• 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.

• 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.

• Research in Mathematical Education
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• v.21 no.1
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• pp.1-13
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• 2018

While the utility of the number line is considerable, articulating its conceptual foundation is often neglected in school mathematics. We suggest that it is important to build up strong conceptual foundations in the earlier grades so that number lines can be used in a more meaningful way and that any misconceptions associated with the number line can be prevented or intervened. This paper addresses unit, direction, and origin as the key elements of number lines and presents activities from Davydov's curriculum for early grades that promote exploration of those key elements and may resolve some students' misconceptions. As shown in sample activities from Davydov's curriculum, this paper suggests that students can broaden their perspectives on the number line and use it versatilely in various areas of mathematics learning when they deeply engage in the construction of a number line and have flexibility in interpreting the relationships between key number line elements.

• 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.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1423-1431
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• 2015

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number is the minimum cardinality of a clique-transversal set in G. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.

• Journal of Korea Society of Digital Industry and Information Management
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• v.12 no.3
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• pp.65-74
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• 2016

The Korean resident registration number has been used since 1962 as a personal identification number. The Korean government assigns this number to each korean citizen and it is not able to be changed. In 2000s, as the Internet was rapidly spreaded out, personal information such as the Korean resident registration number, name, home address, and phone number was leaked. The companies provide diverse internet service while collecting personal information. However, personal information was sometimes leaked because of hacking, poor information management and so on. As s results, some of citizens asked government and court of Korea to change the Korean resident registration number because they suffered material damage and emotional distress. The constitutional court decided to be able to change the number from 2018. In this study, the Korean resident registration number which is possible to change, serial number, public certificate, I-PIN, and My-PIN were analyzed comparatively. In addition, considerations when the Korean resident registration number was changed were discussed. The public certificate and I-PIN were appropriate to the case of on-line Korean resident registration number. The Korean resident registration number, serial number, My-PIN were appropriate to the case of off-line Korean resident registration number. Lastly, it would be efficient to manage the Korean resident registration number separately such as on-line and off-line.

• Journal of the Korea Safety Management & Science
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• v.6 no.1
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• pp.173-185
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• 2004

The production using U-shaped line is studied. This research presents the relationship among machining time, cycle time and production rate in a U-shaped line. The U-shaped line produces shafts by automated machines. In this paper when any production rate is given the U-shaped line always satisfies the production rate. An algorithm is developed for the determination of cycle time, the number of machines and workers of the U-shaped line in order to minimize the total machine capacity and the number of workers for any given production rate. The U-shaped line was successfully designed by applying the proposed algorithm.

• Journal of the Korea Society for Simulation
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• v.11 no.4
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• pp.69-80
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• 2002

This study deals with the productivity improvement on a flow production system with the consideration of line-balancing. In a flow production system, similar product models are produced on a same assembly line, the predefined process order and the limitation of total worker number. The system can be increased the work-in -process(WIP) inventory and the worker's idle time. In this study, the worker assignment model is developed to assign evenly workload of process to each product model in such a manner that each process has the different number of worker. This worker assignment model is the mathematical model that determines worker number in each process such that the idle time of processes is reduced and the utilization of worker is improved. We use a simulation technique to simulate the production line proposed by the mathematical model and apply real production line. With the result of simulation, this study analyzes the propriety of production line and proposes the alternatives of new production line