• Communications of Mathematical Education
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• v.26 no.1
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• pp.85-108
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• 2012

The comprehensive implication in justification activity that includes the proof in the elementary school level where the logical and formative verification is hard to come has to be instructed. Therefore, this study has set the following issues. First, what is the mathematical justification type shown in the Number and Operations, and Geometry? Second, what are the errors shown by students in the justification process? In order to solve these research issues, the test was implemented on 62 third grade elementary school students in D City and analyzed the mathematical justification type. The research result could be summarized as follows. First, in solving the justification type test for the number and operations, students evenly used the empirical justification type and the analytical justification type. Second, in the geometry, the ratio of the empirical justification was shown to be higher than the analytical justification, and it had a difference from the number and operations that evenly disclosed the ratio of the empirical justification and the analytical justification. And third, as a result of analyzing the errors of students occurring during the justification process, it was shown to show in the order of the error of omitting the problem solving process, error of concept and principle, error in understanding the questions, and technical error. Therefore, it is prudent to provide substantial justification experiences to students. And, since it is difficult to correct the erroneous concept and mistaken principle once it is accepted as familiar content that it is required to find out the principle accepted in error or mistake and re-instruct to correct it.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.137-144
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• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.191-209
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• 2008

In this paper, we model grain boundary evolution based on a multiple level set method. Grain boundary migration under a curvature-induced driving force is considered and the level set method is employed to deal with the resulting topological changes of grain structures. The complexity of using a level set method for modeling grain structure evolution is due to its N-phase nature and the associated geometry compatibility constraint. We employ a multiple level set method with a predictor-multicorrectors approach to reduce the gaps in the triple junctions down to the grid resolution level. A ghost cell approach for imposing periodic boundary conditions is introduced without solving a constrained problem with a Lagrange multiplier method or a penalty method. Numerical results for both uniform and random grain structures evolution are presented and the results are compared with the solutions based on a front tracking approach (Chen and Kotta et al. 2004b).

• School Mathematics
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• v.3 no.2
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• pp.447-473
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• 2001

Since the greater part of mathematical concepts have been developed in the direction of “from the concrete and realistic aspects to the abstract level”, children should be secured to learn mathematics genetically with various manipulative materials. The aim of this study is to instigate the active use of geoboards in mathematics classroom. To achieve this arm, we first embodied the several significances on the use of geoboards in mathematics instruction. And we then performed an instruction that children discover and justify the formula related to the area of trapezoid by exploring with geoboards, and analyzed the instructional episode to support our assertion about some secure merit accompanied by using geoboards. From this study, we obtained the conclusion that geoboard activity contains many significances such as children can explore congruence, symmetry, similarity, fundamental properties of figures, and pattern. Futhermore, geoboard activity enable children to transform a figure into other equivalently, develop spatial sense, have basic experiences for coordinate geometry, build a concrete model to explain abstract ideas, and foster the ability of problem solving and mathematical thinking.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.83-97
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• 2010

The purposes of this study were to explore in depth about 5th graders' mathematical speaking and writing abilities and to investigate differences on those abilities. The study involved 3 5th graders and their speaking and writing abilities in geometry area were analyzed. According to the results of the study, the children had difficulties in selecting and using appropriate mathematical languages to explain mathematical concepts, mathematical ideas, and problem solving steps. The children who participated in the study showed higher ability in speaking than writing.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.759-768
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• 2004

The torsion of a penny-shaped crack in a transversely isotropic strip is investigated in this paper. The shear moduli are functionally graded in such a way that the mathematics is tractable. Hankel transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by taking the asymptotic behavior of Bessel function into account. The effects of material property parameters and geometry criterion on the stress intensity factor are investigated. Numerical results show that increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface can suppress crack initiation and growth, and that the stress intensity factor varies little with the increasing of the strip's height.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.7
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• pp.989-1002
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• 1995

In this paper, we propose a new algorithm, so called the Signal Decorrelation via Virtual Translation of Array (SDVTA) algorithm, for estimating the directions of arrival(DOA's) of narrowband coherent signals incident on a general array. An effective procedure is composed of transforming the steering matrix of the original array into that of the virtually translated sensor array and taking the average of the transformed covariance matrices in order to decorrelate the coherent signals. The advantage of this approach is in that 1) it can estimate the DOA's of m-1 coherent signals(M : the number of array sensors) since the effective aperture size is never reduced. 2) a geometry of array is unrestricted for solving the narrowband coherency problem. 3) the efficiency of signal decorrelation does not depend on the phase differences between coherent signals unlike the Coherent Signal Subspace Method (CSM). Simulation results are illustrated to demonstrate the superior performance of this new algorithm in comparison with the normal MUSIC and examine the comparative performance with the various choices of the optimal transformation matrix under coherent signal environments.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.723-743
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• 1998

This study was designed for the purpose of finding some gender differences in the mathematical creative problem-solving ability. For this research, we selected two problems. One is "counting marbles" of algebra, and the other is "drawing figures" of geometry. And we examined and analyzed the written responses of the students with classifying the four categories; fluency, flexibility, originality, and elaboration. These are the factors of the creativity. There were no significant gender differences in the fluency, flexibility, and originality in both problems. but girls got significantly higher scores than boys in elaboration. In conclusion, boys tried unusual and special responses but gave many incorrect and many similiar answers, whereas girls had low scores in high originality but gave less incorrect and less overlapping answers than boys did.swers than boys did.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.41-55
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• 2001

The purpose of this study was to compare and analyze the curricula of kindergarten and elementary school and to present a plan for connecting the two curricula. The curricula emphasized mathematical thinking and problem solving instead of fragmentary knowledge and adopted the streamed curriculum based on children’s ability and interest. And both of them consisted of number and operation, geometry, measurement, statistics, and put emphasis on activity such as real life experience, play, manipulation of concrete objects, and communication. However, there are some kinds of differences between them, because the kindergarten curriculum is not included in the common curriculum, from 1st grade to 10th grade. Thus, this study recommended several ideas based. Thus, this study recommended several ideas based on theories to connect the mathematics curricula of kindergarten and elementary school.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.518-519
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• 2006

A connection between pulse-periodical laser radiation power and stability of liquid-metal contacts between powder particles during selective laser sintering (SLS) is determined based on analysis solving the problem of stability of liquid column in the gravity and capillary forces field. On the grounds of obtained relationships the optimization of pulse-periodical laser radiation power and SLS-process duration is realized, that allows to produce voluminous powder porous materials with pre-determined physical and mechanical properties and surface geometry. Results of metallographic investigations of powder porous materials of titanium powder produced with technological regimes calculated by means of obtained relationships are given in the work