• Journal for History of Mathematics
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• v.17 no.1
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• pp.61-68
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• 2004

This paper aims at investigating the algebraic solution of cubic and quartic equation and eliciting the didactical meanings of them. First, I examine the event which relates to the equation in the history of mathematics and investigate the algebraic solution of cubic and quartic equation. And then I elicit the didactical suggestions which are required of teachers and students when they investigate the algebraic solution of cubic and quartic equation. In general, the investigation of these solutions is the valuable task which requires the algebraic intuition and technique for students and certificates expert knowledge for teachers.

• School Mathematics
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• v.10 no.1
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• pp.23-42
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• 2008

The purpose of this study was to describe characteristics of thinking in elementary gifted students' solutions to algebraic tasks. Especially, this paper was focused on the students' strategies to develop generalization while problem solving, the justifications on the generalization and metacognitive thinking emerged in stildents' problem solving process. To find these issues, a case study was conducted. The subjects of this study were four 6th graders in elementary school-they were all receiving education for the gifted in an academy for the gifted attached to a university. Major findings of this study are as follows: First, during the process of the task solving, the students varied in their use of generalization strategies and utilized more than one generalization strategy, and the students also moved from one strategy toward other strategies, trying to reach generalization. In addition, there are some differences of appling the same type of strategy between students. In a case of reaching a generalization, students were asked to justify their generalization. Students' justification types were different in level. However, there were some potential abilities that lead to higher level although students' justification level was in empirical step. Second, the students utilized their various knowledges to solve the challengeable and difficult tasks. Some knowledges helped students, on the contrary some knowledges made students struggled. Specially, metacognitive knowledges of task were noticeably. Metacognitive skills; 'monitoring', 'evaluating', 'control' were emerged at any time. These metacognitive skills played a key role in their task solving process, led to students justify their generalization, made students keep their task solving process by changing and adjusting their strategies.

• School Mathematics
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• v.18 no.4
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• pp.819-838
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• 2016

This research analyzed proportional reasoning abilities of the 5th grade students who learned only the basis of ratio and rate and 6th grade students who also learned proportion and cross product strategy. Data were collected through the proportional reasoning tests and the interviews, and then the achievement of the students and their proportional reasoning strategies were analyzed. In the light of such analytical results, the conclusions are as follows. Firstly, there is not much difference between 5th and 6th grade students in the achievement scores. Secondly, both 5th and 6th graders are less familiar with the geometric, qualitative and comparisons tasks than the other tasks. Thirdly, not only 5th graders but also 6th graders used informal strategies much more than the formal strategy. Fourthly, some students can't come up with other strategies than the cross product strategy. Finally, many students have difficulties in discerning proportional situation and non-proportional situations. This study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: focusing on letting students use their informal strategies fluently in geometric, qualitative, and comparisons tasks as well as algebraic, quantitative, and missing value tasks focusing on the concept of ratio and proportion instead of enforcing the formal strategy.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.218-223
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• 2012

Maintenance and improvement of the graph connectivity is very important for decentralized multi-agent systems. Although the CBBA (Consensus-Based Bundle Algorithm) guarantees suboptimal performance and bounded convergence time, it is only valid for connected graphs. In this study, we apply a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimation, we design a decentralized gradient controller to maintain the graph connectivity while agents are traveling to perform assigned tasks. Simulation result for fully-actuated first-order agents that move in a 2-D plane are presented.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.4
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• pp.38-49
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• 1998

A fossil power plant can be modeled by a lot of algebraic equations and differential equations. When we simulate a large, complicated fossil power plant by a computer such as workstation or PC, it takes much time until overall equations are completely calculated. Therefore, new processing systems which have high computing speed is ultimately needed for real-time or high-speed(faster than real-time) simulators. This paper presents an enhanced strategy in which high computing power can be provided by parallel processing of DSP processors with communication links. DSP system is designed for general purpose. Parallel DSP system can be easily expanded by just connecting new DSP modules to the system. General urpose DSP modules and a VME interface module was developed. New model and techniques for the task allocation are also presented which take into account the special characteristics of parallel I/O and computation. As a realistic cost function of task allocation, we suggested 'simulation period' which represents the period of simulation output intervals. Based on the development of parallel DSP system and realistic task allocation techniques, we cound achieve good efficiency of parallel processing and faster simulation speed than real-time.

• The Mathematical Education
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• v.51 no.1
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.159.2-159
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• 2001

The new approach of homogeneous robust control systems synthesis, both linear, and nonlinear and non-stationary is offered. The control is carried out, providing the given phase constrains varied in acceptable limits, in view of constrains on its value and incompleteness of the information about functioning disturbances. The approach is based on introduction of auxiliary integral surfaces, on which the initial moving is projected. As a result the reduced equivalent moving is forming, described by the scalar equation which in many important cases can be integrated directly. On the basis of the obtained equation solving of a synthesis task is carried out and can be reduced to algebraic or integral inequalities. The final relations defined for linear equivalent moving are presented.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.492-495
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• 1997

This paper aims to derive a mathematical model of the dynamics of handling task in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraints of tight area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of contact-area are discussed. Finally, it is shown that even in the simplest case of dual single D.O.F. manipulators there exists a sensory feedback from sensing data of he rotational angle of the object to command inputs to joint actuators and this feedback connection from sensing to action eventually realizes secure grasping of the object, provided that he object is of rectangular shape and motion is confined to a horizontal