In the paper, we sugest a regularity method for efficient table vectorization.