• 한국수학교육학회지시리즈E:수학교육논문집
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• 제36권1호
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• pp.139-170
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• 2022

수준별 수학교육과 관련하여 러시아는 우리나라보다 오랜 연구와 실천의 경험을 가지고 있다. 현재 러시아에서 사용 중인 10-11학년 수학과 교육과정은 수준별 교육과정으로 기본수준과 심화수준으로 구성되어 있으며, 기본수준과 심화수준은 다루는 최소필수내용, 학생들에게 요구되는 수준 등에서 차이를 보인다. 그리고 10-11학년의 수학교과서도 수준별 교과서이다. 본 연구에서는 러시아의 10학년 '대수와 해석의 기초'의 교과서들 중에서 같은 저자 그룹에 의해 집필된 기본수준 교과서, 심화수준 교과서를 분석 대상으로 삼았다. 심화수준 교과서에만 있는 '실수', '복소수' 단원의 내용을 조사하여 심화의 성격으로 추가된 주요 학습 내용과 교과서 기술의 특징을 분석하였다. 그리고 기본수준 교과서와 심화수준 교과서에 모두 포함된 단원인 '함수', '삼각함수', '삼각방정식', '삼각함수 식들의 변환', '도함수'에 대해서는 기본수준과 심화수준 교과서의 주요 학습 내용을 비교, 분석하였고, 두 수준의 교과서에 제시된 정의와 정리의 서술상 특징도 비교, 분석하였다.

• Advances in aircraft and spacecraft science
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• 제5권1호
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• pp.51-71
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• 2018

This work proposes a theoretical and numerical study on the behavior of a tapered shaft rotor made of composite materials by the classical version h and the version p of the finite element method. Hierarchical form functions are used to define the model. The purpose of this paper is to determine the expressions of the kinetic and potential energies of the tree necessary for the results of the equations of motion. A comparison between the version h and the p version of the finite element method of the functions of polynomial and trigonometric hierarchical forms with six degrees of freedom per node, of a composite tapered and cylindrical shaft which rotates at a constant speed about its axis. It is found that when the number of functions of form (the version p) is increased, the solution converges. It is also observed that the conicity of the shaft increases the rigidity with respect to a uniform shaft having the same mechanical properties. The numerical simulation allowed us to determine the natural frequencies and the critical speeds of the composite shaft systems are compared with those available in the literature and the effectiveness of the methods used are discussed.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권2호
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• pp.283-302
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• 2007

한국의 대학수학교육은 학생들의 질적 그리고 수적 감소로 인해 많은 어려움을 겪고 있다. 이 논문에서는 다항함수, 유리함수, 무리함수, 로그.지수함수와 같이 고등학교 수학과정에서 이미 습득한 기본적인 함수들에 대한 이해도를 측정하였다. 대전과 충청지역 4개 대학의 신입생 354명을 대상으로 조사한 결과, 다항함수를 제외한 주어진 함수들의 그래프를 그리지 못한 학생들이 절반 이상이었으며, 또한 함수가 지니고 있는 정보들(정의역, 치역, 최대.최소값, 주기, 평행이동)에 대한 이해가 부족한 것으로 나타났다.

• Smart Structures and Systems
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• 제13권1호
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• pp.1-24
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• 2014

The present study deals with two dimensional electro-elastic analysis of a functionally graded piezoelectric (FGP) cylinder under internal pressure. Energy method and first order shear deformation theory (FSDT) are employed for this purpose. All mechanical and electrical properties except Poisson ratio are considered as a power function along the radial direction. The cylinder is subjected to uniform internal pressure. By supposing two dimensional displacement and electric potential fields along the radial and axial direction, the governing differential equations can be derived in terms of unknown electrical and mechanical functions. Homogeneous solution can be obtained by imposing the appropriate mechanical and electrical boundary conditions. This proposed solution has capability to solve the cylinder structure with arbitrary boundary conditions. The previous solutions have been proposed for the problem with simple boundary conditions (simply supported cylinder) by using the routine functions such as trigonometric functions. The axial distribution of the axial displacement, radial displacement and electric potential of the cylinder can be presented as the important results of this paper for various non homogeneous indexes. This paper evaluates the effect of a local support on the distribution of mechanical and electrical components. This investigation indicates that a support has important influence on the distribution of mechanical and electrical components rather than a cylinder with ignoring the effect of the supports. Obtained results using present method at regions that are adequate far from two ends of the cylinder can be compared with previous results (plane elasticity and one dimensional first order shear deformation theories).

• Structural Engineering and Mechanics
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• 제27권2호
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• pp.243-257
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• 2007

A numerically efficient superelement is proposed as a low degree of freedom model for dynamic analysis of rotating tapered beams. The element uses a combination of polynomials and trigonometric functions as shape functions in what is also called the Fourier-p approach. Only a single element is needed to obtain good modal frequency prediction with the analysis and assembly time being considerably less than for conventional elements. The superelement also allows an easy incorporation of polynomial variations of mass and stiffness properties typically used to model helicopter and wind turbine blades. Comparable results are obtained using one superelement with only 14 degrees of freedom compared to 50 conventional finite elements with cubic shape functions with a total of 100 degrees of freedom for a rotating cantilever beam. Excellent agreement is also shown with results from the published literature for uniform and tapered beams with cantilever and hinged boundary conditions. The element developed in this work can be used to model rotating beam substructures as a part of complete finite element model of helicopters and wind turbines.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.453-474
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• 1998

This study is focused on the possibility if we can use graphic calculators in teaching and learning school mathematics. This study is consisted with four main chapters. In chapter II, the functions of the graphic calculator EL-9600 produced by Sharp Corporation was analyzed focused on the possibilities if the functions could be used in teaching and learning school mathematics. Calculating of real numbers and complex numbers, solving equations and system of linear equations, calculating of matrices, graphing of several functions including polynomial functions, trigonometric functions, exponential and logarithmic functions, calculation of differential and integrals, arranging of statical data, graphing of statistical data, testing of statistical hypotheses, and other more useful functions were founded. In Chapter III, a mathematics textbook developed by Core-Plus Mathematics Project was analyzed focused on how a graphic calculator was used in teaching and learning mathematics, In the textbook, graphic calculator was used as a tool in understanding mathematical concepts and solving problems. Graphic calculator is not just a tool to do complex computations but a tool used in the processes of doing mathematics, In chapter IV, the 7th mathematics curriculum for korean secondary schools was analyzed to find the contents could be taught by using graphic calculators. Most of the domains, except geometric figure, were found that they could be taught by using graphic calculators, In chapter V, a model of a unit using graphic calculator in teaching 7th mathematics curriculum was developed. In this model, graphic calculator was used as a tool in the processes of understanding mathematical concepts and solving problems. This study suggests the possibilities that we can use graphic calculators effectively in teaching and learning mathematical concepts and problem solving for most domains of secondary school mathematics.

• 대한수학교육학회지:수학교육학연구
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• 제27권4호
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• pp.833-855
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• 2017

본 연구는 삼각함수 각의 크기를 표현하기 위해 라디안 단위를 새로 도입하는 이유로서 호의 길이를 이용한 각의 측도라는 호도법의 의미와, 삼각함수의 정의역이 일반각을 나타내는 실수로 확장된 이유를 재조명하고자 한다. 이를 위해 라디안 개념의 다각적인 교수학적 분석을 하고자, 역사적, 수학적, 응용수학적 분석을 수행하였다. 이를 통해 첫째, 호도법은 각도에 내재된 본질이고, 라디안은 원주율(${\pi}$)과 밀접한 이론적이고 절대적인 단위이며, 삼각함수를 실함수로 함을 밝혔다. 둘째, 라디안은 동심원에서 비와 비례 관계의 공변성을 거쳐 불변성을 인식하도록 할 것, 라디안으로 표현한 코사인과 사인의 직교성이 임의의 함수의 급수 표현을 가능하게 함, 라디안은 호의 길이를 반지름으로 측도하는 가장 단순화한 표준임을 인식하도록 할 것, 분할 전략을 통해 육십분법과의 연결성을 찾을 수 있음을 밝혔다. 셋째, 각과 각도의 구별로, 라디안 단위의 생략 여부에 대한 정당화와, 호와 반지름 사이의 곱셈 관계 전략이 필요함을 밝혔다. 이로써 도출한 교수학적 시사점은 라디안 개념의 유용성과 가치를 드러내고, 호도법의 실질적인 지도에 기여할 수 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권2호
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• pp.151-170
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• 2009

This study reports a research which was conducted on how frequently and where the students use the unit circle method while dealing with trigonometric functions in solving the trigonometry questions. Moreover, the reasons behind the choice of the methods, which could be the unit circle method, the ratio method, or the use of trigonometric identities, are also investigated to get an insight about their understanding. In this study, the relationship between the students' choices of methods in solving questions is examined in terms of instrumental or relational understanding. This is a multi-method research which involves a range of research strategies. The research techniques used in this study are test, verbal protocol (think aloud), and interview. The test has been applied to ten tenth grade students of a public school to get students' solution processes on the paper. Later on, verbal protocol has been performed with three students of these ten who were of the upper, middle and lower sets in terms of their performance in the test. The aim was to get much deeper data on the students' thinking and reasoning. Finally, interview questions have been asked both these three students and other three from the initial ten students to question the reasons behind their answers to the trigonometry questions. Findings in general suggest that students voluntarily choose to learn instrumentally whose reasons include teachers' and students' preference for the easier option and the anxiety resulting from the external exam pressure.

• Steel and Composite Structures
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• 제34권4호
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• pp.511-524
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• 2020

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

• 대한수학교육학회지:수학교육학연구
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• 제18권2호
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• pp.263-281
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• 2008

라디안에 관한 기존의 교육적 논의는 대부분 학생들의 라디안 이해 실태 조사에 한정되고, 학습 지도에 관한 논의는 본격적으로 이루어지지 않았다. 라디안의 효과적인 지도에 관한 연구를 비롯한 라디안에 관한 교육적 논의는 라디안의 본질에 대한 이해에 기초해야 한다. 이에 이 연구에서는 라디안에 대한 이론적 분석을 통해 이후 라디안의 교수 학습 실제에 관한 연구의 기초를 놓는다. 라디안은 각의 크기와 동질량의 비라는 두 측면을 복합적으로 지니고 있는 개념이다. 라디안의 개념지도는 라디안이 가진 이 양면적 특성과 관련하여 라디안의 좋은 점과 유용성을 학생들이 인식하게 하는 방향으로 이루어져야 한다.