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수학적 창의성과 개방형 문제(open ended problem)

  • Gwon, O-Nam;Jo, Yeong-Mi;Park, Jeong-Suk;Park, Ji-Hyeon;Kim, Yeong-Sil
    • Communications of Mathematical Education
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    • v.16
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    • pp.217-218
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    • 2003
  • 제7차 교육과정의 기본방향인 '21세기의 세계화 정보화 시대를 주도할 자율적이고 창의적인 한국인 육성'에서 볼 수 있듯이, 새로운 교육과정에서는 학생들의 창의력을 신장시키기 위한 방안으로 교과별 교육과정이나 재량활동 운영 등을 제시한 바 있다. 수학교육에서도 이러한 시대적 흐름에 발맞추어 수학적 창의력의 신장이 강조되고 있는 상황이다. 그동안 이론적인 측면과 실제적인 측면에서 수학적 창의성에 대한 성과가 축적되었다. 이론적인 측면에서 볼 때, Haylock(1987)등에 의해 창의력과 수학적 창의력의 구분되었으며, 특히 '수학적' 창의력에 대한 다양한 정의가 제안되었다. 실제적인 측면에서도 수학적 창의력을 측정하려는 평가 도구들이 그 동안 여러 가지로 개발하였다. 그러나, 이러한 수학적 창의력에 관한 전반적인 연구는 종국적으로 교실 수학수업에 반영되어야 함에도 불구하고, 그리 만족스럽지 못한 상황이다. 특히, 교실에서 수학수업을 실제로 담당하는 교사들이 수학적 창의력을 위한 수업을 하고자 하더라도 당장 가까이에서 구할 수 있는 교수 학습 자료가 여전히 부족한 상황이다. 물론 그 동안 교실 수학수업에서 사용할 수 있는 창의력 개발 프로그램이 전무한 것은 아니다. 그런데 그들 대부분은 게임이나 퍼즐을 이용한 것으로 그 수준이 단순 흥미유발에 그치고 있거나 소수의 영재아를 위한 소재를 중심으로, 특히 수학적 사고 과정을 따르기보다는, 시행착오를 거쳐 원하는 결과를 얻을 가능성이 많으며, 수학과의 연계성이 불분명한 채로 단순놀이에 그치는 경우가 적지 않아, 수업과 연관되어 창의력의 신장이라는 측면에서 볼 때, 적용하기 어려운 사례가 많다. 이러한 상황을 개선하는 데 기여하고자, 현재 교과교육공동연구 지원사업의 하나로 한국 학술 진흥재단의 지원을 받아, '개방형 문제(open-ended problems)'를 중심 소재로 한 '수학적 창의성'을 신장하기 위한 교수학습 프로그램을 개발하여, 중학교 1학년을 대상으로 연구를 진행하고 있다. 개방형 문제라 함은 명백한 정의가 어렵지만 Pehkeon(1995)는 개방형문제의 정의를 명백히 하기위한 시도로서 그 반대로 닫힌 문제에 대한 정의로부터 시작하여, 어떤 문제가 닫혀있다고 하는 것은 그 문제의 출발 상황과 목표 상황이 닫혀 있는 것, 즉 명백히 설명되어있을 때라면 개방형 문제는 이와 반대의 개념임을 시사하였다. Silver(1995)는 개방형 문제를 문제 자체가 다른 해석이 가능하거나 서로 다를 인정할만한 답을 가질 수 있는 문제 또는 풀이과정이 다양한 문제, 자연스럽게 다른 문제들을 제안하거나 일반화를 제시할 수 있는 문제라고 정의하였다. 따라서 개방형 문제란 출발상황이나 목표 상황의 일부가 닫혀있지 않을 때를 말하고 문제의 조건을 만족하는 해답이 여러 가지로 존재하는 문제를 뜻한다. 수학적 창의력을 개발하는 데, 다른 문제 유형보다도, 개방형 문제가 유리하다는 점은 이미 여러 학자들에 의해 주장되어왔다. 미국 국립영재교육센터(NRCG/T)는 기존의 사지선다형이나 단답형 문제와 질문들은 학생들의 사고 능력에 관한 정보를 거의 알려주지 못하기 때문에 한 가지 이상의 답을 요구하는 ‘open-ended' 또는 ’open-response' 문제와 질문을 가지고 수학 분야에서의 창의적 사고 능력과 표현능력을 측정해야 한다고 하였고, 개방형 문제가 일반적으로 정답이 하나인 문제보다 고차원적인 사고를 요구하게 하는 문제 형태라고 하였다. 본 연구에서는 이러한 근거를 바탕으로 개방형 문제의 유형을 다양한 답이 존재하는 문제, 다양한 해결 전략이 가능한 문제, 답이 없는 문제, 문제 만들기, 일반화가 가능한 문제 등으로 보고, 수학적 창의성 중 특히 확산적 사고에 초점을 맞추어 개방형 문제가 확산적 사고의 요소인 유창성, 독창성, 유연성 등에 각각 어떤 영향을 미치는지 20주의 프로그램을 개발, 진행하여 그 효과를 검증하고자 한다. 개방형 문제를 활용한 수학적 창의력 신장 프로그램을 개발하고 현장 학교에 실험 적용하여 그 효과를 분석하고자 하는 본 연구는 창의력 신장에 비중을 두는 수학과 교수-학습 과정에 실제적인 교수 학습 자료를 제공하는 것뿐만 아니라 교사들에게는 수학교실에서 사용 가능한 실제적인 활용방안을, 학생들에게는 주어진 문제를 여러 가지 각도에서 생각하면서 다양한 사고를 경험하는 기회를 가질 수 있어, 수학을 보는 학생들의 태도에도 긍정적인 변화를 가져올 수 있을 것이라 기대한다.

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A Landscape of Joseon Dynasty in Late 19th Century through Experience Record of Modern Westerners - Focused on Landscape Vocabulary and Content Analysis - (근대기 서양인들의 조선견문기를 통해 본 19세기 말 조선의 경관 - 경관 관련 어휘와 내용 분석을 중심으로 -)

  • Kim, Dong-Hyun;Shin, Hyun-Sil
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.36 no.1
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    • pp.20-33
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    • 2018
  • This study aims to illuminated landscape of Joseon Dynasty in the end of 19th century when Joseon dynasty began to modernize through the perspective of Westerners. Historical meaning to Western people's landscape records has been preceded. And landscape typology and their perception were analyzed. The results were as follows. First, the Westerners who visited Joseon dynasty at that time were involved in the historical and political situation of the Joseon Dynasty or understood their culture through traveling for so long. And record of Westerners is a significant data to analyze scenery at that time because common contents appear in various books. Second, the landscape of Joseon dynasty that appears in Western records was mainly recorded in small towns and villages, natural environments, scenic sites, historic sites, modern facilities, and cultivated areas. Small towns and villages are mainly mentioned with shabby alleys and dense houses. And natural landscape were identified to mountain landscapes and diverse geomorphological landscape that surrounding vegetation along the coast and rivers. The palaces, fortress and temples were recorded as main objects of scenic sites and historic site. And western-style buildings such as foreign legations and settlements, churches and schools were mentioned in the modernized facilities. A cultivated land was confirmed to be underdeveloped and neglected, but as range of view became wider, it was seen to a peaceful and prosperous rural landscape. Third, Westerners' landscape perception of Joseon dynasty at that time can be deduced from positive or negative perceptions. The residential environment was perceived as negative because it was unsanitary and backward. On the contrary, outstanding natural landscapes, scenic sites and historic sites, and upper class gardens were perceived as positive. For modernized landscapes, positive and negative perceptions were similarly mentioned. Positive perceptions were formed in improvement of civilized landscape, and appeared negative perception because damaged traditional landscapes and heterogeneity.

Projection of Potential Cultivation Region of Satsuma Mandarin and 'Shiranuhi' Mandarin Hybrid Based on RCP 8.5 Emission Scenario (RCP 8.5 기후변화시나리오에 근거한 온주밀감과 '부지화'의 잠재적 재배지 변화 예측)

  • Moon, Young-Eel;Kang, Seok-Beom;Lee, Hyejin;Choi, Young-Hun;Son, In-Chang;Lee, Dong-Hoon;Kim, Sung-Ki;An, Moon-Il
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.19 no.4
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    • pp.215-222
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    • 2017
  • The potential change of the cultivation area of main citrus cultivars, satsuma mandarin (Citrus unshiu Marc.) and 'Shiranuhi' mandarin hybrid [(Citrus unshiu ${\times}$ C. sinensis) ${\times}$ C. reticulata] were determined with base year (1981 to 2010) to 2090. The meteorological data provided by the Korea Meteorological Administration (KMA), and the digital agricultural climate map of 30m-solution based on the Representative Concentration Pathways (RCP) 8.5 was used for projection of potential cultivation area. As a result, the potential suitable region of satsuma mandarin included almost Jeju region during base year. At the 2030s, the potential suitable region of satsuma mandarin increased and the cultivable region also increased focused on the coast region of Jeonnam province. From the 2060s, the suitable area spread out to mountain area of Jeju, Jeonnam, Gyeongnam, and the coast region of Kangwon, and the cultivable region expanded to the area of Gyeongbuk, Chungnam, and Jeonbuk. In the case of 'Shiranuhi' mandarin hybrid, the suitable region included only the partial coast area of Jeju, and cultivable area covered Jeju region and the partial southern coast of Jeonnam during the standard period. At the 2030s, the suitable region of 'Shiranuhi' included the current cultivation area of satsuma mandarin, and the cultivable region moved to northward by the partial southern coast region. At the 2090s, the slightly increased suitable region covered all Jeju regions, Jeonnam, Gyeongnam, and the coast area of Kangwon, and the cultivable region proceeded northward focusing on the coastline. In conclusion, the prediction of the potential land for citrus cultivation based on the RCP 8.5 showed that the suitable region of satsuma mandarin decreased, whereas that of cultivation of 'Shiranuhi' increased. Moreover, it was forecasted that citrus cultivation area would extend to Kangwon region at the end of the $21^{st}$ century.

A Semantic Interpretation of the Design Language in the ChwuiseokJeong Wonlim of Gochang - Focusing on the Alegory and Mimesis in 'Chwuiseok' and 'Chilseongam' - (취석정원림에 담긴 조형언어의 의미론적 해석 - '취석'과 '칠성암'에 담긴 알레고리와 미메시스를 중심으로 -)

  • Rho, Jae-Hyun;Lee, Hyun-Woo;Lee, Jung-Han
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.30 no.1
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    • pp.76-89
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    • 2012
  • This study aimed at carrying out a semantic interpretation of the core Design language that seemed to influence deeply in the creation of the ChwuiseokJeong wonlim of Gochang. Especially, this paper aimed at inferring how the spiritual culture of seclusion of the 16th century influenced the creation of the wonlim by understanding the metaphor and symbolism by grasping the transmission meaning and reception meaning of the creators and the people concerned with keywords like Eunil(隱逸: seclusion), Chwuiseok(醉石), and Chilseongam(七星巖). 'Building up a wall' was intentionally carried out in order to represent 'Seven Stars(The Big Dipper)' inside of the wonlim. This is a kind of two-dimensional 'enframement', and a result of active creation of a meaningful landscape. From Chilseongam that was created by assembling, we presumed that Kyung-Hee Kim, Nohgye(蘆溪), the creator showed the recognition and thoughts of astronomy as a Confucian scholar that the ChwuiseokJeong Wonlim where he secluded is the center of the universe. The interpretation of words in Nohgyezip, an anthology, showed that the articles and writtings of Nohgye, his decsendants, and the people of ChwuiseokJeong included alcohols, Chwuiseok, Yeon-Myung Do, and Yuli(栗里) where Do secluded; this means that Nohgye ranked himself with Do because Nohgye also lived in peace by drinking alcohols and enjoying nature like Do did. 'Drinking' was what expressed the mind of Nohgye who wanted to be free and have the joy of enjoying mountains, water, and their landscape like Do did. In other words, 'Drinking' is the symbol of freedom that makes him forget himself and equate himself with nature. These are the representation, imitation, and mimesis of respecting Yeon-Myung Do. As the alegory of 'speaking something with other things' suggested, it is possible to read 'Chwuiseok', came from the story of Yeon-Myung Do, in multiple ways; it superficially points out 'a rock on which he laid when he was drinking', but it also can be interpreted as 'an object' that made him forget his personal troubles. In addition, it means freewill protecting unselfish mind with the spiritual aberration of drinking, 'Chwui(醉)', mentally; also, it can be interpreted metaphorically and broadly as a tool that makes Nohgye reach to the state of nature by the satisfied mind of Yeon-Myung Do. 'Chwuiseok' was a design language that showed the situation of Nohgye by comparing his mind with the mind of Yeon-Myung Do from the Confucian point of view, and a kind of behavioral mimesis based on his respect to Do and 'aesthetic representation of objective reality.' It is not coincidental that this mimesis was shown in the engraved words on Chwuiseok and the creation of ChwuiseokJeong that has the same name with Chwuiseok in Korea and China.

Mencius Thoughts on Social Welfare (맹자사상의 사회복지적 함의)

  • Kim, Young-Min
    • The Journal of Korean Philosophical History
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    • no.57
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    • pp.91-125
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    • 2018
  • This study aims at attempting to make a new interpretation of Mencius from the point of social welfare. The thoughts of social welfare, found from Mencius, are temporal and humanistic and near to those in nowadays. Social welfare began under the name of philanthropic work, relief work, charitable work or social work from the Industrial Revolution in the 18th century on. Welfare means the whole social activities such as satisfying the fundamental desires of the social members, ensuring the conditions of their lives, and ultimately achieving social integration and stability. It means the conditions of their lives and wellbeing. Wellbeing means the minimal physical desires and psychological stability. The realization of the economic system through concept of steady livelihood and steady mind, tax system and well-field system, proposed by Mencius, can be ensured by the whole social activities such as ensuring the stable lives of the social members, enriching and satisfying their happiness and ultimately achieving social integration and stability. The thoughts of Mencius include people-as-root idea, which regards people as most important and tries to solve the instability and inequality that are the structural vulnerabilities in modern capitalist society. His concept of Way of the king means promoting people's sense of happiness through education of morality, based upon the people-as-root idea and filial and fraternal responsibilities. The main ideas of social welfare include living like a human being, ensuring minimal physical and psychological stabilities through social welfare system and welfare policy, enriching human dignity and freedom and enhancing the quality of lives. The thoughts of Mencius include all the above ideas. In particular, he desired to establish ethically and morally stable society by economically implementing the well-field system in Zhou dynasty, based upon politically benevolent governance of the politicians. That society was the people-as-root society, the realization of which was the ideal society Mencius desired to establish, and the goal of his thoughts on social welfare. This study, among the thoughts of Mencius, investigated his ideas on social welfare and the practical ethics for applying them to real society. In addition, to understand his ideas on social welfare, not only the social and economic backgrounds and conditions but also the political ideas at that time were also investigated. This will provide the opportunity to make more in-depth research of the elements of social welfare intrinsically contained in his thoughts.

Effects and Roles of Korean Community Dance (한국 커뮤니티 댄스의 효과와 역할)

  • Park, Sojung
    • Trans-
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    • v.9
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    • pp.37-66
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    • 2020
  • Entering the 21st century, the flow of society and culture is emerging as a cultural phenomenon in which one experiences, enjoys, and experiences on one's own. This trend has emerged as community dance, which has been active since 2010. Community dances can be targeted by anyone and can be divided into children's, adult and senior citizens' dances depending on the characteristics and age of the group, allowing them to work in various age groups. It also refers to all kinds of dances for the happiness and self-achievement of everyone who can promote gender, race and religion health or meet the needs of expression and improve their physical strength at meetings by age group, from preschoolers to senior citizens. Community dance is a dance activity in which everyone takes advantage of their leisure time and voluntarily participates in joyous activities, making it expandable to lifelong education and social learning. It is a voluntary community gathering conducted by experts for the general public. The definition of community dance can be said to be the aggregate of physical activities that enrich an individual's daily life and enhance their social sense to create a bright society, while individuals achieve the goals of health promotion and aesthetic education. In the contemporary community dance, the dance experience in body and creativity as self-expression reflects the happiness perspective by exploring the positive psychological experience and influence of the participants in the process of participation, and participants have continued networking through online offline to enjoy the dance culture. Although research has been conducted in various fields for 10 years since the boom in community dance began, the actual methodology of the program has been insufficient to present the Feldenkrais Method, hoping that it will be used as a methodology necessary for local community dance, and will be used as part of the educational effects and choreography creation methods of artists that can improve the physical functional aspects of dance and give a sense of psychological stability.

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Prediction of Soil Erosion from Agricultural Uplands under Precipitation Change Scenarios (우리나라 강우량 변화 시나리오에 따른 밭토양의 토양 유실량 변화 예측)

  • Kim, Min-Kyeong;Hur, Seong-Oh;Kwon, Soon-Ik;Jung, Goo-Bok;Sonn, Yeon-Kyu;Ha, Sang-Keun;Lee, Deog-Bae
    • Korean Journal of Soil Science and Fertilizer
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    • v.43 no.6
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    • pp.789-792
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    • 2010
  • Major impacts of climate change expert that soil erosion rate may increase during the $21^{st}$ century. This study was conducted to assess the potential impacts of climate change on soil erosion by water in Korea. The soil loss was estimated for regions with the potential risk of soil erosion on a national scale. For computation, Universal Soil Loss Equation (USLE) with rainfall and runoff erosivity factors (R), cover management factors (C), support practice factors (P) and revised USLE with soil erodibility factors (K) and topographic factors (LS) were used. RUSLE, the revised version of USLE, was modified for Korean conditions and re-evaluate to estimate the national-scale of soil loss based on the digital soil maps for Korea. The change of precipitation for 2010 to 2090s were predicted under A1B scenarios made by National Institute of Meteorological Research in Korea. Future soil loss was predicted based on a change of R factor. As results, the predicted precipitations were increased by 6.7% for 2010 to 2030s, 9.5% for 2040 to 2060s and 190% for 2070 to 2090s, respectively. The total soil loss from uplands in 2005 was estimated approximately $28{\times}10^6$ ton. Total soil losses were estimated as $31{\times}10^6$ ton in 2010 to 2030s, $31{\times}10^6$ ton in 2040 to 2060s and $33{\times}10^6$ ton in 2070 to 2090s, respectively. As precipitation increased by 17% in the end of $21^{st}$ century, the total soil loss was increased by 12.9%. Overall, these results emphasize the significance of precipitation. However, it should be noted that when precipitation becomes insignificant, the results may turn out to be complex due to the large interaction among plant biomass, runoff and erosion. This may cause increase or decrease the overall erosion.

Simulation and Post-representation: a study of Algorithmic Art (시뮬라시옹과 포스트-재현 - 알고리즘 아트를 중심으로)

  • Lee, Soojin
    • 기호학연구
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    • no.56
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    • pp.45-70
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    • 2018
  • Criticism of the postmodern philosophy of the system of representation, which has continued since the Renaissance, is based on a critique of the dichotomy that separates the subjects and objects and the environment from the human being. Interactivity, highlighted in a series of works emerging as postmodern trends in the 1960s, was transmitted to an interactive aspect of digital art in the late 1990s. The key feature of digital art is the possibility of infinite variations reflecting unpredictable changes based on public participation on the spot. In this process, the importance of computer programs is highlighted. Instead of using the existing program as it is, more and more artists are creating and programming their own algorithms or creating unique algorithms through collaborations with programmers. We live in an era of paradigm shift in which programming itself must be considered as a creative act. Simulation technology and VR technology draw attention as a technique to represent the meaning of reality. Simulation technology helps artists create experimental works. In fact, Baudrillard's concept of Simulation defines the other reality that has nothing to do with our reality, rather than a reality that is extremely representative of our reality. His book Simulacra and Simulation refers to the existence of a reality entirely different from the traditional concept of reality. His argument does not concern the problems of right and wrong. There is no metaphysical meaning. Applying the concept of simulation to algorithmic art, the artist models the complex attributes of reality in the digital system. And it aims to build and integrate internal laws that structure and activate the world (specific or individual), that is to say, simulate the world. If the images of the traditional order correspond to the reproduction of the real world, the synthesized images of algorithmic art and simulated space-time are the forms of art that facilitate the experience. The moment of seeing and listening to the work of Ian Cheng presented in this article is a moment of personal experience and the perception is made at that time. It is not a complete and closed process, but a continuous and changing process. It is this active and situational awareness that is required to the audience for the comprehension of post-representation's forms.

The Damage Assessment, Construction Point of Time and Deterioration Diagnosis and Conservation Maintenance of Stone Statues Around the Stone Pagoda in Mireuksaji Temple in Iksan (익산 미륵사지 석탑 석인상의 조영시기와 훼손도 진단 및 보존관리)

  • Lee, Dong-sik;Lee, Yeon-gyeong
    • Korean Journal of Heritage: History & Science
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    • v.47 no.4
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    • pp.74-91
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    • 2014
  • The stone statues in the site of Mireuksaji Temple(Iksan, South Korea) were created after the stone pagoda was built in 639. They, transitional statues between animal sculptures and human shaped statues made from the late Goryeo dynasty until the early Joseon dynasty, were set up at the four corners of the stone pagoda by way of guardians. In the case of three statues, their surfaces were denudated and their iconographies have been indiscernible. However, the one in the southwest clearly shows its iconography. It is inferior in properties to the other three statues in the northwest, the northeast and the southeast respectively, but on the other hand its iconography has been well maintained. The reason is related to exposure to harmful environments; specifically, the retaining wall, built around the stone pagoda in the 17th century, had the southwest statue inside and could naturally worked as a buffer against harmful environments. As a result, for about 400 years there has been difference in weathering conditions between the three stone statues and the southwest statue, which brought denudation, the consequent indiscernibleness of iconography and biological invasion to the three statues, notwithstanding superior properties(northwest statue:$176kgf/cm^2$, northeast statue:$109kgf/cm^2$, southeast statue:$273kgf/cm^2$). In contrast, the southwest statue significantly shows its iconography with black contaminants and granule decomposition, despite inferior properties($133kgf/cm^2$). Defenseless exposure to external environment is not recommended for the stone statues, because it is hard to preserve the extant iconography. Herein lies the application of the data on microclimate around Mireuksaji Temple. As regards the weathering zone in which the stone statues are located, Conservation increases in acidity and frequency as years go by, Hereat, in the approach to the Conservation of stone statues, the first consideration needs to be morphological historicity rather than geographical location.

Study on Pile Cloth Rugs Produced after the Late Joseon Period (조선 말기 이후 첨모직 깔개에 관한 연구)

  • Park, Yoon-Mee;Oh, Joon Suk
    • Korean Journal of Heritage: History & Science
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    • v.51 no.4
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    • pp.84-107
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    • 2018
  • Cheommojik is a pile cloth, a type of textile whose surface is covered with short piles. The term chaedam was used during the late Joseon dynasty to refer to pile cloth rugs, while the terms yoongjeon, dantong and yangtanja were used in the early twentieth century. Various documents, newspaper articles and photographs confirm that pile cloth rugs were used by the general public as well as the royal family from the late Joseon dynasty onward, and that there were domestic manufacturers of such rugs at that time. This study investigated six pile cloth rugs that were produced after the late Joseon dynasty, five of which feature Persian knots made of cut pile, the other being made with the loop pile method. The cut pile rugs are rectangular in shape and measure between 72-98cm by 150-156cm; and they are decorated in the middle with patterns of butterfly, deer, and tiger or the ten longevity symbols, and along the edges with patterns composed of 卍 symbols. The ground warp of all six rugs are made from cotton yarn, while the ground weft is made of cotton yarn on three pieces, wool on one piece and cotton and viscose rayon. The ground weft yarn from four pieces are Z-twist yarn made with two or more S-twist cotton yarn. Four to six colors were used for the pile weft, all being natural colors except for red. Two or more S- or Z-twist yarn were twisted together in the opposite twist for the pile weft, with the thickness determining the number of threads used. Six or more weft threads were used to make the start and end points of the rug; and the ground warp ends were arranged by tying every four of them together. For the left and right edges, three or more threads were wrapped together into a round stick-like form, and the second and third inner ground warps from the edges were stitched on to the wrapped edge. For the loop pile, loops were made in the direction of the warp; the ground warp and the ground weft may have been made with cotton, the pile warp with wool yarn. An analysis of the components of three rugs was conducted to determine which types of animal hair were used for the pile weft. Despite some inconclusive results, it was revealed that goat hair and fat-tailed sheep hair were used, raising the possibility that various kinds of animal fur were used in the production of pile cloth rugs. The six rugs examined in this study are estimated to have been made between the late 1800s and the early 1900s. Although the manufacturer of the rugs cannot be confirmed, we concluded that the rugs were produced in Korea after referring to the documentation of the domestic production of pile cloth rugs during the aforementioned period and the form and placements of the patterns on the rugs.