• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.239-259
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• 2011

This study investigated the elementary school students' ability on the algebraic reasoning as generalized arithmetic. It analyzed the written responses from 648 second graders, 688 fourth graders, and 751 sixth graders using tests probing their understanding of the properties of whole number operations. The result of this study showed that many students did not recognize the properties of operations in the problem situations, and had difficulties in applying such properties to solve the problems. Even lower graders were quite successful in using the commutative law both in addition and subtraction. However they had difficulties in using the associative and the distributive law. These difficulties remained even for upper graders. As for the associative and the distributive law, students had more difficulties in solving the problems dealing with specific numbers than those of arbitrary numbers. Given these results, this paper includes issues and implications on how to foster early algebraic reasoning ability in the elementary school.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.121-124
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.249-251
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• 2005

In this paper, an algorithm of path planning and obstacle avoidance for mobile robot is proposed. We call the proposed method Random Access Sequence(RAS) method. In the proposed method, a small region is set first and numbers are assigned to its neighbors. By processing assigned numbers all regions are covered and then the path from start to destination is selected by these numbers. The RAS has an advantage of fast planning because of simple operations. This implies that new path selection may be possible within a short time and helps a robot to avoid obstacles in any direction. The algorithm can be applied to unknown environments. When moving obstacles appear, a mobile robot avoids obstacles reactively. then new path is selected by RAS.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.563-588
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• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.37-45
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• 2024

The aim of this article is to consider the sequences generated by repeatedly performing matrix multiplication operations, define the stable, amicable pair, sociable matrix sequences, and analyze the results obtained through iteration. Lastly, numbers are changed to colors to make them easier to understand.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.4
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• pp.878-894
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• 2013

Secure multimedia multicast applications involve group communications where group membership requires secured dynamic key generation and updating operations. Such operations usually consume high computation time and therefore designing a key distribution protocol with reduced computation time is necessary for multicast applications. In this paper, we propose a new key distribution protocol that focuses on two aspects. The first one aims at the reduction of computation complexity by performing lesser numbers of multiplication operations using a ternary-tree approach during key updating. Moreover, it aims to optimize the number of multiplication operations by using the existing Karatsuba divide and conquer approach for fast multiplication. The second aspect aims at reducing the amount of information communicated to the group members during the update operations in the key content. The proposed algorithm has been evaluated based on computation and communication complexity and a comparative performance analysis of various key distribution protocols is provided. Moreover, it has been observed that the proposed algorithm reduces the computation and communication time significantly.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.21-24
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• 2001

In this paper, we investigate some properties of the Skorokhod metric on the space F(R$\^$p/) of upper semicontinuous fuzzy subsets of R$\^$p/ with compact support, which include the continuity of operations, the translation inveriance and convexity.

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.251-278
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• 2022

The purpose of this study is to obtain implications for mathematical education by analyzing how the multiplication and division of decimal numbers are presented in the elementary mathematics textbooks in Korea, Japan, Singapore, and Finland. Compared to the fact that students often have misconceptions about multiplication and division of decimal numbers, there have been not many comparative studies in recent elementary mathematics textbooks. For this study, we selected elementary mathematics textbooks those are widely used in Japan, Singapore, and Finland along with Korean elementary mathematics textbooks. We chose the textbooks because the students in the selected countries have scored high in international achievement studies such as TIMSS and PISA. The analysis was examined in terms of elementary mathematics curriculum related to multiplication and division of decimal numbers, introduction and content, real-life situations, use of visual models, and formalization methods of algorithms. As a result of the study, the mathematics curricula related to multiplication and division of decimal numbers includes estimation in Korea and Finland, while Japan and Singapore emphasize real-life connections more, and Finland completes the operations in secondary schools. The introduction and content are intensively provided in a short period of time or distributed in various grades and semesters. The real-life situations are presented in a simple sentence format in all countries, and the use of visual models or formalization of algorithms is linked to the operations of natural numbers in unit conversions. Suggestions were made for textbook development and teacher training programs.

• Journal of Soil and Groundwater Environment
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• v.21 no.4
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• pp.50-59
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• 2016

Spatial and temporal changes in nitrification activities and distribution of microbial population of ammonia oxidizing bacteria (AOB) and ammonia oxidizing archaea (AOA) in paddy soils were investigated. Soil samples were collected in March and October 2015 from rice paddy with and without the presence of confined animal feeding operations. Incubation experiments and quantitative polymerase chain reaction showed that AOA's contribution to nitrification kinetics was much higher in locations where organic nitrogen in animal waste is expected to significantly contribute to overall nitrogen budget, and temporal variations in nitrification kinetics were much smaller for AOA than AOB. These differences were interpreted to indicate that different microbial responses of two microbial populations to the types and concentrations of nitrogen substrates were the main determining factors of nitrification processes in the paddy soils. The copy numbers of ammonium monooxygenase gene showed that AOA colonized the paddy soils in higher numbers than AOB with stable distribution while AOB showed variation especially in March. Although small in numbers, AOB population turned out to exert more influence on nitrification potential than AOA, which was attributed to higher fluctuation in AOB cell numbers and nitrification reaction rate per cells.