• Title/Summary/Keyword: symbolic numbers

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The Type of Fractional Quotient and Consequential Development of Children's Quotient Subconcept of Rational Numbers (분수 몫의 형태에 따른 아동들의 분수꼴 몫 개념의 발달)

  • Kim, Ah-Young
    • Journal of Educational Research in Mathematics
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    • v.22 no.1
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    • pp.53-68
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    • 2012
  • This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.

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A Comparison between Methods of Generalization according to the Types of Pattern of Mathematically Gifted Students and Non-gifted Students in Elementary School (초등수학영재와 일반학생의 패턴의 유형에 따른 일반화 방법 비교)

  • Yu, Mi Gyeong;Ryu, Sung Rim
    • School Mathematics
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    • v.15 no.2
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    • pp.459-479
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    • 2013
  • The Purpose of this study was to explore the methods of generalization and errors pattern generated by mathematically gifted students and non-gifted students in elementary school. In this research, 6 problems corresponding to the x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns were given to 156 students. Conclusions obtained through this study are as follows. First, both group were the best in symbolically generalizing ax pattern, whereas the number of students who generalized $a^x$ pattern symbolically was the least. Second, mathematically gifted students in elementary school were able to algebraically generalize more than 79% of in x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns. However, non-gifted students succeeded in algebraically generalizing more than 79% only in x+a, ax patterns. Third, students in both groups failed in finding commonness in phased numbers, so they solved problems arithmetically depending on to what extent it was increased when they failed in reaching generalization of formula. Fourth, as for the type of error that students make mistake, technical error was the highest with 10.9% among mathematically gifted students in elementary school, also technical error was the highest as 17.1% among non-gifted students. Fifth, as for the frequency of error against the types of all patterns, mathematically gifted students in elementary school marked 17.3% and non-gifted students were 31.2%, which means that a majority of mathematically gifted students in elementary school are able to do symbolic generalization to a certain degree, but many non-gifted students did not comprehend questions on patterns and failed in symbolic generalization.

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Interpreting the Urban Forest in the Genre Paintings of Joseon Dynasty (조선시대 풍속화에 나타난 도시숲의 현대적 해석)

  • Ahn, Myung June;Pae, Jeong-Hann
    • Journal of the Korean Society of Environmental Restoration Technology
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    • v.11 no.6
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    • pp.11-25
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    • 2008
  • In broad agreement on the need for forests in the city, researches on the urban forest are being actively carried out. Nonetheless, since these researches focus on functional usage within living spaces, finding methods for creation of urban forests and technical solutions have remained chief issues as a consequence. This paper, which attempts to historically examine the properties of the urban forest within living space, has the characteristics of researching basic angles for approaching the creation of contemporary urban forests. For this purpose Joseon Dynasty genre paintings, which represent living conditions of Joseon era, have been decided as theme of the paper. Particularly the focus was limited to genre paintings depicting trees, giving phenomenal observations. As a result, some remarkable characteristics emerged as functional urban forest, symbolic urban forest, topological urban forest, and appreciative urban forest. Urban forest within living space mainly appear as functional, showing an even distribution in small numbers rather than gathering in large groups. The following can be inferred regarding this and related to the setting up of the scope of, and creating of, contemporary urban forest : First, from the viewpoint of urban forest creation there is a need to study more subdivided and refined types of the urban forest and to actually realize these types. Second, from the viewpoint of urban forest usage, one needs to approach existing forests, ranging from small-scale including invididual trees, to mid-, large-, and super scale, as urban forests. In this, a network of major trees, and thereby a matrix of all trees formed by that network, will be formed. Third, from the viewpoint of urban forest improvement, approaches need to be based on planting trees in even distribution across the whole city.

Comparative Study in Algebra Education with CAS: Korea and US cases (컴퓨터 대수체계(CAS) 대비 중등대수교육 기초 연구)

  • Chang, Kyung-Yoon
    • School Mathematics
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    • v.10 no.2
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    • pp.297-317
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    • 2008
  • This study was designed to gain insight to adopt CAS into secondary level algebra education in Korea. Most inactive usage of calculators in math and most negative effects of calculators on their achievements of Korean students were shown in International studies such as TIMSS-R. A comparative study was carried out with consideration of mathematical backgrounds and technological environments. 8 Korean students and 26 US students in Grade 11 were participated in this study. Subjects' Problem solving process and their strategies of CAS usage in classical Box-problem with CAS were analyzed. CAS helped modeling by providing symbolic manipulation commands and graphs with students' mathematical knowledge. Results indicates that CAS requires shifts focus in algebraic contents: recognition of decimal & algebraic presentations of numbers; linking various presentations, etc. The extent of instrumentation effects on the selection of problem solving strategies among Korea and US students. Instrumentation

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The Actual Wearing Condition and Preference of the Working Uniform Design in the Industrial Complex (공단근로자의 작업복 디자인 실태 및 선호도 연구)

  • Park, Hye-Won;Park, Gin-Ah
    • Journal of Fashion Business
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    • v.12 no.2
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    • pp.134-152
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    • 2008
  • Functional, aesthetic and symbolic working uniforms in the industrial complex are demanded by employees and employers. The purpose of this research was to find out the actual wearing condition and preference of the working uniform design in the industrial complex. The research selected 7 enterprise subjects located in the Changwon National Industrial Complex and adopted a questionnaire method. 912 workers categorized into 4 work groups according to their work posts replied in total. The data and the degrees of satisfaction/preference of the working uniforms were analysed into descriptive statistics and F-tests by using the SPSS S/W package. The results were as follows: First, the style of the working uniform was the standard two-piece style. Second, the degree of the satisfaction with the entrepreneurial image implied to the working uniform was 2.83 throughout the 5-scale evaluation. In addition, the degree of the satisfaction with the working uniform colors was in between 2.94 and 2.96. Third, unsatisfied parts of the upper and lower uniform garments were: sleeve > pocket > collar; and waist belt loop > hip pocket > hem line respectively. Fourth, beige was the most preferred color for the working uniform top and bottom both. The most preferred color images were the calm and safety and the bright and light in order. Especially, the demand on the safety factors and soil proof colors of the outside field workers was much higher than the clerical workers. Fifth, the blouson type jacket with shirts collar or soutien roll collar was more preferred to than the casual style; and the straight formal pants were more preferred to than the casual/sweat sports pants styles. Sixth, inner pockets to keep the mobile phone and pens were required for upper garment details specially by manufacture workers. Increase of the waist belt loop numbers was required by all work groups.

A Study on the Middle Age Costume Expression of France (프랑스 <마카이요프스키 성경(Maciejowski Bible)>의 중세복식 표현에 관한 연구)

  • Kim, Hee-Jung
    • The Research Journal of the Costume Culture
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    • v.16 no.2
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    • pp.263-277
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    • 2008
  • In picture bible, the picture is helpful for showing story more vividly and specifically and it is helpful for finding the meaning of bible hidden behind familiarity. It plays the role of the most powerful testimony and expression, with which human provides himself. The purpose of study was to grasp the relation among historical background of the middle age, human's characteristic and symbolic color by considering the fact that the costume expressed in Maciejowski Bible, which is a picture bible of the middle age and observing type, color and decoration of costume. Among 46 folios organizing Maciejowski Bible, 129 pictures explaining the Book of Genesis, the Book of Exodus, the Book of Leviticus, the Book of Numbers, the Book of Deuteronomy, the Book of Joshua and the Book of Judges, which belong to the former 400 years of the old Testament, were analyzed for people's costumes. The pictures shown in Maciejowski Bible portrays object, costume and behavior on the background of France of the 13th century so we can find out the precious natures of middle age's costume, weapon and armor. Especially, the portrait about finger armor of chain mail attached in hauberk becomes the outstanding evidence that can encroach the discussion over whether it was used in the end of 1300s. Regarding costumes of main characters, they wore chemise and braies as underwear, wore tunic or cotte having various lengths from the length reaching knee to the length reaching 8round as basic costume and wore mantle with different-colored lining and hose with various colors. In the war picture, we can see hauberk made with chain mail and cyclas with long slit, which was worn over hauberk, barrel helmet, norman helmet and steel school cap. Regarding cap. man usually wore coif, beret, shade-shaped cap, straw hat and woman wore the decoration using veil and hairlace and used the method to wrap whole hair with net. As the colors used in the costume of the picture bible, scarlet, blue, green and brown were usually used in order. They usually wore costumes decorated splendidly with the colors haying hish brightness and chroma.

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A STUDY ON THE CHUMSUNGDAE'S FIGURES AND FUNCTIONS (첨성대 수치와 역할에 대한 연구)

  • Kim, Kwang-Tae
    • Publications of The Korean Astronomical Society
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    • v.28 no.2
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    • pp.25-36
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    • 2013
  • Chumsungdae is an ancient astronomical observatory whose main role was doing 'chunmoon'. It was administrate by a royal advisory agency on state affairs. The observers observed the heaven on the observatory platform, recorded peculiar events, and watched and interpreted the signs displayed in the heaven. Chumsungdae is an stonemasonry which represents almanac principles with its peculiar shapes and the numbers of strata and stones. The numbers were thoroughly invented to match exactly the almanac constants. Chumsungdae is comprised largely of three main parts, namely the square base, the stratified cylindrical body, and the top #-shaped stonework, and the total number of stones is 404. The number of the strata (27) and the height of the cylindrical body (27 尺) stand for the days in a sidereal month (27.3 days), which implies that the motion of the Moon with respect to the stars was given more priority than to the Sun at that time of geocentricism. And the cylindrical body was thoroughly designed to consist of 365 stones, which is of course the number of days in a solar year. In addition, there are 12 strata each under and above the south entrance and this in sum makes the 24 divisions of the year. Also there is 182 stones below the 13th stratum and this represents the number of days in the winter ~ summer solstice period, and the rest 183 stones the vice versa. The #-shaped top stonework was aligned in such a way that one of the diagonals points the direction of sunrise on the winter solstice. The square base also layed with the same manner. The south entrance was built 16 degrees SE, and the upright direction of the right pillar stone coincides with the meridian circle. This was a kind of built-in standard meridian circle facilitating the observations. In a symbolic sense, Chumsungdae was thought as the tunnel reaching the heaven, where the observers wished to be enlightened with the signs and inspirations in need. With the craftsmanship and skill, the builder reinforced the stratified cylindrical body with two sets of #-shaped beam stones, piercing at a right angle at 19th ~ 20th and 25th ~ 26th strata. Likewise, by placing the double #-shaped stonework with 8 beam stones on the platform of the observatory, both the stability of the stonemasonry and a guard rail for the nightly observers were securely provided.

A problem of authenticity in the chapter 'Confucius became aged, and liked "The Book of Changes"' of yao 要, "essentials," seen throughout 『帛書周易』 the Mawangdui Boshu Zhouyi Manuscript. -in relation to Confucius and 『易』"The Changes"- (『백서주역(帛書周易)』 「요(要)」의 '부자노이호역(夫子老而好易)'장의 진위(眞僞) 문제 -공자와 『역』의 관계를 중심으로-)

  • Kim, Sang-sup
    • Journal of Korean Philosophical Society
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    • v.129
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    • pp.1-22
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    • 2014
  • Columns 12-18 record a conversation between an aged Confucius and his disciple Zi Gong concerning the Changes and especially the role of divination in its use. The last section, from the bottom of column 24, concerns the hexagrams Sun損, "Decrease," and Yi益, "Increase," which Confucius is here made to regard as the culmination of wisdom in the Zhouyi. The conversation between Confucius and Zi Gong, and especially Zi Gong's apparent misunderstanding of Confucius's interest in the text, has already attracted considerable scholarly interest. Zi Gong criticizes Confucius for changing his teaching about the importance of the Zhouyi and for performing divinations. Confucius responds that while he does indeed perform divinations. there is a major difference between his use of the text and that of others: he regards the I Ching as a repository of an ancient wisdom. This would seem to signal recognition of a dramatic change in the function and status of the text. Zi Gong said: "Does the Master also believe in milfoil divination?" The Master said: "I am right in only seventy out of one hundred prognostications. Even with the prognostications of Liangshan of Zhou one necessarily follows it most of the time and no more." The Master said: "As for the Changes, I do indeed put its prayers and divinations last, only observing its virtue and property. Intuiting the commendations to reach the number, and understanding the number to reach virtue, is to have humaneness and to put it into motion properly. If the commendation do not lead to the number, then merely acts as a magician; if the number does not lead to virtue, then one merely acts as a scribe. The divinations of scribes and magicians tend toward it but are not yet there; delight in it but are not correct. Perhaps it will be because of the Changes that sires of later generations will doubt me. I seek its virtue and nothing more. I am on the same road as the scribes and magicians but end up differently. The conduct of the gentleman's virtue is to seek blessings; that is why he sacrifices, but little; the righteousness of his humaneness is to seek auspiciousness; that is why he divines, but rarely. Do not the divinations of priest and magicians come last!" Although Confucius says two ways of the symbolic numbers and virtue-property, he emphasizes his way of virtue and property more important. In fact he who wrote in Yao 要, "essentials," Confucius's saying describes his own viewpoints of the Changes throughout the conversations between Confucius and his disciple Zi Gong, and is only to borrow the name of Confucius. Furthermore, quoting the original text in Yao 要, "essentials," in sequence, also comparing the materials of "the Analects of Confucius論語," with "the Shih chi史記," this thesis will be centered to a great extent on the relative similarity and differences between the Mawangdui Boshu Zhouyi Manuscript and the received text, and discussed the authencity of Yao 要, "essentials," of the contents shown in the chapter of 'Confucius became aged, and liked "The Book of Changes."' the relation of Confucius and the Changes will be clarified naturally through this progress.

A Study on Commemoration Characteristics of Vietnam War Memorials in the United States of America (미국에 있는 베트남전쟁 메모리얼에 나타난 기념성)

  • Lee, Sang-Seok
    • Journal of the Korean Institute of Landscape Architecture
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    • v.43 no.1
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    • pp.1-15
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    • 2015
  • The purpose of this study was to analyze the commemoration characteristics of Vietnam War Memorials(VWM) in the United States(VWMUS). Through site survey and internet research, the researcher selected 87 VWMUS except monuments simply with markers, and analyzed 5 analysis items: design concepts, spatial characteristics, landscape details, sculptures, and interpretive texts and symbols. The results are as follows: 1. The analysis revealed that the main concepts of VWMUS were to cherish victims of the Vietnam War(85 sites (97.7%)), show veteran's dedication for country(85 sites(97.7%)), and publicize the contribution of groups by troop, regional, and membership(84 sites(96.6%)). 2. Most VWMUS were located in memorial parks and plazas. 59 memorials(67.8%) were designed to pursue the completion of each memorial assuming the form of symmetry and circles. On the other hand, 12 memorials(13.8%) were typed memorial walls and 11 memorials(12.6%) were formed by spatial sequence including various landscape details and grading. 3. Stone walls were mainly used to cherish victims of the War at 65 memorials(74.7%), and also, Flags like the Stars and Stripes, POW MIA flags, and state flags were hoisted to symbolize memorial's identity at all memorials. Additionally, Benches, monuments, markers, posts and columns, ponds and channels, Helicopters were partially introduced some memorials. 4. Sculptures were used 21 memorials(24.1%) which were smaller in numbers than other War Memorial in the U.S.A., for black stonewall were used for the main element of VWMUS. Except for a few sculptures that aimed to represent the Vietnam War symbolically and narratively, 16 memorials(18.4%) were formed to realistically express the image of wounded soldiers and their hardship in the Vietnam War. 5. KIA, MIA, Veteran's name were written and their images depicted on walls, Also, the symbolic phrase, 'ALL GAVE SOME, SOME GAVE ALL' and 'DUTY, HONOR, COUNTRY' were written on the memorials walls, and the POW MIA symbols were printed on the flags and engraved on walls. 6. In the United States of America, Democratic patriotism was considered a main ideological value in VWMUS by engraving KIA MIA's names on the walls, hoisting flags Stars and Stripes and POW MIA, and writing symbolic phrases 'ALL GAVE SOME, SOME GAVE ALL' and 'DUTY, HONOR, COUNTRY'. On the contrary, in Vietnam, nationalism, patriotism, and socialism were emphasized as main ideologies through raising war victory and resistance to foreign power as well as writing the symbolic phrase 'TO-QUOC-GUI-CONG' meaning 'our country remember your achievement' on memorial towers. Further study will be required to comparatively analyze VWM in order to understand national characteristics in Korea, Australia, U.S.A, and Vietnam.

A Study on the Communication of the Functional Family (기능적인 가족의 커뮤니케이션에 관한 이론적 접근)

  • 조윤경
    • Journal of Families and Better Life
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    • v.2 no.1
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    • pp.131-150
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    • 1984
  • The purpose of this study is to explore the family as an interaction system, concentrating on the mutual influences between communication and family development; (1) how Communication patterns affect family relationships, and (2) how relationships among family members affect communication. In order to do this Galvin, Brommel used the following frame work; family is a system in which communication regulates cohesion and adaptability by a flow of message patterns through a defined network of evolving interdependent relationships. A family system consists of members, the relationships among them, the family attributes, the members attributes and an environment in which family functions. Within the framework of common cultural communication patterns, each family has the capacity to develop its own communication code based on the experiences of individual members and the collective family experience. Most of us develop our communication skills within the family context learning both the general cultural language and the specific familial communication code. Communication may be viewed as a symbolic, transactional process as the process of creating and sharing meanings. To say that communication is a process implies a continuous interaction of an indefinite large numbers of variables with a concomitant,. continuous change in the values taken by these variables. Finally the process implies change, Family functions include the primary functions of cohesion and adaptability, and supporting functions of family images, themes, boundaries, and biosocial issues. The primary functions reveal concepts integrated family interaction and supporting function, along with those of cohesion and adaptability, give shape to family life. the characteristics of developed relationships of richness, uniqueness efficiency, substitutability, pacing , openness spontaneity, and evaluation are reflected in the verbal and nonverbal behaviors with which family members negotiated a set of common meanings and develop thier own unique message system. The message system is the major element of communication process and influences both the form and the content of thier relationship and in create and share meanings. Family systems need to provide order and predictability for thier members, specifically focusing on communication rules and the networks by which messages are transmitted. Most rules emerge as a result of multiful interactions. There are basic rules and rules about rules, or metarules. Perceiving the rules of family system is very difficult because often family members don't think about the basic rules, much less the metarules. Breaking the rule may result in the creation of a new set because the system may recalibrate itself to accept more variety of behavior. Families develop communication networks to deal with the general issue. Family adaptability may be seen through the degree of flexibility in forming and reforming networks and networks become a vital part of the decision- making process and relate to the power dynamics operating within the family. Networks also play an integral part in maintaining the roles and rules operating with the family system. Thus networks and rules have mutual influence. The family -of -origin issues influence all aspects of family communication and account for many of the communication patterns, rules and networks and the role of the family -of-origin influences as a primary force for communication on behavior of newly forming systems. Each family system develops its own communication meanings. There is not one right way to communicate within a family but may be indefinitly large change of family life and communication behavior. Study on functional family communication helps to gain a better understanding of dynamics of family communication and ability of a new insight into the family.

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