• Journal of Gifted/Talented Education
• /
• v.18 no.1
• /
• pp.53-77
• /
• 2008

This study was conducted with the focus on the process of constructing 3 definition and produced definitions as well as gifted students' conceptions of a mathematical definition In the study, the students made five types of regular polyhedrons (section1), observed them and stated their characteristics (section2) and then constructed a definition of regular polyhedrons based on their observations (section3). We divided students into two groups by analyzing students' definitions. One group made definitions that were consist with a mathematical definition of regular polyhedrons, the other one made definitions that were not. We checked if they fulfilled requirements for a mathematical definition. Researchers sought to gain various suggestions through the analysis of the observations and definition laid down by the students and through the characteristics shown by the students in the process of defining the concept.

• Communications of Mathematical Education
• /
• v.13 no.2
• /
• pp.527-534
• /
• 2002

멀티미디어 환경에 익숙한 중 ${\cdot}$ 고등학생들에게 친숙하고 손쉽게 기하도형을 공부할 수 있는 교육환경으로 제공하기 위한 방법을 제시하기 위해, 본 논문에서는 정다면체(4, 6, 8, 12, 20면체)의 접기와 펼치기를 GSP(Geometer's Skechpad)로 구현한 후에 JAVA 언어를 사용하여 웹으로 변환시켰다.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.2
• /
• pp.351-370
• /
• 2013

The purpose of this study is to analyze the modes of visualization which appears in the process of thinking that mathematically gifted 6th grade students get to understand components of the three-dimensional shapes on the duality of regular polyhedrons, find the duality relation between the relations of such components, and further explore on whether such duality relation comes into existence in other regular polyhedrons. The results identified in this study are as follows: First, as components required for the process of exploring the duality relation of polyhedrons, there exist primary elements such as the number of faces, the number of vertexes, and the number of edges, and secondary elements such as the number of vertexes gathered at the same face and the number of faces gathered at the same vertex. Second, when exploring the duality relation of regular polyhedrons, mathematically gifted students solved the problems by using various modes of spatial visualization. They tried mainly to use visual distinction, dimension conversion, figure-background perception, position perception, ability to create a new thing, pattern transformation, and rearrangement. In this study, by investigating students' reactions which can appear in the process of exploring geometry problems and analyzing such reactions in conjunction with modes of visualization, modes of spatial visualization which are frequently used by a majority of students have been investigated and reactions relating to spatial visualization that a few students creatively used have been examined. Through such various reactions, the students' thinking in exploring three dimensional shapes could be understood.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.18 no.4
• /
• pp.155-159
• /
• 2008

In this work, we report synthesis of free-standing ZnO/Zn core-shell micro-polyhedrons using metal Zn pellets as a source material by the thermal chemical vapor deposition process. Scanning and transmission electron microscopy measurements were introduced to investigate morphologies and structural properties of as-grown ZnO/Zn core-shell micro-polyhedrons. It was found that micro-polyhedrons were composed of inner single-crystalline metal Zn surrounded by single-crystalline ZnO nanorod arrays. The inner single crystalline metal Zn with micro-scale diameter has a hexagonal crystal structure. Diameter and height of ZnO nanorods covering the metal Zn surface are below 10 nm and 100 nm, respectively. It was also confirmed that c-axis oriented ZnO nanorods are single crystalline with a hexagonal crystal structure.

• Proceedings of the Korea Society of Mathematical Education Conference
• /
• 2009.10a
• /
• pp.31-33
• /
• 2009

• Journal of Educational Research in Mathematics
• /
• v.14 no.1
• /
• pp.19-37
• /
• 2004

In school mathematics, polygon and polyhedron are defined by vague terms such as "surrounded" or "formed" Moreover, the inclusion of boundary and interior in the definition of polygon and polyhedron is varied according to the context. Polygon and polyhedron are considered as "context-dependent concept" in school mathematics. Elementary school mathematics introduces a surface only in the context of solid, yet secondary school mathematics explains a surface as the trace of the line movement. From the perspective of fallabilism, it is possible and desirable to lead students to revise and improve their conceptions on polygon, polyhedron, and surface. It is more appropriate to name a face, an edge, and a vertex rather than to express a face of polyhedron, an edge of polyhedron, and a vertex of polyhedron in textbooks. The term "surface as a polygon" in secondary mathematics textbooks shows a conflict between intuitive approach in elementary school and logical approach in secondary school.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2022.05a
• /
• pp.32-32
• /
• 2022

• The Mathematical Education
• /
• v.53 no.4
• /
• pp.493-507
• /
• 2014

The purpose of this study is to analyze how high school students form and interpret the mental image in the process of solving regular polyhedron problems. For this purpose, a set of problems about the regular polyhedron's vertex is developed on the base of the regular polyhedron's duality and circulation. and applied to 2 students of the 12th graders in D high school. After 2 hours of teaching and learning and another 2 hours of mental image-analysis process, the following research findings are obtained. Fisrt, a student who recorded medium high-level grade in the national scholastic test can build the dynamic image or the patten image in the process of solving regular polyhedron's vertex problems by utilizing the 3D geometry program. However, the other student who recorded low-level grade can build the concrete-pictorial image. Second, pattern image or dynamic image can help students solve the regular polyhedron's vertex problems by proper transformation of informations and the mental images while the concrete-pictorial image does not help. Hence, it is recommended that the mathematics teachers should develop teaching and learning materials about the regular polyhedron's duality and circulation and also give students suitable questions to build the various mental images.

• Korean Journal of Crystallography
• /
• v.6 no.2
• /
• pp.88-92
• /
• 1995

Higly pure silicon crystals with an almost perfect lattice structure constityte a powerful metrological tool. The streographic standard prohection for the (111) orientation of diamond structure found by the Laue method shows angles between net planes of 60°. This value is known to be certain to some 10-8 rad. We have made a six-faced silicon polygon, and the (220) lattice planes of the polygon act as a reference angular standard. The information of angles between lattice planes could be taken by the X-ray diffraction. The angle of the rotary encoder have been calibrated using the silicon angle standard. The X-ray optics was double crystal arrangement.

• The Mathematical Education
• /
• v.45 no.2 s.113
• /
• pp.191-204
• /
• 2006

Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.