• Title/Summary/Keyword: 수학적 지식

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Teaching and Learning of University Calculus with Python-based Coding Education (파이썬(Python) 기반의 코딩교육을 적용한 대학 미적분학의 교수·학습)

  • Park, Kyung-Eun;Lee, Sang-Gu;Ham, Yoonmee;Lee, Jae Hwa
    • Communications of Mathematical Education
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    • v.33 no.3
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    • pp.163-180
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    • 2019
  • This study introduces a development of calculus contents which makes to understand the main concepts of calculus in a short period of time and to enhance problem solving and computational thinking for complex problems encountered in the real world for college freshmen with diverse backgrounds. As a concrete measure, we developed 'Teaching and Learning' contents and Python-based code for Calculus I and II which was used in actual classroom. In other words, the entire process of teaching and learning, action plan, and evaluation method for calculus class with Python based coding are reported and shared. In anytime and anywhere, our students were able to freely practice and effectively exercise calculus problems. By using the given code, students could gain meaningful understanding of calculus contents and were able to expand their computational thinking skills. In addition, we share a way that it motivated student activities, and evaluated students fairly based on data which they generated, but still instructor's work load is less than before. Therefore, it can be a teaching and learning model for college mathematics which shows a possibility to cover calculus concepts and computational thinking at once in a innovative way for the 21st century.

Exploring the power of physics-informed neural networks for accurate and efficient solutions to 1D shallow water equations (물리 정보 신경망을 이용한 1차원 천수방정식의 해석)

  • Nguyen, Van Giang;Nguyen, Van Linh;Jung, Sungho;An, Hyunuk;Lee, Giha
    • Journal of Korea Water Resources Association
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    • v.56 no.12
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    • pp.939-953
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    • 2023
  • Shallow water equations (SWE) serve as fundamental equations governing the movement of the water. Traditional numerical approaches for solving these equations generally face various challenges, such as sensitivity to mesh generation, and numerical oscillation, or become more computationally unstable around shock and discontinuities regions. In this study, we present a novel approach that leverages the power of physics-informed neural networks (PINNs) to approximate the solution of the SWE. PINNs integrate physical law directly into the neural network architecture, enabling the accurate approximation of solutions to the SWE. We provide a comprehensive methodology for formulating the SWE within the PINNs framework, encompassing network architecture, training strategy, and data generation techniques. Through the results obtained from experiments, we found that PINNs could be an accurate output solution of SWE when its results were compared with the analytical method. In addition, PINNs also present better performance over the Artificial Neural Network. This study highlights the transformative potential of PINNs in revolutionizing water resources research, offering a new paradigm for accurate and efficient solutions to the SVE.

Development and Application of Integrative STEM (Science, Technology, Engineering and Mathematics) Education Model Based on Scientific Inquiry (과학 탐구 기반의 통합적 STEM 교육 모형 개발 및 적용)

  • Lee, Hyonyong;Kwon, Hyuksoo;Park, Kyungsuk;Oh, Hee-Jin
    • Journal of The Korean Association For Science Education
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    • v.34 no.2
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    • pp.63-78
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    • 2014
  • Integrative STEM education is an engineering design-based learning approach that purposefully integrates the content and process of STEM disciplines and can extend its concept to integration with other school subjects. This study was part of fundamental research to develop an integrative STEM education program based on the science inquiry process. The specific objectives of this study were to review relevant literature related to STEM education, analyze the key elements and value of STEM education, develop an integrative STEM education model based on the science inquiry process, and suggest an exemplary program. This study conducted a systematic literature review to confirm key elements for integrative STEM education and finally constructed the integrative STEM education model through analyzing key inquiry processes extracted from prior studies. This model turned out to be valid because the average CVR value obtained from expert group was 0.78. The integrative STEM education model based on the science inquiry process consisted of two perspectives of the content and inquiry process. The content can contain science, technology, engineering, and liberal arts/artistic topics that students can learn in a real world context/problem. Also, the inquiry process is a problem-solving process that contains design and construction and is based on the science inquiry. It could integrate the technological/engineering problem solving process and/or mathematical problem solving process. Students can improve their interest in STEM subjects by analyzing real world problems, designing possible solutions, and implementing the best design as well as acquire knowledge, inquiry methods, and skills systematically. In addition, the developed programs could be utilized in schools to enhance students' understanding of STEM disciplines and interest in mathematics and science. The programs could be used as a basis for fostering convergence literacy and cultivating integrated and design-based problem-solving ability.

Using GSP Construction Improving Figure Analysis Ability of Pre-service Elementary Teachers (예비 초등 교사의 도형 분석 능력 신장을 위한 GSP 작도의 활용)

  • Roh, Eun Hwan;Kang, Jeong Gi;Kim, Min Jeong;Jeong, Sang Tae
    • Education of Primary School Mathematics
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    • v.17 no.2
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    • pp.127-157
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    • 2014
  • The purpose of the study is to enhance the figure analysis ability for pre-service elementary teacher by using GSP. To do this, we limited to teaching competence divide into ability various problem-solving, extract key elements, predict the difficulty of student and investigated the initial of them, the reality of GSP construction. As results, pre-service elementary teachers made errors, proposed teaching focused on the character using in the problem solving, and found that in one particular difficulties to find the students. The reality of GSP construction activity was possible to explore through the partially constructed a number of various properties, but we found to have difficulty in the connection between concepts. and integrated view of the problem analysis. After visual identification and exploration through the GSP construction, problem-solving ability became a little more variety and changed their direction in order to focus the student's anticipated difficulties. From these results, we could extract some pedagogical implications helping pre-service teachers to reinforce teaching competence by GSP construction.

An empirical study for a better curriculum reform of statistical correlation based on an abduction (중등학교 상관관계 지도 내용 개선을 위한 가추적 실증 연구)

  • Lee, Young-Ha;Kim, So-Hyun
    • Journal of Educational Research in Mathematics
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    • v.22 no.3
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    • pp.371-386
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    • 2012
  • This research assumes two facts; One is that the mathematics curriculum reform of Korea in 2007 would have been better if it had been a revise instead of deletion and the other is that every school curriculum should be of help for the sound enhancement of all 6 types of logical concepts that appears in the Piaget's theory of cognitive development. What our mathematics curriculum has introduced as a correlation is not the one of the 6 logical concepts that Piaget had thought in his theory of cognitive development. In order to see the reason of that difference, we check the difference of jargons among the academic denominations, such as Pedagogy, Psychology and Statistics through their college textbooks. Because we suppose that the mismatch of 'Piaget's vs Curriculum's correlation' is due to the mis-communication among scholars of different academic denominations. With what we learned via the above analytical study leaned on an abduction and to get some idea on them for the potential future construction of school Statistics curriculum when it should be returned, which we believe so, we observe two foreign highschool mathematics textbooks briefly. As a result of the study, we found that the concept of correlation in Pedagogy contain all kinds of relation while it was stingy in Statistics. Here we report a main result; A careful discretion among similar concepts of correlation, such as linear relationship(correlation), stochastic change along conditions(dependence), central comparison(other relation) are needed for the potential future curriculum. And if new curriculum contains the linear correlation then we strongly recommend to involve the regression line to connect it with the linear function chapter.

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Analyzing Perceptions of Small Group Inquiry Activity in the Gifted Education of Korea (한국영재교육에서 소집단 탐구활동에 대한 인식 분석)

  • Jeong, Hyun-Chul;Park, Young-Shin;Hwang, Dong-Jou
    • Journal of the Korean earth science society
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    • v.29 no.2
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    • pp.151-162
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    • 2008
  • This study quantitatively investigated the actual situations and perceptions of gifted students and their teachers during small group inquiry activities in Korea. Some 1,670 gifted math students and 1,732 gifted science students as well as 614 of their teachers were selected through random sampling to participate in this study. Data were collected by means of a survey developed by the researchers of this study, based on reviews of literature related to inquiry and small group cooperative learning. The results were as follows: (1) In Korean gifted education, small group inquiry activities were frequently used as teaching and learning strategies, and both the students and teachers perceived its effects to be very positive in terms of cognition and affection. (2) Gifted education teachers emphasized the development of students' procedural inquiry skills as well as logical thinking skills, whereas they were indifferent to the essential elements of small group cooperative learning and therefore the lessons did not surpass the level of traditional group activities. (3) The fact that the actual small group inquiry activities did not reflect the characteristics of well-organized small group activities is due to a lack of knowledge on the teacher's part as to effective teaching strategies concerning cooperative learning. This study implies that gifted education teachers require the opportunity to reflect on and develop their knowledge and understanding of small group inquiry activities through professionally developed programs in order to maximize the effectiveness of small group inquiry activities in gifted education.

The Grounding Method Application of Power Plant Simulator (발전소 시뮬레이션시스템 접지방식 연구를 위한 타시스템 접지방식 분석)

  • 오영일
    • Proceedings of the Korea Society for Simulation Conference
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    • 1999.10a
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    • pp.70-74
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    • 1999
  • 발전소 시뮬레이션 시스템 기술은 종합적인 지식을 바탕으로 자료수집 및 분석, 소프트웨어 개발 환경, 수학적 모델, 전산기 구성, 각종 계기류 설계 및 구매 장착 등의 노하우를 알아야만 제작할 수 있는 종합적인 기술이다. 또 지시기반의 기술이며 부가가치가 높은 기술이기 때문에 선진 각국에서는 계측제어 시스템의 기술개발 및 시장 확대를 위하여 힘을 쓰는 동시에 타국으로의 기술정보 유출을 경계하는데 신경을 곤두세우고 있다. 현재 복잡화되어 가고 있는 산업 사회의 전력 수요에 대한 대폭적인 증가 추세에 따라 발전소에서는 보다 효율적이며 합리적이고 경제적인 전력 공급을 위해서 전력 생산에 대한 신뢰성 향상 및 안정성 확보는 물론, 효율성 높은 운전이 절실히 요구되고 있다. 한편, 국내의 시뮬레이션 시스템 분야 기술은 아직도 완벽한 수준에는 미치지 못하며, 이 분야의 기술력 확보 및 신기술 개발은 향후 미래의 모든 시스템산업의 성쇄를 판가름하는 아주 중요한 척도가 될 것이다. 이 중에서 접지 분야는 고전압 혼촉에 의한 저압측 선로의 전압상승 방지, 모선(Bus)이나 전력 기기의 절연보호 및 회로전압의 안정등으로 시스템 성능을 한층 증가 시켜줄 뿐아니라 기기의 오동작이나 낙뇌등으로 인명피해 발생을 없애주는 아주 중요한 분야임에도 불구하고 이 분야의 국내 관련법규등이 미비한 사항이다. 그래서 발전소 분산제어 시스템분야의 장기간 신뢰성 및 안정성을 가지고 있고, 국내에서 많이 사용하는 미국 Bailey의 infi-90 및 독일 ABB의 Procontrol-P를 비교 분석하여 발전소 시뮬레이션 시스템의 접지에 응용 하고져 한다.상호 발생기를 이용한 다양한 시스템 검증 및 분석에 이용할 수 있을 것이다. 본 논문은 가상호 발생기의 구조와 최대 용량 시험 방법을 소개하고, 더 나아가 호 Traffic에 대한 최대 용량 시험뿐 아니라 QoS를 향상시키기 위한 교환 시스템의 제반 성능 시험 및 분석에 이를 이용하기 위해 개선이 필요함을 서술하고자 한다.textrm{m}$~3.4$\mu\textrm{m}$ 범위에서의 투과 및 흡수 스펙트럼을 측정하였다. 결정 성장 결과 B3+, Er3+, Cr3+ 이온은 Ti4+ 이온과 이온의 크기 차이가 심하여 결정의 정상적인 성장을 방해하는 물성을 나타냈고, V5+, Cr3+ 이온은 흑색의 결정, Fe3+ 이온은 적갈색의 결정으로 성장되었다. Al3+, Zr4+, Al3+의 순서로 투과도가 높아지는 것이 관찰되었다. 불순이온의 농도에 따른 영향으로서 Al3+ 이온의 경우 주입농도가 높아질수록 low angle boundary와 oxygen deficiency가 감소하였고, 투과율은 조금 감소하거나 큰 차이가 없는 것으로 나타났다. 반면에 Cr3+ 이온을 주입한 경우 0.003 atomic%에서 최적의 물성을 보였으며, 주입농도가 높아질수록 결정성장이 어려워지고 광의 투과도가 급격히 저하되었다.은 1.3을 나타내었다.로 보인다.하면 수평축과 수직축의 분산 장벽의 비에 따라 cluster의 두께비가 달라지는 성장을 볼 수 있었고, 한 축 방향으로의 팔 넓이는 fcc(100) 표면의 경우 동일한 Ed+Ep값에 대응하는 팔 넓이와 거의 동일한 결과가 나타나는 것을 볼 수 있다. 따라서 이러한 비대칭적인

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Segmentation of Lung and Lung Lobes in EBT Medical Images (EBT 의료 영상에서 폐 영역 추출 및 폐엽 분할)

  • 김영희;이성기
    • Journal of KIISE:Software and Applications
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    • v.31 no.3
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    • pp.276-292
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    • 2004
  • In this paper. we present methods that extract lung regions from chest EBT(electron beam tomography) images then segment the extracted lung region into lung lobes. We use histogram based thresholding and mathematical morphology for extracting lung regions. For detecting pulmonary fissures, we use edge detector and knowledge-based search method. We suggest this edge detector, which uses adaptive filter scale, to work very well for real edge and insensitive for edge by noise. Our experiments showed about 95% accuracy or higher in extracting lung regions and about 5 pixel distance error in detecting pulmonary fissures.

Problem-Solving Model to Improve Scientific Literacy of Youth (청소년의 과학적 소양 향상을 위한 문제해결 모형 개발 연구)

  • Kwak Seung-Jin
    • Journal of Korean Library and Information Science Society
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    • v.36 no.3
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    • pp.21-38
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    • 2005
  • This study aims to find methods to improve the scientific literacy of the youth, which comprise the group who will lead the upcoming era of knowledge and science. To do this, the study focuses on improving the youth's understanding of science and their ability to utilize it. It is widely recognized that scientific literacy Is highly essential in this era of scientific revolution and innovations. Accordingly, various kinds of programs are being developed in Korea and other countries. In particular, 'Project 2061' is designed to enable a permanent learning system by improving problem-solving ability through the scientific process. This system plays an Important role In supporting the Americans' Pursuit of Increased literacy in the fields of science, mathematics, and engineering. To improve the scientific literacy of young people, content development in relation with school courses as well as information services that arouse Interest and curiosity In the field of science is very important. In addition, It is necessary to develop a problem-solving program by stages. Further studies focusing on methods of improving scientific literacy of the youth are recommended.

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Prediction of Shore Tide level using Artificial Neural Network (인공신경망을 이용한 해안 조위예측)

  • Rhee Kyoung Hoon;Moon Byoung Seok;Kim Tae Kyoung;Oh jong yang
    • Proceedings of the Korea Water Resources Association Conference
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    • 2005.05b
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    • pp.1068-1072
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    • 2005
  • 조석이란, 해면의 완만한 주기적 승강을 말하며, 보통 그 승강은 1일 약 2회이나, 곳에 따라서는 1일 1회의 곳도 있다. 조석에 있어서는 이 밖에 수일의 주기를 갖는 약간 불규칙한 승강, 반년, 또는 1년을 주기로 하는 다소 규칙적인 승강까지 포함하여 취급한다. 그러나, 각 항만마다 갖는 특정적인 주기인 수분내지 수십분의 주기의 승강은 조석으로 취급하지 않는다. 조석은 해양의 제현상 중에서 예측가능성이 가장 큰 현장으로 이는 조석이 천체의 운행과 연관되기 때문이다. 조석이란 지구로부터 일정한 거리에서 각 고유의 속도를 가지는 적도상을 운행하는 무수의 가상천체에 기인하는 규칙적인 개개의 조석을 합성한 것이며 이 개개의 조석을 분조(Constituent)라 한다. 여기에서 사용되는 신경망 모형은 입력과 출력으로 구성되는 블랙박스 모형으로서 하나의 시스템을 병렬적으로 비선형적으로 구축할 수 있다는 장점 때문에 과거 하천유역의 강우-유출과정에서의 경우 유출현상을 해석하고 유출과정을 모형화 하기 위해 사용하였다. 본 연구에서는 기존의 조위 예측방법인 조화분석법이 아닌 인공신경망을 이용하여 조위예측을 실시하였다. 학습이라는 최적화 과정을 통해 구조와 기능이 복잡한 자연현상을 그대로 받아들여 축적시킴으로써 이를 지식으로 현상에 대한 재현능력이 뛰어나고, 또한 신경회로망의 연상기억능력에 적용하여 수학적으로 표현이 불가능한 불확실한 조위곡선에 적용하기에 유리한 장점을 가지고 있다. 본 연구의 목적은 과거 조위이론을 통해 이루었던 조위예측을 우리가 알기 쉬운 여러 기후인자(해면기압, 풍향, 풍속, 음력 등)에 따른 조위곡선을 예측하기 위해 신경망 모형을 이용하여 여수지역의 조위에 적용하여 비교 분석하고자 한다. May가 제안한 공식을 더 확장하여 적용할 수 있는 실험 공식으로 개선하였으며 다양한 조건에 대한 실험을 수행하여 보다 정밀한 공식으로 개선할 수 있었다.$10,924m^3/s$ 및 $10,075m^3/s$로서 실험 I의 $2,757m^3/s$에 비해 통수능이 많이 개선되었음을 알 수 있다.함을 알 수 있다. 상수관로 설계 기준에서는 관로내 수압을 $1.5\~4.0kg/cm^2$으로 나타내고 있는데 $6kg/cm^2$보다 과수압을 나타내는 경우가 $100\%$로 밸브를 개방하였을 때보다 $60\%,\;80\%$ 개방하였을 때가 더 빈번히 발생하고 있으므로 대상지역의 밸브 개폐는 $100\%$ 개방하는 것이 선계기준에 적합한 것으로 나타났다. 밸브 개폐에 따른 수압 변화를 모의한 결과 밸브 개폐도를 적절히 유지하여 필요수량의 확보 및 누수방지대책에 활용할 수 있을 것으로 판단된다.8R(mm)(r^2=0.84)$로 지수적으로 증가하는 경향을 나타내었다. 유거수량은 토성별로 양토를 1.0으로 기준할 때 사양토가 0.86으로 가장 작았고, 식양토 1.09, 식토 1.15로 평가되어 침투수에 비해 토성별 차이가 크게 나타났다. 이는 토성이 세립질일 수록 유거수의 저항이 작기 때문으로 생각된다. 경사에 따라서는 경사도가 증가할수록 증가하였으며 $10\% 경사일 때를 기준으로 $Ro(mm)=Ro_{10}{\times}0.797{\times}e^{-0.021s(\%)}$로 나타났다.천성 승모판 폐쇄 부전등을 초래하는 심각한 선

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