• Journal of the Korean School Mathematics Society
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• v.20 no.3
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• pp.325-344
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• 2017

Since PISA2006, the computer based assessment in mathematics(CBAM) was introduced for the first times and at last PISA2015 used all items in CBAM for problem solving. In this study, we focused on which important properties were considered in constructing geometric 'fence items' used in PISA 2015 to find the future direction over our teacher education, especially for constructing 'computer based assessment items.' For the purpose of the study, we analyzed the fence items on three components such as dependency, invariant, and path found in dragging activities, within a computer environment using the dynamic Geometry Software, GSP. Also, for the future, we provided an open-ended problem related to the fence items, which we could use as the merit of computer-based environment.

• Journal of Science Education
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• v.41 no.3
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• pp.405-425
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• 2017

This study aimed to investigate the life and works of Robert Hooke, an ingenious scientist in the era of scientific revolution, and to give some implications of invention education for science education. The publications and critics of Robert Hooke were analyzed to find out the personal setbacks how he showed excellent performances across the fields of science. The research finding showed that he tried to make geometric and visualized reasoning based on the empirical phenomenon, had much interest in the devices and methods for measurement and observation in the experiment, and made technical devices by himself. The ingenuity of Robert Hooke could be revealed by the rich resources in his childhood, his talent of drawing for depiction, and his colleagues and teachers with favors of diverse fields of disciplines and empirical tradition. As well, it was likely that his monistic viewpoint between the reality and scientific theories, led himself to develop interesting instruments for scientific experiments. Thus, this study suggested some implications to combine invention education with science education.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.503-523
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• 2010

The current mathematics curriculum are consist of the following domains: 'Characteristics', 'Objectives', 'Contents', 'Teaching and learning method', and 'Assessment'. The mathematics standards which students have to learn in the school are presented in the domain of 'Contents'. 'Contents' are consist of the following sub-domains: 'Number and Operation', 'Geometric Figures', 'Measures', 'Probability and Statistics', and 'Pattern and Problem-Solving' (Elementary School); 'Number and Operation', 'Geometry', 'Letter and Formula', 'Function', and 'Probability and Statistics' (Junior and Senior High School). These sub-domains of 'Contents' are dealing with mathematical subjects, except 'Problem-Solving' at the elementary school level. In this study, the sub-domain of 'mathematical process' was suggested in an equal position to the typical sub-domains of 'Contents'.

• School Mathematics
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• v.10 no.2
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• pp.181-197
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• 2008

Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.223-239
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• 2017

In this paper, it is aimed to design the teaching units 'Inquiry into the isoperimetric problem of triangle and quadrilateral' to give elementary gifted students experience of mathematization. For this purpose, the teacher and the class observer (researcher) made a discussion about the design of the teaching unit through the analysis of the class based on the thought processes appearing during the problem solving process of each group of students. The following is a summary of the discussions that can give educational implications. First, it is necessary to use mathematical materials to reduce students' cognitive gap. Second, it is necessary to deeply study the relationship between the concept of side, which is an attribute of the triangle, and the abstract concept of height, which is not an attribute of the triangle. Third, we need a low-level deductive logic to justify reasoning, starting from inductive reasoning. Finally, there is a need to examine conceptual images related to geometric figure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.2
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• pp.1-15
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• 1986

The algorithm Proposed utilizes the two-levels technique. In the first level which consists of two phases, the cross-sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Rahson method. In the second level, the geometric shape is optimized utilizing the unindirectional search technique of the Powell method which make it possible to minimize only the objective function. The algorithm Proposed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examine its applicability and stability. The numerical comparisons show that the two-Levels algorithm Proposed in this study is safely applicable to any design criteria, and the convergency rate is relathely fast and stable compared with other iteration methods for the geometric optimization of truss structures.

• Journal of The Korean Association of Information Education
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• v.22 no.3
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• pp.385-396
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• 2018

This research supports the idea that manipulative devices can be an effective modality tool for learning abstract concepts involved with identifying geometric shapes and enhance learners' problem solving and motivation. Until recently specified manipulative device has been adapted only in traditional classroom environment and it has been very rare to find devices that is designed for online-basis. This study focused on designing and implementing an educational software which guide learners with geoboard in identification and characteristics of polygons. In addition to the function to draw and to delete various shapes, this software helps learners immediately assess the outcome. The results of the Delphi Technique show promising evidence for it being a very efficient means to learn geometric shapes and increase learners' motivation to learn the subject matter.

• Advances in nano research
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• v.16 no.5
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• pp.473-487
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• 2024

The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the α range of 0 to 1.5, where the impact of geometric nonlinearity on CC nanobeams can be disregarded. Furthermore, the nonlinear frequency ratio exhibits an increasing trend as the parameter µ is incremented, with a diminishing dependency on nanobeam length (L). Additionally, it is established that as the nanobeam length increases, a critical point is reached at which a sharp rise in the nonlinear frequency ratio occurs, particularly within the nanobeam length range of 10 nm to 30 nm. These findings collectively contribute to a comprehensive understanding of the nonlinear vibration behavior of BFG nanobeams in relation to various parameters.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.245-263
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• 2013

Mathematical learning via projects, which enables the reconstruction of curriculum through integration and emphasizes the process of solving problems by posing questions, has attracted the attention of the department of mathematics. This research is aimed at exploring the link between mathematics and project learning by analyzing an example of student-oriented project 'the secrets of pyramid' focused on understanding 'triangle' specifically designed for forth graders. From 115-hour process of subject-oriented project, this study reinterpreted the mathematical meaning of only 24 hours directly related to mathematics, especially to figure exploration. Consequently, this problem solving involved a variety of geometric activities as a process, such as measuring an angle, constructing a triangle, etc. Thus students attempt to actively participate in the process, thereby allowing them to learn how to measure things more accurately. Moreover, project learning improved students' understanding on not only plane figures but solid figures. This indicates that by project learning, learning from given problems or contents can be extended to other mathematical areas.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.247-250
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• 2007

Flexible media such as the paper, the film, etc. are thin, light and very flexible. They behave in geometrically nonlinear. Any of small force makes large deformation. So we must including aerodynamic effect when its behavior is predicted. Thus, it becomes fully coupled fluid-structure interaction(FSI) problem. In FSI problems, where the fluid mesh near the structure undergoes large deformations and becomes unacceptably distorted, which drive the time step to a very small value for explicit calculations, the arbitrary Lagrangian-Eulerian(ALE) methods or rezoning are used to create a new undistorted mesh for the fluid domain, which allows the calculations to continue. In this paper, FE sheet model considering geometric nonlinearity is formulated to simulate the behavior of the flexible media. Aerodynamic force to the media by surrounding air is calculated by solving the incompressible Navier-Stokes equations. Q2Q1(Taylor-Hood) element which means biquadratic for velocity and bilinear for pressure is used for fluid domain. Q2Q1 element satisfies LBB condition and any stabilization technique is not needed. In this paper, cantilevered sheet in the viscous incompressible Navier-Stokes flow is simulated to check the mesh motion and numerical integration scheme, and then falling paper in the air is simulated and the effects of some representative parameters are investigated.