• Communications of Mathematical Education
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• v.15
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• pp.29-34
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• 2003

물리학, 공학, 경제학, 생물학, 생태학 등의 자연현상, 사회 현상 그리고 심리상황 등과 관련된 내용들의 모델링 과정을 거쳐 나온 미분방정식의 해를 구하고 해의 의미를 파악하는 작업은 바로 우리의 생활의 진면목을 직접 확인하는 것과 같다. 모델링 과정의 효율성은 교사와 학생간의 충분한 수학적 대화속에서 더욱 의미가 커질 것이다. 아울러 학생들에게 미분방정식의 해의 실제적인 의미를 상상하게 하고 그 결과를 발표하게 하는 것과 해를 구하는 과정에 관한 이론의 이해를 돕는 것이 바람직한 학습 지도 방법이 될 것이다. 전 교육과정을 통해 미분방정식의 모델링 과정을 소개하면서 해의 존재성, 해의 유일성, 해법, 해의 의미 등의 학습 및 지도를 학습자 중심으로 운영할 필요가 있다.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.91-117
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• 2017

In this paper, we develop a logarithm units' teaching learning materials using genetic modeling which is designed for students to construct by themselves and figure out mathematical knowledge conceptually, and we analyze the process of students' comprehension of logarithm concepts through genetic modeling activities. For this purpose, we divide logarithm units into three subunits and develop teaching learning materials which include genetic original contexts and are framed by the four pedagogic phases of genetic modeling, application, extraction, comprehension, and construction so that students themselves are capable of construct the concepts of logarithm units. The developed teaching learning materials are applied into lessons for two intermediate-basic students and two intermediate-advanced students. Through this, we examine students' conceptual construction process about logarithms units with the four pedagogical stages of genetic modeling applied, and analyze the depth of their comprehension about the logarithm units based on the general phases of mathematics-learning introduced by van Hiele, and then we suggest several pedagogical implications.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.47-62
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• 2016

Cultivating mathematical creativity is one of the aims in the recently revised mathematics curricular. However, there have been lack of researches on how to nurture mathematical creativity for ordinary students. Perspective of Realistic Mathematics Education(RME), which pursues education of creative person as the ultimate goal of mathematics education, could be useful for developing principles and methods for cultivating mathematical creativity. This study reanalyzes RME from the points of view in mathematical creativity education. Major findings are followed. First, students should have opportunities for mathematical creation through mathematization, while seeking and creating certainty. Second, it is vital to begin with realistic contexts to guarantee mathematical creation by students, in which students can imagine or think. Third, students can create mathematics in realistic contexts by modelling. Fourth, students create the meaning of 'model of(MO)', which models the given context, the meaning of 'model for(MF)', which models formal mathematics. Then, students create MOs and MFs that are equivalent to the intial MO and MF given by textbook or teacher. Flexibility, fluency, and novelty could be employed to evaluate the MOs and the MFs created by students. Fifth, cultivation of mathematical creativity can be supported from development of local instructional theories by thought experiment, its application, and reflection. In conclusion, to employ the education model of cultivating mathematical creativity by RME drawn in this study could be reasonable when design mathematics lessons as well as mathematics curriculum to include mathematical creativity as one of goals.

• Communications of Mathematical Education
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• v.3
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• pp.207-228
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• 1997

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.627-629
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• 1998

본 논문에서는 파티클 시스템(Particel System)을 이용한 실시간 기체 모델링 알고리즘을 제시한다. 일반적으로 그래픽스 분야에서, 주요한 자연현상의 하나인 기체의 운동은 수학적으로 복잡한 모델을 사용하여 그 모델링이 매우 복잡하였다. 따라서 빠른 구현시간을 얻기 위해서는 고성능의 컴퓨터가 요구되어왔다. 이 알고리즘에서는 물리학에서 수학적으로 정의된, 기체의 움직임에 적용되는 요소 각각을 추계 모델(Stochastic Model)로 다시 재 정의하여 기체 입자각각에 적용시켜 계산과정을 간단히 하였다. 따라서 일반적으로 사용되는 연구용 컴퓨터시스템에서도 실시간 애니메이션의 구현이 가능하다.

• The Mathematical Education
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• v.55 no.1
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• pp.41-71
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• 2016

The purpose of this study is to investigate elementary students' communication in process of applying mathematical modeling. For this study, 22 fifth graders in an elementary school were observed by applying mathematical modeling process (presentation of problem ${\rightarrow}$ model inducement activity ${\rightarrow}$ model exploration activity ${\rightarrow}$ model application activity). And the level of their communication with their activity sheets and outputs, observation records and interviews were also analyzed. Additionally, by analyzing the activity cases of and , this study researched that what is a positive influence on students' communication skills. Whereas showed significant advance in the level of communication, who communicated actively on speaking area but not on every areas showed insensible changes. To improve communication abilities, cognitive tension and debate situation are needed. This means, mathematical education should continuously provide students with mathematical communication learning, and a class which contains mathematical communication experiences (such as mathematical modeling) will be needed.

• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1151-1152
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• 2011

본 논문에서는 부스트-플라이백(Integrated Boost-Flyback Converter, IBFC) 직렬 연결 구조 컨버터의 동작 특성 해석 및 정확한 제어기 설계를 위한 개선된 모델링 방법을 제시한다. 주 스위치에 의해 IBFC의 부스트, 플라이백 컨버터가 서로 다른 도통 모드로 동시에 동작 하기 때문에 2대 컨버터의 모델링과 회로 해석을 위한 이론적인 모델링 접근방법과 수학적인 계산과정이 복잡하다. 따라서 IBFC를 등가 전류 소스를 포함한 부스트, 플라이백 컨버터로 각각 나누어 상태 공간 평균화 방법을 이용하여 회로 방정식을 독립적으로 유도한 후, 이 회로 방정식을 종합하여 IBFC의 완전한 상태 공간 방정식을 얻을 수 있다. 제안된 방법은 IBFC의 복잡한 모델링을 간단하게 해 주며, 수학적인 계산 과정도 간소화 시킬 수 있는 장점이 있다. 이를 바탕으로 정상 상태 해석 및 높은 출력 전압 추종 제어기를 설계하였다. 시뮬레이션과 실험 결과를 제시하여 제안된 방법의 유효함을 검증하였다.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.

• Proceedings of the KAIS Fall Conference
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• 2010.11a
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• pp.363-366
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• 2010

본 논문에서는 원형구조의 전파환경을 위한 경로손실을 다각형모델링과 수학적 모델링을 통해 분석하였다. 원형의 통신환경은 비교적 좁은 반경에 곡률이 거의 없고, 내부는 공기저항을 고려한 감압상태로 Ray-tracing 기법은 원형이라는 구조적 특징을 완벽히 적용하는데 문제가 있기 때문에 원에 가까운 다각형을 모델링하였다. 다각형 모델링 방법와 수학적 방법의 전파손실분석결과 반사횟수와 관계없이 유사한 전파손실성능을 확인하였다. 본 논문은 무선을 이용한 튜브 즉, 원형의 철도운영환경도 고려되고 있는 시점에서, 기존의 철도환경과 다른 환경에 대한 무선환경분석을 위한 기초자료로 사용될 수 있을 것이다.