• Title/Summary/Keyword: 수학용어

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환경분야를 위한 공간정보 분석 기술의 동향과 전망 - 지구통계학을 중심으로

  • Park, No-Uk
    • Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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    • 2010.06a
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    • pp.187-187
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    • 2010
  • 공간자료를 다루는 일반적인 과정은 연구자의 정의에 따라 달라질 수 있지만, 일반적으로 자료 수집, 자료 구축, 분석 및 결과 도출의 일반적인 과학/공학적 분석 절차와 유사하다. 산업체의 관점에서 볼 때, 1990년대 초기 국가GIS 사업이 시작될때부터 현재까지는 공인된 자료 구축에 많은 주안점을 두어서 기존 아날로그 자료의 디지털화, 자료 가공, 데이터베이스 구축, 자료의 시각화 등의 일반적인 자료 구축 및 도시에 주안점을 두어왔다. 또한 다양한 공간해상도의 원격탐사 자료와 같이 다중 근원 자료의 이용이 빈번해짐에 따라 공간자료의 갱신 또한 중요한 부분을 차지하고 있다. 그러나, 공간자료를 다루는 일련의 과정이 궁극적으로는 특정 분야에서의 의사 결정보조자료의 제공 등을 지향한다고 간주할 때, "from data to information to knowledge"의 중간 혹은 최종 단계의 결과물을 산출하기 위한 적절한 분석 기술의 개발 및 적용 또한 중요한 부분을 차지한다. 공간분석을 별도의 학문분야로 간주하느냐 아니냐의 문제와는 상관없이, 최근 20년간 공간분석은 GIS 및 원격탐사 분야뿐만 아니라 기본적으로 공간자료를 다루는 많은 응용분야에서 공간자료의 이해와 부가정보의 생산을 위한 중요한 기술 분야로 간주되어 왔다. 공간분석의 여러 응용 분야중에서 환경분야에의 적용 연구는 또한 환경과학이라는 별도의 분야 뿐만 아니라, 기존 학문들인 지리학, 생태학, 지구과학, 사회학, 경제학, 도시 계획 등의 하위분야에서 중요한 방법론으로 자리 잡고 있다. 이 기술 세미나에서는 환경분야에 직간접적으로 활용이 가능한 공간정보 분석 기술의 동향을 지구통계학을 중심으로 소개하고자 한다. 국내에서 크리깅으로 대표되어온 지구통계학은 적용하는 학문 분야에 따라 보다 넓은 의미를 가지는 공간 통계학이라는 용어로 사용되고 있지만, 보다 학문적/기술적 의미로 살펴보면 공간분석의 특화된 분야로 간주할 수 있다. 1950년대 알려진 광상의 위치 정보를 이용하여 은둔 광상의 위치를 추정하기 위해 기본 개념이 소개된 이후에 수학적으로 이론이 1960년대 정립된 지구통계학은 많은 발전을 이루어 현재 다양한 분야에서 적용되고 있다. 그러나 외국과 달리 국내에서는 크리깅을 고급 내삽 기법으로만 간주하여 단순 주제도 작성에 제한적으로 사용하고 있다. 이 기술 세미나에서는 특정 학문분야에서 적용되기 보다는 일반적으로 통용될 수 있는 지구통계학의 기본 개념을 우선 소개한 후에, 국내외 학계에서의 환경주제도 제작과 관련된 주요 응용분야를 소개하고자 한다. 이후에 지구통계학이 적용될 수 있으면서, 다학제적 관점에서의 이슈가 될 수 있는 분야를 제시하고자 한다.

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A Study on the Definition of a Circumcenter and an Incenter of Triangle (삼각형의 외심, 내심의 정의에 관한 고찰)

  • Jun, Young-Bae;Kang, Jeong-Gi;Roh, Eun-Hwan
    • Journal of the Korean School Mathematics Society
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    • v.14 no.3
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    • pp.355-375
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    • 2011
  • This paper was designed for the purpose of helping the functional comprehension on the concept of a circumcenter and an incenter of triangle and offering the help for teaching-learning process on their definitions. We analysed the characteristic of the definition on a circumcenter and an incenter of triangle and studied the context, mean and purpose on the definition. The definition focusing on the construction is the definition stressed on the consistency of the concept through the fact that it is possible to draw figure of the concept. And this definition is the thing that consider the extend of the concept from triangle to polygon. Meanwhile this definition can be confused because the concept is not connected with the terminology. The definition focusing on the meaning is easy to memorize the concept because the concept is connected with the terminology but is difficult to search for the concept truth. And this definition is the thing that has the grounds on the occurrence but is taught in a made-knowledge. The definition focusing on both the construction and meaning is the definition that the starting point is vague in the logical proof process. We hope that the results are used to improve the understanding the concept of a circumcenter and an incenter of triangle in the field of mathematical education.

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De Morgan's view on the development of algebra (대수 발달의 단계에 관한 드모르간의 관점 연구)

  • Yu, Mi-Kyung;Kim, Jae-Hong;Kwon, Seok-Il;Park, Sun-Yong;Choi, Ji-Sun;Park, Kyo-Sik
    • Journal for History of Mathematics
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    • v.21 no.4
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    • pp.61-78
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    • 2008
  • In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.

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Analysis of Highschool Students' Error types and Correction in Learning Function (고등학생들의 함수단원 학습과정에서 나타나는 오류유형 분석과 교정)

  • Yang, Ki-Yeol;Jang, You-Sun
    • Journal of the Korean School Mathematics Society
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    • v.13 no.1
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    • pp.23-43
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    • 2010
  • This study is to investigate how much highschool students, who have learned functional concepts included in the Middle school math curriculum, understand chapters of the function, to analyze the types of errors which they made in solving the mathematical problems and to look for the proper instructional program to prevent or minimize those ones. On the basis of the result of the above examination, it suggests a classification model for teaching-learning methods and teaching material development The result of this study is as follows. First, Students didn't fully understand the fundamental concept of function and they had tendency to approach the mathematical problems relying on their memory. Second, students got accustomed to conventional math problems too much, so they couldn't distinguish new types of mathematical problems from them sometimes and did faulty reasoning in the problem solving process. Finally, it was very common for students to make errors on calculation and to make technical errors in recognizing mathematical symbols in the problem solving process. When students fully understood the mathematical concepts including a definition of function and learned procedural knowledge of them by themselves, they did not repeat the same errors. Also, explaining the functional concept with a graph related to the function did facilitate their understanding,

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A Study on Design Education in Primary School -With Emphasis on Analysing the Present Condition of Design Education in Korean Primary School- (초등학교 디자인 교육에 관한 연구 -국내 디자인 교육의 현황 분석을 중심으로-)

  • 김혜숙;권은숙
    • Archives of design research
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    • v.12 no.4
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    • pp.191-200
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    • 1999
  • Improving the design ability of idea developing and creative problem solving should be started from the primary school. Design education in the primary school should be not education for design but education by design. It helps students can naturally understand the basic concept of design and experience the process of activities. Therefore primary educational circle use the term of 'Design-related activities', or 'Design-Based Education'. It can be applied to variable themes of mathematics, science, music, society as well as Art. On the Basis of these literature review, the traditional design education as a part of the art education is analyzed in two aspects of its contents and behaviors. The contents in design education involve aesthetic·symbolic, useful·functional, and scientific·technological area. And, the basic design behaviors are classified with 'know', 'perceive', 'inquire', and so on. This concept becomes the analytic frame of the present condition of design education in Korean primary school. Through the analysis, it is found that the portion of scientific·technological area in contents and 'inquire' related behaviors are relatively very low. Also, the planning and teaching methods for leading children's opportunity of creative expression are found inadequate. This study proposes the potential capability and the integrative contents of design education in primary school.

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An Analysis of the Characteristics of Teachers' Adaptive Practices in Science Classes (과학 수업에서 교사의 적응적 실행의 특징 분석)

  • Heekyong Kim;Bongwoo Lee
    • Journal of The Korean Association For Science Education
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    • v.43 no.4
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    • pp.403-414
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    • 2023
  • In this study, we examined the adaptive practices of science teachers in their classrooms and their perspectives on the distinguishing features of these practices within science subjects. Our analysis comprised 339 cases from 128 middle and high school science teachers nationwide, and 199 cases on the characteristics of adaptive practices in science disciplines. The primary findings were as follows: First, the most significant characteristic of adaptive practice in science disciplines pertained to experimental procedures. Within the 'suggestion of additional materials/activities' category, the most frequently cited adaptive practice, teachers incorporated demonstrations to either facilitate student comprehension or enhance motivation. Additionally, 'experimental equipment manipulation or presentation of inquiry skills' emerged as the second most common adaptive practice related to experiments. Notably, over 50% of teacher responses regarding the characteristics of adaptive practices in science pertained to experiment guidance. Second, many adaptive practices involving difficulties experienced by students in learning situations were presented, particularly in areas such as numeracy and literacy. Many cases were related to the basic ability of mathematics used as a tool in science learning and understanding scientific terms in Chinese characters. Third, beyond 'experiment guidance', the characteristic adaptive practices of science subjects were related to 'connections between scientific theory and the real world', 'misconception guidance in science', 'cultivation of scientific thinking', and 'convergence approaches'. Fourth, the cases of adaptive practice presented by the science teachers differed by school level and major; therefore, it is necessary to consider school level or major in future research related to adaptive practice. Fifth, most of the adaptive action items with a small number of cases were adaptive actions executed from a macroscopic perspective, so it is necessary to pay attention to related professionalism. Finally, based on the results of this study, the implications for science education were discussed.

Static Effect in Magnetotelluric Responses: An Implication from the EM Integral Equation (MT 탐사 반응에서 정적효과: 적분방정식을 통한 고찰)

  • Yoonho Song
    • Geophysics and Geophysical Exploration
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    • v.27 no.3
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    • pp.181-195
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    • 2024
  • This tutorial explains that the static effect in the magnetotelluric (MT) survey is a physical phenomenon caused by charges accumulated on the boundaries of subsurface inhomogeneities. To facilitate understanding of the physical phenomenon, differences between static induction and charge accumulation on the boundary are explained and analyzed with help of schematic illustrations. Subsequently, from the electromagnetic (EM) integral equation formulation, it is clearly shown that the secondary electric field due to charges accumulated on the interface in the presence of the primary field appears as the static effect. Therefore, except in the cases of the layered earth or a two-dimensional earth with transverse magnetic (TM) mode excitation, the static effect always exists in MT responses and further, it is not 'static' but rather frequency dependent. Despite the fact that the static effect is a secondary electric field due to inhomogeneity, inevitable under-sampling in the frequency and spatial domains prevent the effect from being handled properly in numerical inversion. Therefore, considering the practical aspects of the MT survey, which cannot be a continuous measurement covering the entire survey area over a wide frequency band, a three-dimensional (3-D) inversion incorporating the static shift as a constraint with the Gaussian distribution is introduced. To enhance understanding of the integral equation EM modeling, the formulation of the 3-D integral equation and mathematical analyses of the Green tensor and scattering current are described in detail in the Appendix.

The Effect of the Use of Concept Mapping on Science Achievement and the Scientific Attitude in Ocean Units of Earth Science (해양단원 개념도 활용 수업이 과학성취도 및 태도에 미치는 효과)

  • Han, Jung-Hwa;Kim, Kwang-Hui;Park, Soo-Kyong
    • Journal of the Korean earth science society
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    • v.23 no.6
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    • pp.461-473
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    • 2002
  • Concept mapping is a device for representing the conceptual structure of a subject discipline in a two dimensional form which is analogous to a road map. In the teaching and learning of earth science, each concept depends on its relationships to many others for meaning. Using concept mapping in teaching helps teachers and students to be more aware of the key concepts and relationships among them. The purpose of this study is to investigate the effect of the use of concept mapping on science achievement and the scientific attitude in ocean units of earth science. The results of this study are as follows; first, the science achievement of a group of concept mapping teaching is significantly higher than that of the group of traditional teaching. Also, when the achievement levels are compared among different cognitive ability groups, the effect is more significant in mid or lower level student groups than in high level groups. The use of concept mapping is more effective when the concepts have a distinct concept hierarchy. Second, the scores of the test of ‘attitude toward scientific inquiry’ and ‘application of scientific attitude’ of the group of concept mapping teaching are significantly higher than those of the group of traditional teaching, whereas the scores of the test of ‘interest in science learning’ of concept mapping teaching is not different from those of group of traditional teaching. Third, the survey on the use of concept mapping shows a positive response across the tested groups. The use of concept mapping is more beneficial in fostering the comprehension of the topic. A concept map of student's own construction facilitates the assessment of learning, thus promising the usefulness of concept mapping as a means of evaluation. In regard to retention aspect, concept mapping is considered to be more effective in confirming and remembering the topic, while less effective in the aspects of activity and interest. In conclusion, the use of concept maps makes learning an active meaningful process and improves student's academic achievement and scientific attitude. If the concept mapping is more effectively as an active teaching strategy, more meaningful learning will be attained.

Ultimate Reality in Daesoon Thought as Viewed from Perennial Philosophy (영원철학(The Perennial Philosophy)으로 본 대순사상의 궁극적 실재)

  • Heo, Hoon
    • Journal of the Daesoon Academy of Sciences
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    • v.32
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    • pp.137-173
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    • 2019
  • Modern scientists are trying to find the basic unit of order, fractal geometry, in the complex systems of the universe. Fractal is a term often used in mathematics or physics, it is appropriate as a principle to explain why some models of ultimate reality are represented as multifaceted. Fractals are already widely used in the field of computer graphics and as a commercial principle in the world of science. In this paper, using observations from fractal geometry, I present the embodiment of ultimate reality as understood in Daesoon Thought. There are various models of ultimate reality such as Dao (道, the way), Sangje (上帝, supreme god), Sinmyeong (神明, Gods), Mugeuk (無極, limitlessness), Taegeuk (太極, the Great Ultimate), and Cheonji (天地, heaven and earth) all of which exist in Daesoon Thought, and these concepts are mutually interrelated. In other words, by revealing the fact that ultimate reality is embodied within fractal geometry, it can be shown that concordance and transformation of various models of ultimate reality are supported by modern science. But when the major religions of the world were divided along lines of personality (personal gods) and non-personality (impersonal deities), most religions came to assume that ultimate reality was either transcendental or personal, and they could not postulate a relationship between God and humanity as Yin Yang (陰陽) fractals (Holon). In addition, religions, which assume ultimate reality as an intrinsic and impersonal being, are somewhat different in terms of their degree of Holon realization - all parts and whole restitution. Daesoon Thought most directly states that gods (deities) and human beings are in a relationship of Yin Yang fractals. In essence, "deities are Yin, and humanity is Yang" and furthermore, "human beings are divine beings." Additionally, in the Daesoon Thought, these models of ultimate reality are presented through various concepts from various viewpoints, and they are revealed as mutually interrelated concepts. As such, point of view regarding the universe wherein Holarchy becomes a models in a key idea within perennial philosophy. According to a universalized view of religious phenomena, perennial philosophy was adopted by the world's great spiritual teachers, thinkers, philosophers, and scientists. From this viewpoint, when ultimate reality coincides, human beings and God are no longer different. In other words, the veracity of the theory of ultimate reality that has appeared in Daesoon Thought can find support in both modern science and perennial philosophy.