• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.337-362
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• 2008

Nowadays the education of Mathematics is more important than any other courses in the school. But the most students have felt the difficulty and uncomfortableness in studying Mathematics, especially the geometry course. Moreover teachers also consider that the teaching of geometry is the hardest part of Mathematics. Therefore we suggest an effective method of teaching the geometry course for the middle school students. We provide the activity papers which contain mathematics problems based on the practical life of students. And we analyze the effects of the activity papers using the questionnaire.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.101-122
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• 2004

It has been always the issue to discuss 'how we teach mathematics' for the mathematical learning. As for an answer to this, it was suggested to use the history of mathematics. The reason is simple that is, the education of mathematics requires to understand mathematics and to know the history of mathematics is effective for mathematical understanding. In particular, the history of algebra was discussed to some extent as an illustration. This study focuses on the history of geometry from this point of view. We review the history of geometry by comparison in terms of three criteria from the origin of geometry to modem differential geometry in the middle of the 20th century, which are backgrounds (inner or outer ones), characterizations (approach, method, object), influences to modem mathematics. As an application of such historical data to the education of mathematics, we pose the problem to determine the order of instruction in mathematics.

• International Journal of Contents
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• v.5 no.4
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• pp.55-61
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• 2009

In this paper, we propose a hierarchical method for segmenting a given 3D mesh, which hierarchically clusters sharp vertices of the mesh using the metric of geodesic distance among them. Sharp vertices are extracted from the mesh by analyzing convexity that reflects global geometry. As well as speeding up the computing time, the sharp vertices of this kind avoid the problem of local optima that may occur when feature points are extracted by analyzing the convexity that reflects local geometry. For obtaining more effective results, the sharp vertices are categorized according to the priority from the viewpoint of cognitive science, and the reasonable number of clusters is automatically determined by analyzing the geometric features of the mesh.

• Journal of Information Science Theory and Practice
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• v.7 no.2
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• pp.32-39
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• 2019

A convolutional neural network (CNN) has been widely used in facial expression recognition (FER) because it can automatically learn discriminative appearance features from an expression image. To make full use of its discriminating capability, this paper suggests a simple but effective method for CNN based FER. Specifically, instead of an original expression image that contains facial appearance only, the expression image with facial geometry visualization is used as input to CNN. In this way, geometric and appearance features could be simultaneously learned, making CNN more discriminative for FER. A simple CNN extension is also presented in this paper, aiming to utilize geometric expression change derived from an expression image sequence. Experimental results on two public datasets (CK+ and MMI) show that CNN using facial geometry visualization clearly outperforms the conventional CNN using facial appearance only.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.185-206
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• 2009

In the study, I conducted the teaching experiment designed to instruct proof to four 7th grade students by utilizing the analysis method. As the results of this study I could identified that it is effective to teach and learn to find proof methods using the analysis. The results of the study showed that four 7th grade students succeeded in finding the proof methods by utilizing the analysis and representing the proof after 15 hours of the teaching experiment. In addition to the difficulties that students faced in learning proof utilizing the analysis were related to the search for the light conditions for triangles to be congruent, symbolic representation of the proof methods, reinterpretation of drawings given in the proof problems.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.701-722
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• 2010

Students have to investigate, experiment and inquire using the manipulative materials and real-world thing for studying Geometry. Manipulative materials activities encourage to understand mathematical concept and connection of symbol. Experiment activities using the computer focused the student's intuitive and inquisitive activities because of visualization of an abstract mathematics concept. This study developed a workbook through the use of manipulative materials and computer for operating and experimenting, and suggested a method for inquiry of geometrical properties and proved an effect. Manipulative materials-experiment activities was proven effective to middle level and lower level students in understanding the geometrical properties, and was proven effective to high level and lower level students when it comes to mathematical communication ability. When students operate, at first, they have to know about the feature and information of the materials, and the teacher has to make an elaborate plan and encourages the students to discuss about this.

• Steel and Composite Structures
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• v.36 no.1
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• pp.47-62
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• 2020

In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.