• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• School Mathematics
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• v.15 no.4
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• pp.723-742
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• 2013

The purpose of this study was to analyze children's proportional reasoning process on an ill-structured "architectural drawing" problem solving and to investigate their level and characteristics of proportional reasoning. As results, they showed various perspective and several level of proportional reasoning such as illogical, additive, multiplicative, and functional approach. Furthermore, they showed their expanded proportional reasoning from the early stage of perception of various types of quantities and their proportional relation in the problem to application stage of their expanded and generalized relation. Students should be encouraged to develop proportional reasoning by experiencing various quantity in ration and proportion situations.

• East Asian mathematical journal
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• v.35 no.4
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• pp.467-488
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• 2019

The purpose of this study is to analyze multiplication facts(1st and 0th multiplication) in elementary mathematics. In the 2015 revised curriculum, students learn multiplication and multiplication facts in the 2nd grade. Many teachers experience difficulties in organizing the multiplication problem situation in multiplication facts(1st and 0th multiplication). This study aims to consider the causes of these difficulties and devise teaching methods. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2015 revised curriculum) and the six foreign elementary mathematics textbooks(Taiwan, Japan, Finland, Unites States, Hongkong, Singapore). As a result, the multiplication problem situation and the multiplication model assume the same bundle and bundle model. Also, we must consider the teaching timing of multiplication facts(1st and 0th multiplication) and the use of commutative law. In this study, we proposed a multiplication teaching scheme in consideration of the multiplication problem situation and teaching model, teaching period and commutative law etc.. to teach multiplication facts(1st and 0th multiplication) in elementary mathematics.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.9
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• pp.1699-1709
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• 2015

Moving terminals like high-speed-train undergo high Doppler frequency shift, and this leads to carrier frequency offsets that have to be compensated to avoid degradation of communication performance. In multiple access mechanism like OFDMA, base-stations need complex hardware to compensate the uplink frequency offset. In this paper, we propose a method, which can reduce burden of the base-station and makes frequency offset estimation and compensation simple. This method contains transmitting new synchronization signal, estimating frequency offsets in base-station, transmitting feedback information to terminal, and compensating the offset in uplink transmission. Simulation results show the proposed method operates well in high Doppler frequency shift conditions of 500 km/h which is the requirements of 5G mobile communication.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.6
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• pp.1409-1418
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• 1998

The recent audio CODEC(Coding/Decoding) algorithms are complex of several coding techniques, and can be divided into DSP tasks, controller tasks and mixed tasks. The traditional DSP processor has been designed for fast processing of DSP tasks only, but not for controller and mixed tasks. This paper presents a new architecture that achieves high throughput on both controller and mixed tasks of such algorithms while maintaining high performance for DSP tasks. The proposed processor, YSP-3, operates four algorithms while maintaining high performance for DSP tasks. The proposed processor, YSP-3, operates functional units (Multiplier, two ALUs, Load/Store Unit) in parallel via 4-issue super-scalar instruction structure. The performance evaluation of YSP-3 has been done through the implementation of the several DSP algorithms and the part of the AC-3 decoding algorithms.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.43-57
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• 2019

The meaning of zero as a number signifying nothing is introduced as a number 1 less than 1 in the first grade mathematics textbook. In addition, the first appearance of the properties of zero are described by exemplary situations of adding zero, subtracting zero, and multiplying by zero in the first and second grade mathematics textbooks. The meaning and the properties of 0, however, are not explicitly dealt with any longer in the follow-up learning. In this study, we discuss the way of introducing zero and the applications of the properties of zero for solving number sentences so that they could help elementary school students understand the meaning and the properties of zero. Based on these results, we suggest some educational implications on teaching and learning mathematics of zero.

• 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.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.4
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• pp.78-86
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• 1999

In this paper, a distributed arithmetic digital neural network with learning and testing phase implemented in a body has been studied. The proposed technique is based on the two facts; one is that the weighting coefficients adjusted will be stored in registers without shift, because input values or input patterns are not changed while learning and the other is that the input patterns stored in registers are not changed while testing. The proposed digital neural network is simulated by hardware description language such as VHDL and verified the performance that the neural network was applied to the recognition of seven-segment. To verify proposed neural networks, we compared the learning process of modified perceptron learning algorithm simulated by software with VHDL for 7-segment number recognizer. The results are as follows: There was a little difference in learning time and iteration numbers according to the input pattern, but generally the iteration numbers are 1000 to 10000 and the learning time is 4 to 200$\mu\textrm{s}$. So we knew that the operation of the neural network is learned in the same way with the learning of software simulation, and the proposed neural networks are properly operated. And also the implemented neural network can be built with less amounts of components compared with board system neural network.