• 대한수학회지
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• 제37권3호
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• pp.463-471
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• 2000

A central limit theorem is obtained for stationary linear process Xt = aj$\varepsilon$t-j, where {$\varepsilon$t} a strictly stationary associated sequence with Et < and {aj} is a sequence of real numbers with <. A functional central limit theorem is also derived.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권1호
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권2호
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• pp.253-263
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• 2001

Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing student's self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students'acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student's degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

• 대한수학회논문집
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• 제10권1호
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• pp.195-205
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• 1995

• 한국수학교육학회지시리즈A:수학교육
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• 제53권2호
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• pp.163-184
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• 2014

The purpose of this study was to develop the assessment tools using graphing calculators for the assessment of the mathematical process which was emphasized in 2009 reformed mathematics curriculum. In this paper, we presented three sample calculator-based test items for the assessment of students' mathematical process abilities and scoring rubrics for the paper and pencil assessment and assessment based on observation on each item. In order to improve mathematics teachers' understanding of the assessment tools using graphing calculators and to show the procedures of assessment using technological devices, we also drew up assessment guidelines. We hope the results of the study contribute to the promotion of assessment environment encouraging the use of graphing calculators in assessments.

• Journal of Welding and Joining
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• 제15권3호
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• pp.118-127
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• 1997

With the trend towards welding automation and robotization, mathematical models for studying the influence of various variables on the weld bead geometry in gas metal arc (GMA) welding process are required. Partial penetration, single-pass bead-on-plate welds using the GMA welding process were fabricated in 12mm mild steel plates employed four different process variables. Experimental results has been designed to investigate the analytical and empirical formulae, and develop mathematical equations for understanding the relationship between process variables and weld bead geometry. The relationships can be usefully employed not only for open loop process control, but also for adaptive control provided that dynamic sensing of process output is performed.

• 품질경영학회지
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• 제11권2호
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• pp.2-9
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• 1983

As will be seen, this paper is tries that the research on the mathematical structure of Markov process and Markovian sequential decision process (the policy improvement iteration method,) moreover, that it analyze the logic and the characteristic of behavior of mathematical model of Markov process. Therefore firstly, it classify, on research of mathematical structure of Markov process, the forward equation and backward equation of Chapman-kolmogorov equation and of kolmogorov differential equation, and then have survey on logic of equation systems or on the question of uniqueness and existence of solution of the equation. Secondly, it classify, at the Markovian sequential decision process, the case of discrete time parameter and the continuous time parameter, and then it explore the logic system of characteristic of the behavior, the value determination operation and the policy improvement routine.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권1호
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• pp.45-57
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• 2011

Mathematical thinking is a core element in mathematics education and classroom learning. This paper wish to investigate how primary four (grade 4) students develop their mathematical thinking through working on tasks in multiplication where greatest products of multiplication are required. The tasks include the format of many digit times one digit, 2 digits times 2 digits up to 3 digits times 3 digits. It is found that the process of mathematical thinking of students depends on their own representation in obtaining the product. And the solution is obtained through a pattern/analogy and "pattern plus analogy" process. This specific learning process provides data for understanding structure and mapping in problem solving. The result shows that analogy allows successful extension of solution structure in the tasks.

• 대한수학회논문집
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• 제12권3호
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• pp.725-741
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• 1997

This paper considers the problem of deriving exponential probability inequalities for product symmetric Poisson processes. As an application they are used to show the existence of regular version of some product process derived from L$\acute{e}$vy process.

• 디자인학연구
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• 제20권
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• pp.61-72
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• 1997

본 연구의 목적은 수학적 Model에 대한 이해도 제고와 제품디자인 과정에의 응용방법 및 필요성에 대한 인식 제고, 그리고 입 문자를 위한 가이드라인으로서의 어프로우치 및 응용 방법의 제안에 있다. 연구의 절차 및 방법으로서는, 먼저 제품디자인을 위한 과학적 분석의 방법 및 필요성을 제품디자인의 특성과 디자인 프로세스에 대한 고찰을 통해 강조하였다. 다음은 수학적 Model은 디자인 문제와 어떤가 대응관계에 있는가에 대해 논의하였다. 그리고, 수학적 Model은 제품디자인 과정에 어떻게 응용될 수 있는가에 대하여 검토하였다. 마지막으로는, 앞에서 기술한 내용들을 근거로 하여 초보자를 위한 어프로우치 및 응용의 방법을 제안하였다. 연구의 결과, 다음 몇 가지점이 성과 또는 문제점으로 도출되었다. 첫째, 수학적 Model은 여러 가지 요소가 복잡하게 얽혀 있는 디자인 문제를 정량적, 구조적으로 파악하는데 유용하며, 그 필요성은 특히 디자이너 자신의 결론을 관계자에게 정당화하고 납득시키는 도구로서 이용될 수 있는 점. 둘째, 수학적 Model이 디자인 과정에 능숙하게 응용하기 위해서는 무엇보다 응용 가능한 모든 수학적 Model의 실체를 우선 이해해야 하며, 컴퓨터를 사용하지 않고서는 완전한 방법으로 구사하기가 쉽지 않다는 점. 셋째, 수학적 Model에 사용되는 수학적 Model에는 그 종류가 많고 디자인 문제의 해결에 응용될 수 있는 Model은 디자인 타입과 디자인 프로세스에 따라 각기 다르기 때문에 그 응용의 방법을 한 가지로 표준화하거나 구체적으로 제시할 수 없다는 점. 넷째, 처음으로 수학적 Model에 대해 어프로우치 하는 경우는 약간의 수학적 지식 및 컴퓨터 프로그램에 대한 이해를 바탕으로 하여 디자인 프로세스 단계별 및 디자인 타입에 부합되는 Model을 선택하는 것으로 시작할 수 있다는 점 등.