• 제목/요약/키워드: introducing the concept of function

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예비 중등 수학교사들의 함수 개념의 도입 방식 탐색 (A Study on the Prospective Mathematics Secondary Teachers' Introduction of Concepts of Function)

  • 마민영
    • 한국학교수학회논문집
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    • 제25권3호
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    • pp.225-241
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    • 2022
  • 본 연구의 목적은 예비교사들이 함수 개념을 도입하는 수업을 설계할 때 함수 개념의 어떤 측면을 강조하여 지도하는지를 분석하여 제시하는 것이다. 이를 위해 예비교사 중 한 명의 발표자(예비교사 A)가 수행한 가상 수업과 동료 예비교사 10명(예비교사 A1~A10)이 이 수업에 대해 반성한 내용을 분석하였다. 그 결과, 예비교사들은 과정과 대응의 관점으로 함수 개념을 도입하는 것이 우세하였고, 변화와 종속성 관점으로 도입하는 경우는 극히 드물었다. 또한 예비교사들이 함수 도입에서 강조하는 측면은 상황·언어적 표현, 표, 그래프, 식, 그림 등과 같이 함수를 표현하는 양식과 밀접하게 관련됨을 확인하였다. 이러한 결과는 2015 개정 교육과정에 제시된 종속적인 변화 관계에 기반하여 함수 개념을 도입하기 위한 예비교사 교육 및 연구에 시사점을 제시하는 하나의 경험적 근거자료가 될 것으로 사료된다.

2015 개정 교육과정에 따른 <수학II> 교과서의 정적분의 도입 및 활용 분석 (An analysis of the introduction and application of definite integral in textbook developed under the 2015-Revised Curriculum)

  • 박진희;박미선;권오남
    • 한국수학교육학회지시리즈A:수학교육
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    • 제57권2호
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    • pp.157-177
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    • 2018
  • The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

임상가를 위한 특집 3 - NAT/NFR 교합의 임상적용 (The clinical application of NAT/NFR occlusal concept)

  • 정승미
    • 대한치과의사협회지
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    • 제51권5호
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    • pp.255-264
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    • 2013
  • Many concept of occlusion have been introduced in the past, but there isn't any generally accepted unified theory since a single occlusion theory cannot represent the natural perfection, especially considering the difference in clinical experience, the dynamic occlusion, and individual diversity in mastication pattern. NAT(Naturgemasse Aufwachstechnik)/NFR((Natur Funktionsgerechte Rekonstruktion) occlusion is not just a theory on occlusion, but a clinical occlusion that can be practically applied to clinical practice by providing dynamic occlusion adjusted to the individual mastication pattern and biomechanics. This report aims to provide a guide to a clinically biomechanical occlusion through the teamwork of both the dentist and the lab technician by introducing the NAT occlusion through following: reviewing the concept of occlusion in terms of morphology, its correlation with NAT/NFR occlusion, reviewing the limitation of conventional occlusion theories, and introducing the clinical application of NAT/NFR.

우리나라 중학생의 함수 개념화 특성 (Korean middle school students' conception of function)

  • 변희현;주미경
    • 대한수학교육학회지:수학교육학연구
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    • 제22권3호
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    • pp.353-370
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    • 2012
  • 중학교의 함수 개념 도입과 관련하여 7차 교육과정의 개정 시 종속적인 변화관계에 기반하여 도입하도록 큰 변화를 시도하였고 이러한 방향은 현재 2009 개정 교육과정에서도 유지되고 있다. 이에 본 연구에서는 이러한 교육과정의 변화가 학생들의 함수개념 이해에 어떤 변화를 가져왔는지 그리고 실제 교수 학습 장면에서 함수가 어떻게 지도되고 있는지를 탐색하였다. 이를 위해 학생들의 경우 과제기반 심층 면담을 통해 함수 개념화의 특성을 살펴보았고 또 다른 한편으로는 학생들의 지도교사들을 대상으로 면담을 실시하여 수업에서 함수를 도입하는 방식에 대해 질문하였다. 연구결과 학생들은 종속적 변화관계에 기반하여 함수를 인식하는 정도가 매우 미약하며 교사들 또한 종속적 변화관계에 기반하여 함수를 지도하는데 어려움을 겪고 있음을 확인할 수 있었다. 이러한 논의를 바탕으로 학교수학에서 함수 지도와 관련한 몇 가지 제언을 하였다.

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Transient oscilaltion analysis for MEMS resonant accelerometer

  • Sangkyung Sung;Lee, Jang-Gyu;Taesam Kang;Sung, Woon-Tahk;Chul Hyun
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2002년도 ICCAS
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    • pp.98.1-98
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    • 2002
  • In principle, a resonance type sensor generally has an oscillation characteristic. Thus, an analysis on transient oscillation response takes a great interest since it is related to the performance of resonant sensor. In particular, system bandwidth has tradeoff with oscillation accuracy, i.e. quality factor. For an efficient analysis of the oscillation characteristic, several analytic methods are introduced and summarized. The results are fundamentally based on the classical describing function method, but can explain the transient oscillation by introducing time varying concept about the predicted limit cycle. After introducing those methods, the application results to the specified system...

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열차의 속도 하중을 고려한 강우시 성토사면의 안정성 변화 (Variation of Slope Stability under rainfall considering Train Speed)

  • 김정기;김현기;박영곤;신민호;김수삼
    • 한국철도학회:학술대회논문집
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    • 한국철도학회 2002년도 추계학술대회 논문집(I)
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    • pp.601-607
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    • 2002
  • Infiltration of rainfall causes railway embankment to be unstable and may result in failure. Basic relationship between the stability of railway embankment and rainfall introducing the partial saturation concept of ground are defined to analyze the stability of embankment by rainfall. A pressure plate test is also peformed to obtain soil-water characteristic curve of unsaturated soils. Based on this curve, the variables in the shear strength function and permeability function are also defined. These functions are used fur the numerical model for evaluation of railway embankments under rainfall. As comparing the model and case studies, the variation of shear strength, the degree of saturation and pore-water pressure for railway embankment during rainfall can be predicted and the safety factor of railway embankment can be expressed as the function of rainfall amount namely rainfall index. Therefore, the research on safety factor on railway embankment considering train speed and rainfall infiltration with the variation of rainfall intensity and rainfall duration was carried out in this paper.

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The Function Discovery of Closed Curve using a Bug Type of Artificial Life

  • Adachi, Shintaro;Yamashita, Kazuki;Serikawa, Seiichi;Shimomura, Teruo
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2003년도 ISIS 2003
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    • pp.90-93
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    • 2003
  • The function, which represents the closed curve, is found from the sampling data by S-System in this study. Two methods are proposed. One is the extension of S-System. The data x and y are regarded as input data, and the data z=0 as output data. To avoid the trap into the invalid function, the judgment points (x$\_$j/, y/sug j/) are introduced. They are arranged in the inside and the outside of the closed curve. By introducing this concept, the functions representing closed curve are found by S-System. This method is simple because of a little extension of S-System. It is, however, difficult for the method to find the complex function like a hand-written curve. Then another method is also proposed. It uses the system incorporating the argument function. The closed curve can be expressed by the argument function. The relatively complex function, which represents the closed curve like a hand-written curve, is found by utilizing argument function.

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마이크로 에너지 네트워크의 중앙집중형 최적 운영 모델 (An Optimal Operation Model of A Centralized Micro-Energy Network)

  • 이지혜;김학만;임용훈;이재용
    • 전기학회논문지
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    • 제62권10호
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    • pp.1451-1457
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    • 2013
  • Recently, new concept of energy systems such as microgrid, smart grid, supergrid, and energy network has been introducing. In this paper, the concept of the centralized micro-energy network, which is an energy community of a building group without district heating system, is introduced. In addition, a mathematical model for optimal operation of the micro-energy network as a main function of an energy management system (EMS) for the micro-energy network is proposed. In order to show the validation, the proposed model is tested through the simulation and analyzed.

Fuzzy 계확법의 해법일반화에 관한 연구 (A Study on the Extension of Fuzzy Programming Solution Method)

  • 양태용;김현준
    • 한국경영과학회지
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    • 제11권1호
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    • pp.36-43
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    • 1986
  • In this study, the fuzzy programming is extended to handle various types of membership functions by transformation of the complicated fuzzy programming problems into the equivalent crisp linear programming problems with single objective. It is well-known that the fuzzy programming problem with linear membership functions (i.e., ramp type) can be easily transformed into a linear programming problem by introducing one dummy variable to minimize the worst unwanted deviation. However, until recently not many researches have been done to handle various general types of complicated linear membership functions which might be more realistic than ramp-or triangular-type functions. In order to handle these complicated membership functions, the goal dividing concept, which is based on the fuzzy set operation (i. e., intersection and union operations), has been prepared. The linear model obtained using the goal dividing concept is more efficient and single than the previous models [4, 8]. In addition, this result can be easily applied to any nonlinear membership functions by piecewise approximation since the membership function is continuous and monotone increasing or decreasing.

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균열 회전체의 진동해석 (Vibration Analysis of Cracked Rotor)

  • 전오성
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2005년도 춘계학술대회논문집
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    • pp.925-934
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    • 2005
  • The dynamic response due to the unbalance and crack and the quasi-static response due to gravity are analytically derived based on the complex transfer matrix. The additional slope is expressed as function of the bending moment at crack position based on the fracture mechanics concept, and inversely the bending moment is expressed as function of the additional slope at the crack position. At each angle step during the shaft revolution, the additional slope and bending moment are calculated by an iterative method. The transient behavior is considered by introducing Fourier series expansion concept for the additional slope. Simulation is carried out for a simple rotor similar to those available in the literature and comparison of the basic crack behavior is shown. Using the additional slope, the cracked rotor behavior is explained with the crack depth increased: the magnitude of the additional slope increases and the closed crack duration during a revolution decreases as the crack depth increases. The direction of unbalance is also shown as a factor to affect the crack breathing. Whirl orbits are shown near the sub-critical speed ranges of the rotor.

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