• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.453-474
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• 1998

This study is focused on the possibility if we can use graphic calculators in teaching and learning school mathematics. This study is consisted with four main chapters. In chapter II, the functions of the graphic calculator EL-9600 produced by Sharp Corporation was analyzed focused on the possibilities if the functions could be used in teaching and learning school mathematics. Calculating of real numbers and complex numbers, solving equations and system of linear equations, calculating of matrices, graphing of several functions including polynomial functions, trigonometric functions, exponential and logarithmic functions, calculation of differential and integrals, arranging of statical data, graphing of statistical data, testing of statistical hypotheses, and other more useful functions were founded. In Chapter III, a mathematics textbook developed by Core-Plus Mathematics Project was analyzed focused on how a graphic calculator was used in teaching and learning mathematics, In the textbook, graphic calculator was used as a tool in understanding mathematical concepts and solving problems. Graphic calculator is not just a tool to do complex computations but a tool used in the processes of doing mathematics, In chapter IV, the 7th mathematics curriculum for korean secondary schools was analyzed to find the contents could be taught by using graphic calculators. Most of the domains, except geometric figure, were found that they could be taught by using graphic calculators, In chapter V, a model of a unit using graphic calculator in teaching 7th mathematics curriculum was developed. In this model, graphic calculator was used as a tool in the processes of understanding mathematical concepts and solving problems. This study suggests the possibilities that we can use graphic calculators effectively in teaching and learning mathematical concepts and problem solving for most domains of secondary school mathematics.

• Journal of The Korean Association For Science Education
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• v.37 no.6
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• pp.993-1003
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• 2017

Teachers expect team-based project learning to help students develop collaborative and real-world problem solving skills. In practice, however, students tend to solve problems with simple division of labor, and there is a tendency that learning transfer does not occur in solving problems. The purpose of this study is to develop a collaborative learning model based on the transactive memory system (TMS) and to verify its effectiveness. The collaborative learning model based on the TMS is composed of three stages. The first stage is developing TMS. In this stage, the students learn physics concepts and make knowledge about the expertise of group members through peer instruction. The second stage, activating TMS, is building trust through solving well-defined problems for developing near-transfer. And in the third stage, applying TMS, the students solve an ill-defined problem based on real-world context for practicing far-transfer. Based on this model, a 15-week program including two projects on geometric optics and sound waves was developed and applied to 60 college students. The data for five weeks of one project were collected and analyzed. As a result, the TMS of the experimental group with the TMS-based collaborative learning model improved stepwise. Whereas, the difference between the first week and the last week was statistically significant, while the TMS change of the comparison group using the general project learning model was not significant. Also, the experimental group showed that the learning transfer occurred better in the project than the comparison group. A collaborative learning model based on TMS can be used to learn how students gain synergy through collaboration and how students collaboratively transfer the learned concepts in problem solving.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• Journal for History of Mathematics
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• v.31 no.2
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• pp.93-108
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• 2018

In Nuri curriculum, Korean traditional culture has presented by 'Our country's plays and arts'. Games in the traditional play culture for children include ones such as tangram, top-spinning game, game of slap-match, sabangchigi. In this paper, we analyse concepts of mathematics in Korean childhood traditional plays. In detail, we show that number concepts, geometric space sense, measure calculation ability and problem-solving capability through 15 Korean traditional games.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.659-667
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• 1994

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$. Note that the ultraweak operator topology coincides with the weak topology on $L(H) (cf. [6]). Several functional analysists have studied the problem of solving systems of simultaneous equations in the predual of a dual algebra (cf. [3]). This theory is applied to the study of invariant subspaces and dilation theory, which are deeply related to the classes $A_{m,n}$ (that will be defined below) (cf. [3]). An abstract geometric criterion for dual algebras with property $(A_{\aleph_0}, {\aleph_0})$ was first given in [1].

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.869-874
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• 2011

This paper addresses the trajectory tracking problem for ship berthing by using sliding mode technique. With significant potential advantages: insensitivity to plant nonlinearities, parameter variations, remarkable stability and robust performance with environmental disturbances, the multivariable sliding modes controller is proposed for solving trajectory tracking of ship in harbor area. In this study, the ship position and heading angle are simultaneously tracked to guarantees that the ship follows a given path (geometric task) with desired velocities (dynamic task). The stability of the proposed control law is proved based on Lyapunov theory. The proposed approach has been simulated on a computer model of a supply vessel with good results.

• The Mathematical Education
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• v.48 no.1
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• pp.33-45
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• 2009

The purpose of this article is to study characteristics of Soma Cube in combinatorial-geometric point of view, and to present basic substances and direction for efficient Soma cube activities in school mathematics upon systematical analysis of methods of finding solutions using Inclusion-Exclusion Method. We can apply Inclusion-Exclusion Method to find all possible solutions in Soma Cube activities not as trial-and-error method but as analytical method. Because Inclusion-Exclusion Method can reduce the number of problem-solving variables by making high conjunction in the choice of pieces. Soma cube pieces can be sorted as 'flat' ones and 'non-flat' ones, which would be another effective method in the manipulation of Soma Cube pieces.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2011.06a
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• pp.349-354
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• 2011

This paper addresses the trajectory tracking problem for ship berthing using sliding mode technique. With significant potential advantages: insensitivity to plant nonlinearities, parameter variations, remarkable stability and performance robustness with environmental disturbances, the multivariable sliding modes controller is proposed for solving trajectory tracking of ship in harbor area. In this study, the ship position and heading angle are simultaneously tracked to guarantees that the ship follows a given path (geometric task) with desired velocities (dynamic task). The stability of the proposed control law is proved based on Lyapunov theory. The proposed approach has been simulated on a computer model of a supply vessel with good results.

• IE interfaces
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• v.12 no.1
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• pp.49-55
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• 1999

There are many types of holes to be machined on dies manufactured in the car industry. In this paper we introduce a CAM software developed for hole machining of press dies. The CAM software automatically generates NC files for machining holes from CAD data modeled in the CATIA system. A procedure generating NC files consists of three steps. First, the geometric information such as types of holes, hole positions, hole diameters, and hole depths is extracted from CATIA models. And then tools to be used and operation orders are standardized to establish a data base. Finally, NC files are generated by considering the machining conditions such as feedrate and rpm. It is efficient that holes with the same type and the same size should be grouped and machined by a tool to reduce the tool change time. The optimal tool path for machining the holes in a group can be determined by applying an algorithm solving the traveling salesman problem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.954-957
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• 2004

Based on the authors' previous work, where a geometric constraint handling technique for stiffener layout optimization problem using geometry algorithms was proposed, stiffener layout optimization to maximize natural frequencies of a curved three-dimensional shell structure was performed with a projection method. The original geometry of the shell structure was first projected on a two-dimensional plane, and then the whole optimization process was performed with the projected geometry of the shell except that the original shell structure was used for the eigenproblem solving. The projection method can be applied to baseline structures with a one-to-one correspondence between original and projected geometries such as automobile hoods and roofs.