• The Mathematical Education
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• v.34 no.2
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• pp.141-202
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• 1995

van Hiele의 사고수준 이론에는 기초수존, 제1수준, 제2수준, 제3수준, 제4수준 등 5가지가 있고, 이 중에서 국민학교에 해당되는 것은 기초수준 (1학년), 제1수준(2, 3학년), 제2주순 (4, 5, 6학년) 등 세 가지 뿐이다. 그리고 기하학적의 구조 인식론에는 관제, 구성, 정의, 공리, 정리, 증명, 척도, 자호, 응용 등 9가지 단계가 있고, 이 9가지 단계를 기초수준, 제 1수준, 제 2수준의 각 수준에 대응시켜서 거기에 해당되는 기하도형 학습을 연구·분석하였다. 기하도형에 관한 학습은 주로 경험성과 창의성을 바탕으로 하는 보기문제를 제시하여 그 흐름을 해결함으로써 각 수준의 각 단계들을 스스로 인식하도록 하였다. 특히 여기에서 처음으로 등장하는 기하학의 구조 인식론이라는 것은 위에서 언급한 9가지 단계를 차례로 거쳐 가야만 아동들은 도형을 올바르게 빠짐없이 인식할 수 있다는 이론이다. 이 이론의 특징을 예를 하나 들어서 설명해 보면, 흔히들 정의를 단순히 무정의어와 정의어로 구분하고 있는데 반하여, 이 이론에서는 서로 역동적인 관계를 갖고 있는 기초정의, 상황정의, 포괄정의, 기본정의, 부수정의, 특수정의 등으로 나누었다는 점이다.

• The Mathematical Education
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• v.33 no.2
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• pp.251-265
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• 1994

• Education of Primary School Mathematics
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• v.13 no.2
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• pp.85-97
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• 2010

The purpose of this study is to develop a teaching program in consideration of the geometrical thinking levels of students to make a contribution to teaching figures effectively. To do this, we checked the geometrical thinking levels of fourth-graders, developed a teaching program based on van Hiele's theory, and investigated its effect on their geometrical thinking levels. The teaching program based on van Hiele's theory put emphasis on group member interaction and specific activities through offering various geometrical experiences. It contributed to actualizing activity-centered, student-oriented, inquiry-oriented and inductive instruction instead of sticking to expository, teacher-led and deductive instruction. And it consequently served to improving their geometrical thinking levels, even though some students didn't show any improvement and one student was rather degraded in that regard - but in the former case they made partial progress though there was little marked improvement, and in the latter case she needs to be considered in relation to her affective aspects above all. The findings of the study suggest that individual variances in thinking level should be recognized by teachers. Students who are at a lower level should be given easier tasks, and more challenging tasks should be assigned to those who are at an intermediate level in order for them to have a positive self-concept about mathematics learning and ultimately to foster their thinking levels.

• East Asian mathematical journal
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• v.28 no.4
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• pp.353-361
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• 2012

In this paper, we apply mathematising activities to geometry contents of corrent in middle and high school in order to actualize learning and teaching through Freudenthal's, Piaget's, and Van Hieles's mathematising among many theories affecting teaching and learning methods. Learners find out mathematical idea through the activities of mathematising that interprete mathematical problemm. And we derive mathematic through the experience of vertical mathematising that expresses it. Based on it, Freudenthal's progressive mathematising process, etc are used in doing the activities of applicative mathematising.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.4D
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• pp.351-360
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• 2010

In 2010, the number of registered vehicles reached almost at 17.48 millions in Korea. This dramatic increase of vehicles influenced to increase the number of traffic accidents which is one of the serious social problems and also to soar the personal and economic losses in Korea. Through this research, an enhanced intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network will be developed in order to obtain the important data for developing the countermeasures of traffic accidents and eventually to reduce the traffic accidents in Korea. Firstly, this research has investigated the influencing factors of road geometric features on the traffic volume of each approaching for the intersections where traffic accidents and congestions frequently take place and, a linear regression model of traffic accidents and traffic conflicts were developed by examining the relationship between traffic accidents and traffic conflicts through the statistical significance tests. Secondly, this research also developed an intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network through applying the intersection traffic volume, the road geometric features and the specific variables of traffic conflicts. Lastly, this research found out that the developed model is better than the existed forecasting models in terms of the reliability and accuracy by comparing the actual number of traffic accidents and the predicted number of accidents from the developed model. In conclusion, it is expect that the cost/effectiveness of any traffic safety improvement projects can be maximized if this developed intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network use practically at field in the future.

• School Mathematics
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• v.13 no.1
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• pp.65-88
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• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.

• Proceedings of the KIEE Conference
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• 2007.11b
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• pp.69-71
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• 2007

최근 들어 전력 계통은 점차 복잡해지고 계통의 규모 역시 빠른 속도로 성장하고 있다. 한국전력거래소는 전력계통의 안정적, 경제적 운영을 담당하고 있는 기관으로 '01년 현재의 에너지관리시스템(EMS)를 도입하여 실시간 전력계통에 대한 정확한 판단을 기반으로 전력계통의 안정성과 경제성 확보에 주력하고 있다. EMS의 대표적인 기능은 계통데이터의 수집(SCADA), 자동발전제어(AGC), 계통해석(NA) 등으로 대별되며, 이중 계통해석 기능은 프로그램 규모면에서 가장 큰 부분을 차지하고 있다. 계통해석 기능은 또다시 상태추정(SE), 상정사고분석(CA), 안전도해석(SENH), 고장해석(SCT) 등의 프로그램으로 구성되어 다양한 실시간 계통해석을 수행하게 된다. 전력계통 해석은 먼저 대상계통을 수학적 모델로 정식화하기 전에 계통망의 기하학적 구조를 기술하는 단계가 필요한데 이를 토폴로지 처리라고 하며, 보통 그래프이론인 노트(Node)와 마디(Branch)를 사용하여 전력계통망을 구성하는 요소들의 연결관계를 정의하게 된다. 본고는 이론적 수준을 넘어 EMS의 계통해석 기능에서 실계통을 해석하기 위해 쓰이고 있는 토폴로지 처리의 기본 알고리즘을 분석하여 국내 전력산업 기술 선진화에 기여하고자 한다.

• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

• Journal of Science and Technology Studies
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• v.3 no.2 s.6
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• pp.1-27
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• 2003

Complexity paradigm is a scientific amalgam that aims to unite a range of theoretical perspectives and research agendas across natural and social sciences. Proponents of complexity paradigm lay claims to an increasing number of areas of study, including artificial life, interpersonal networks, internal/international patterning of organizations, mapping of cyberspace, etc. All of those can be subsumed under the title, 'complexity turn.' Owing to the idea of open system, complexity paradigm has developed a number of new concepts/themes/perspectives that help to account for the complex mechanism of living and non-living creatures. A complex system comprises a number of properties such as disequilibrium, nonlinearity, dissipative structure, self-organization fractal geometry, autopoiesis, coevolution. Following a brief introduction to theoretical development, those properties are succinctly discussed. The complexity turn has provided a wealth of insights that enable to analyze system operations of any kind. It contributes a lot to illuminating the working of social system as well. The most remarkable attempt may be Niklas Luhmann's 'neofunctional system theory.' Merits and shortcomings of complexity paradigm were examined and its future prospect were assessed with the conclusion that complexity paradigm would continue to be useful both as effective transdisciplinary framework and powerful analytical tool.