• 한국초등수학교육학회지
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• 제16권3호
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• pp.451-469
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• 2012

본 연구는 초등학교 6학년 학생들의 넓이 개념 이해의 여러 측면을 조사하고 보고하는 데에 그 목적이 있다. 본 연구에서는 넓이의 의미 이해, 평면도형(직사각형, 평행사변형, 삼각형)의 넓이 구하기, 넓이 공식 제시하기, 넓이 공식의 성립 이유 설명하기 등과 관련된 총 4개의 문항들로 검사지를 구성하였으며, 이 검사지를 활용하여 초등학교 6학년 학생 122명의 넓이 개념을 조사하였다. 본 연구의 결과, 학생들은 넓이의 의미 이해에서 가장 낮은 수행 정도를 나타냈으며, 그 다음으로는 넓이 구하기, 넓이 공식 제시하기, 넓이 공식의 성립 이유 설명하기의 순서로 낮은 수행 정도를 나타냈다. 한편, 학생들은 넓이 공식 제시하기에서 직사각형, 삼각형, 평행사변형의 순서로 낮은 수행 정도를 나타냈으며, 넓이 공식의 성립 이유 설명하기에서는 삼각형, 평행사변형, 직사각형의 순서로 낮은 수행 정도를 나타냈다. 이러한 결과를 바탕으로 본 연구에서는 학생들의 이해가 미흡한 것으로 나타난 부분을 개선하기 위한 교수학적 시사점을 제안하였다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제6권2호
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• pp.85-91
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• 2002

The purpose of this study is to analyze elementary students' understanding the relationship between perimeter and area in geometric figures. In this study, the questionaries were used. In the survey, the subjects were elementary school students in In-cheon city. They were 86 students of the fifth grade, 86 of the sixth. They were asked to solve the problems which was designed by the researcher and to describe the reasons why they answered like that. Study findings are as following; Students have misbelief about the concept of the relationship between perimeter and area in geometric figures. Therefore, 1 propose the method fur teaching about the relationship between perimeter and area in geometric figures. That is teaching via problem solving.. In teaching via problem solving, problems are valued not only as a purpose fur learning mathematics but also a primary means of doing so. For example, teachers give the problem relating the concepts of area and perimeter using a set of twenty-four square tiles. Students are challenged to determine the number of small tiles needed to make rectangle tables. Using this, students can recognize the concept of the relationship between perimeter and area in geometric figures.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.565-586
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• 1998

Like many other school subjects, terminology is a starting point of mathematical thinking, and plays a key role in mathematics learning. Among several areas in mathematics, geometry is the area in which students usually have the difficulty of learning, and the new terms are frequently appeared. This is why we started to investigate geometric terms first. The purpose of this study is to investigate geometric terminology in school mathematics. To do this, we traced the historical transition of geometric terminology from the first revised mathematics curriculum to the 7th revised one, and compared the geometric terminology of korean, english, Japanese, and North Korean. Based on this investigation, we could find and structuralize the following four issues. The first issue is that there are two different perspectives regarding the definitions of geometric terminology: inclusion perspective and partition perspective. For example, a trapezoid is usually defined in terms of inclusion perspective in asian countries while the definition of trapezoid in western countries are mostly based on partition perspective. This is also the case of the relation of congruent figures and similar figures. The second issue is that sometimes there are discrepancies between the definitions of geometric figures and what the name of geometric figures itself implies. For instance, a isosceles trapezoid itself means the trapezoid with congruent legs, however the definition of isosceles trapezoid is the trapezoid with two congruent angles. Thus the definition of the geometric figure and what the term of the geometric figure itself implies are not consistent. We also found this kind of discrepancy in triangle. The third issue is that geometric terms which borrow the name of things are not desirable. For example, Ma-Rum-Mo(rhombus) in Korean borrows the name from plants, and Sa-Da-Ri-Gol(trapezoid) in Korean implies the figure which resembles ladder. These terms have the chance of causing students' misconception. The fourth issue is that whether we should Koreanize geometric terminology or use Chinese expression. In fact, many geometric terms are made of Chinese characters. It's very hard for students to perceive the ideas existing in terms which are made of chines characters. In this sense, it is necessary to Koreanize geometric terms. However, Koreanized terms always work. Therefore, we should find the optimal point between Chines expression and Korean expression. In conclusion, when we name geometric figures, we should consider the ideas behind geometric figures. The names of geometric figures which can reveal the key ideas related to those geometric figures are the most desirable terms.

• 한국학교수학회논문집
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• 제26권2호
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• pp.111-135
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• 2023

본 연구는 도형의 닮음 단원에서 알지오매스를 활용한 학생 중심의 탐구 수업을 진행하고, 학생들이 보이는 학습의 특징을 의사소통 관점에서 분석하여 도형의 닮음과 관련되는 교수학적 시사점을 기술하고자 하였다. 이를 위해 알지오매스를 활용하여 삼각형의 닮음 여부를 탐색하는 교수-학습 자료를 개발하였으며, 이를 적용한 수업에서 학생들이 수행한 탐구 활동의 의사소통 양상에 비추어 학생들이 보인 닮음 학습의 특징을 '닮음비 이해', '삼각형의 닮음 조건 파악', '합동과 닮음 개념 비교'로 범주화하여 기술하였다. 학생들은 알지오매스에 기반한 탐구 활동을 통해 도형의 닮음비와 넓이의 비, 삼각형의 합동 및 닮음의 뜻과 조건 등 닮음과 관련한 주요 개념의 의미와 이들 사이의 수학적 관계를 논하였으며, 이로부터 도형의 닮음에 대한 오개념을 개선함으로써 보다 깊은 수학적 이해를 개발하였다. 이처럼 알지오매스를 활용한 도형의 닮음 교수-학습에서 의미 있는 교수학적 성과를 얻는 데는 알지오매스 환경이 갖는 특징뿐 아니라 학생의 사고를 촉진하는 교사의 조정과 중재가 주요한 역할을 하는 것으로 드러났다.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권2호
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• pp.197-219
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• 2008

Unlike ordinary situations, deifinitions play a very important role in mathematics education in schools. Mathematical concepts have been mainly acquired by given definitions. However, according to didactical intentions, mathematics education in schools has employed mathematical concepts and definitions with less strict forms than those in pure mathematics. This research mainly discusses definitions used in geometry (promising) course in primary schools to cope with possibilities of creating misconception due to this didactical transformation. After analyzing problems with potential misconceptions, a survey was conducted $\underline{with}$ 80 primary school teachers in Jeju to investigate their recognitions in meaning of mathematical concepts in geometry and attitudes toward teaching. Most of the respondents answered they taught their students while they knew well about mathematical definitions in geometry but the respondents sometimes confused mathematical concepts of polygons and circles. Also, they were aware of problems in current mathematics textbooks which have explained figures in small topics (classes). Here, several suggestions are proposed as follows from analyzing teachers' recognitions and researches in mathematical viewpoints of definitions (promising) in geometric figures which have been adopted by current mathematics textbooks in primary schools from the seventh educational curriculum. First, when primary school students in their detailed operational stage studying figures, they tend to experience $\underline{a}$ collision between concept images acquired from activities to find out promising and concept images formed through promising. Therefore, a teaching method is required to lessen possibility of misconceptions. That is, there should be a communication method between defining conceptual definitions and Images. Second, we need to consider how geometric figures and their elements in primary school textbooks are connected with fundamental terminologies laying the foundation for geometrical definitions and more logical approaches should be adopted. Third, the consistency with studying geometric figures should be considered. Fourth, sorting activities about problems in coined words related to figures and way and time of their introductions should be emphasized. In primary schools mathematics curriculum, geometry has played a crucial role in increasing mathematical ways of thoughts. Hence, being introduced by parts from viewpoints of relational understanding should be emphasized more in textbooks and teachers should teach students after restructuring this. Mathematics teachers should help their students not only learn conceptual definitions of geometric figures in their courses well but also advance to rigid mathematical definitions. Therefore, that's why mathematics teachers should know meanings of concepts clearly and accurately.

• 한국환경보건학회지
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• 제36권5호
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• pp.351-359
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• 2010

The objectives of this study were to understand the characteristics of residents in industrial areas and factors affecting exposure to the Volatile Organic Compounds(VOCs : Benzene, Toluene, Xylene) as well as to assess exposure levels according to house-type, and whether residents were indoors or outdoors. This research was designed to assess the differences in exposure levels to indoor, outdoor and personal VOCs in a case group and a control group across all areas, as well as in each different area, from May to October 2007, in. 110 residents of the G, Y and H industrial areas of the Jun-nam province. The geometric mea-levels of airborne benzene for the case group 1.31part per billion(ppb) indoor, 1.29 ppb outdoor, and 1.32 ppb for personal exposure were significantly higher than for the control group 0.99, 0.87 and 0.57 ppb, respectively. The geometric mean level for toluene personal exposure across the G, Y and H areas was 5.70 ppb for the case group and 6.31 ppb for the control group. While the outdoor level was 4.27 ppb for the case group and 5.06 ppb for the control group, The indoor level for the case group was 4.78 ppb, similar to that of the control group 4.69 ppb. The geometric mean levels for airborne xylene across the G, Y and H areas were 0.16 ppb(outdoor), 0.12 ppb(personal exposure) and 0.10 ppb(indoor) for the case group, and for the control group were 0.17(personal exposure) and 0.09 ppb(indoor and outdoor). The indoor/outdoor(I/O) ratio for case group is 1.19, while that of the control group is 1.15, indicating that the indoor level was higher than the outdoor level. The interrelationship differences among the three different types of levels in the air in the G, Y and H areas are statistically significant, except for the difference between the indoor and outdoor figures for xylene. In terms of the different types of houses and energy type uesd, the geometric mean level for airborne benzene, toluene and xylene for houses were 1.61, 5.39 and 0.12 ppb, respectively. while the figures for flats were 0.67, 3.32 and 0.05 ppb, respectively. Outdoors, the levels of benzene and toluene in flats were 0.71 and 2.62 ppb, respectively. and 1.58 and 5.35 ppb in houses. For personal exposure, the house levels of benzene, toluene and xylene were all higher than for flats. Houses using oil for heating have significantly higher levels than flats, which use gas for heating.

• 한국의상디자인학회지
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• 제4권2호
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• pp.139-161
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• 2002

This study investigates the characteristics of Nordic sweaters works from a historical perspective. Specifically, this study deals with the following research topics: 1) development of Nordic sweaters, 2) the characteristics of Nordic sweaters industry according to the change of times, 3) the comparison of local knitting patterns, 4) the symbolic meaning of the designs in the Nordic sweaters and patterns. The results of the study are summarized as follows. 1. Knitted work developed mostly in Northern Europe, a cold area, and the barren, mountainous coastal areas where people frequently used woolen materials for clothes. It was also developed in Scandinavian regions which lead the fashion in modern days. Scandinavian knitting techniques have been diffused into the east coast of England and Northern Europe by Vikings. 2. Scandinavian countries are distinguished from other countries by their conservative but creative cultural tradition. Their knitting patterns are characterized by small geometric figures such as dots, triangles, squares, rhombuses, and crosses used often with stars and roses. Scandinavian knitting is also salient for its vertical stripes and simple motifs repeating at short intervals. 1) Norway ; Simple and geometric Norwegian patterns are classified into three groups of motifs: (a) the motifs of cross, diamond, X, and swastika (equation omitted). (b) the motifs of human figures, animals and birds, (c) floral motifs (especially eight-petal roses). Their use of color is also simple, and is limited to more than two colors. (2) Sweden ; Swedish patterns are colorful and geometric. They are characterized by features such as brocade, complex embroidery, and contrast of red and black colors. They also show Guernsey patterns. Initials and production years were knitted in sweaters which have different patterns in their trunks and sleeves. 3) Denmark ; The Danish pattern is the purl stitch knitted against the stockinette stitch. The technique is used to copy woven damask motifs. The patterns are seen most clearly when they are knit with smooth yarn. The Faeroe sweaters are the representative work of Danish knitting. Faeroe knitting, incorporates stranded pattern and is knit in the round, either with circular needles. 4) Finland ; Finnish patterns are similar to Norwegian patterns. Finnish knitted work show very colorful, variety and free-flowing geometric patterns. 5) Iceland ; Icelandic knitting shows original ribbon pattern. Lope sweater is the representative work. 3. The traditional knitting patterns not only carried symbolic meanings but also served as means of communication. First of all, patterns had incantatory meanings. Patterns were symbolic of one's social standing, too. The colors, motifs and their arrangements were very important features symbolizing one's social position or family line. People often communicated by certain pieces of knitted work or patterns. In short, the knitted work in the Nordic sweaters served the function of admiring the beauty of nature and symbolizing various meanings. The unique designs and colors of the knitted work reflected the characteristics of the culture those works belonged to. This study also turns our attention to the issue of how the traditional colors and designs of the knitted work can contribute to the development of modern designs, and by doing so, if makes us realize the importance of knitted works in modern society.

• East Asian mathematical journal
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• 제36권2호
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• pp.131-146
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• 2020

The isoperimetric problem is a well-known optimization problem from ancient Greek. Among plane figures with the same perimeter, which is the largest area surrounded? The answer to the question is circle. Zenodorus and Steiner's pure geometric proofs, which left a lot of achievements in this matter, looked beautiful with ideas at that time. But there was a fatal flaw in the proof. The weakness is related to the existence of the solution. In this paper, from a view of the existence of the solution, we investigate proofs of Zenodorus and Steiner and get educational implications.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• 복식
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• 제64권7호
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• pp.156-171
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• 2014

This study attempted to comprehend the usage of the modular system in fields through literature review and objective research, as well as analysis of its expression characteristics in fashion. It tried to provide inspiring visual data for the fashion design of the modular system. After analyzing architecture and product-related books, Internet data and advanced research, the four expression characteristics of the modular system were obtained. Firstly, the formative expression characteristics of the modular system in fashion were simplicity, extensibility, variability and diversity. Secondly, of the formative expression characteristics expressed in modern fashion, simplicity (30%) was the highest, followed by extensibility (27%), diversity (22%) and variability (21%). Thirdly, simple silhouette and structure were used to express simplicity, usually simple geometric figures. In contrast, extensibility was expressed through the expansion and exaggeration of the area, length and volume of the clothes. In terms of variability, the typical characteristics of modules were reflected. For diversity, heterogeneous materials were used, and informality was expressed.