• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.283-308
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• 2018

'Divisor and multiple' is the topic included both in the elementary and in the secondary mathematics curriculum, but there has been lack of research on it. It has been reported that students have a difficulty in understanding the meaning of the greatest common divisor (GCD) and the least common multiple (LCM), while they can find out GCD and LCM. Against the lack of research on how to overcome this difficulty, this study designed teaching methods with a model for visualization to emphasize the meanings of divisor and multiple in finding out GCD and LCM, and implemented the methods in one fourth grade classroom. A questionnaire was developed to explore students' solution methods and interviews with focused students were implemented. In addition, fourth-grade students' thinking was compared and contrasted with fifth-grade students who studied divisor and multiple with the current textbook. The results of this study showed that the teaching methods with a specific model for visualization had a positive impact on students' conceptual understanding of the process to find out GCD and LCM. As such, this study provides instructional implications on how to foster the meanings of finding out GCD and LCM at the elementary school.

• The Science & Technology
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• no.4 s.431
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• pp.104-105
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• 2005

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.201-218
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• 2012

In this study, the following topics were investigated targeting elementary school students: Schema formed through precise notion of cognitive and the connection of the concepts when studying common divisor, common multiple, and the lowest common multiple, configuration ability and problem solving of the students when learning using a modified schema, how the schema of the student to advance to a higher level, and how the deformation of the schema is carried out student's configuration of concept and problem solving ability. As a result, it was found out that cognition about precise concept, schema and the modified schema are important factors when a primary concept was developed into a secondary concept, and play important roles when the connection and the formation of the modified schema created by cognition about the precise primary concept rather than by the formation of the secondary concept (formation of the secondary schema) created by the connection between the primary concept.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.17-35
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• 2013

The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.1
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• pp.277-283
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• 2020

In a concentric magnetic gear, which replaces the teeth of a mechanical gear with a permanent magnet, the polar ratio of the magnet that determines the reduction ratio affects the behavior of the magnetic gear dramatically. This study analyzed the density of transmission torque, the efficiency of torque considering the solid loss, and the torque quality, including the cogging characteristics using finite element analysis. When the pole number on the driving side was changed from two to five, it was confirmed that there was an optimal pole ratio, in which the transmission torque was maximized. Because eddy current generation density is proportional to the magnetic field, the transmission efficiency also shows a similar tendency to the transmission torque density, and the efficiency is more than 95% at a low gear ratio. The cogging characteristics due to the interaction of the permanent magnets with the limited number of poles are inversely proportional to the least common multiple between the number of magnets on the drive side and the number of modulator teeth. A test model was built for the transmission torque evaluation.

• The Mathematical Education
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• v.58 no.2
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• pp.319-335
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• 2019

In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.12
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• pp.8700-8706
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• 2015

The first driving device of the power bogies for the Korean high-speed railway vehicle consists of the traction motor (TM) and the motor reduction gears unit (MRU). Although TM and MRU are the mechanically integrated structures, their time between overhauls (TBO) have two separate intervals due to different technical requirements(i.e. TBO of MRU: $1.8{\times}10^6km$, TBO of TM: $2.5{\times}10^6km$). Therefore, to reduce the unnecessary number of preventive maintenances, it is important to evaluate the optimal TBO with a viewpoint of reliability-center maintenance towards cost-effective solution. In this study, derived from the field data in maintenance, fault tree analysis and failure rate of the subsystem considering criticality of the components are evaluated respectively. To minimize the conventional total maintenance cost, the same optimal TBO of the components is derived from genetic algorithm considering target reliability and improvement factor. In this algorithm, a chromosome which comprised of each individual is the minimum preventive maintenance interval. The fitness function of the individual in generation is acquired through the formulation using an inverse number of the total maintenance cost. Whereas the lowest common multiple method produces only a four percent reduction compared to what the existing method did, the optimal TBO of them using genetic algorithm is $2.25{\times}10^6$km, which is reduced to about 14% comparing the conventional method.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.6
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• pp.521-530
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• 2016

Weather radar is observation equipment that transmits electromagnetic waves and receives backscattered signals from the targets. The weather radar systems of the Korea Meteorological Administration have a doppler mode that can extract the target's radial velocity. However, the radial velocity over the maximum unambiguous velocity(${\nu}_m$) for which is in a trade-off relationship with the maximum unambiguous range is folded. Therefore, a dual PRF mode of which transmits and receives signals using two different PRFs(high and low) must be used to extend the vm while maintaining the maximum unambiguous range. Using a dual PRF mode, vm can be extended to the amount of lowest common denominator of two observed vm from high and low PRF. For this extension, we have developed a velocity unfolding algorithm of which uses several criteria for classification considering observed velocity differences between high and low PRF and their error boundary. Then, correction factors are calculated for each class and are applied to unfold radial velocity. The developed algorithm was applied to the Yong-In Testbed(YIT) radar and the generated better performance of radial velocity extraction than those of the previous system.