• 한국수학교육학회지시리즈E:수학교육논문집
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• 제26권1호
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• pp.51-69
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• 2012

본 연구는 Davydov가 언급한 이론적 일반화가 구체적으로 어떻게 이루어지는지를 탐구하는 것을 목적으로 하며, 이를 위해 본질적 속성의 인식을 돕는 전략과, 이 전략을 통해 이루어지는 이론적 일반화의 과정을 제시하는 것을 연구문제로 설정하였다. 본질적 속성의 인식을 돕는 전략으로 WIOS를 제시하였다. WIOS는 일반화하려는 명제의 결론을 고정하여, 명제의 가정으로부터 추출한 여러 속성을 대상으로 WIO를 통해 결론에 영향을 미치는 속성과 그렇지 않는 속성의 인지를 통해 본질을 추출하는 전략이다. 한편, 이 전략을 통해 이루어지는 이론적 일반화의 과정을 '인지, WIOS, 일반화된 명제의 추측, 정당화, 본질적 속성에 대한 통찰'의 순으로 제시하였다. 그리고 WIOS를 통해 이루어지는 이론적 일반화의 과정을 중학교 교과서에 수록된 2가지 정리에 적용하여 보았으며, 이를 통해 이 전략의 과정이 이론적 일반화의 수행을 도울 수 있는 전략임을 확인해 보았다.

• East Asian mathematical journal
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• 제40권2호
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• International Journal of Computer Science & Network Security
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• 제22권8호
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• pp.217-221
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• 2022

The article analyzes the main theoretical approaches to the formation of managerial competencies and establishes the degree of development of the problem. The content of the concept of "managerial competence" has been clarified, to determine the structure of managerial competencies of a future specialist in the education system and indicators of the formation of managerial competencies. The organizational and pedagogical conditions necessary for the effective process of forming the managerial competencies of future specialists are revealed. The following research methods were used in the work: theoretical (analysis of regulatory documents and scientific literature on the problem under study, comparison, generalization, modeling), empirical (diagnostics of the level of formation of managerial competencies of students of the system, questioning, observation, peer review, comparative qualitative and quantitative analysis of diagnostic results the level of formation of managerial competencies).

• 한국학교수학회논문집
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• 제23권1호
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• pp.129-158
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• 2020

본 연구에서는 고등학교 2학년 학생 3명을 대상으로 기하 영역의 두 가지 과제를 제시하여 학생들이 문제 상황에서 문제해결 초기에 갖는 이미지의 특성을 파악하고 각 학생들의 이미지가 문제를 해결하는 동안 어떻게 변화하며 영향을 미치는지 밝히고자 하였다. 첫 번째 과제에서 학생 A는 문제해결 과정 초기에 정적인 이미지(유형1)를 가지고 있었지만, 후에 동적이면서도 문제 상황에서의 양들 사이의 불변의 관계를 인식한 유형3으로 발전하였고 학생 B와 학생 C는 문제해결 과정 전반에 걸쳐 유형3으로 관찰되었다. 첫 번째 과제에서 학생 B와 학생 C의 문제맥락에 대한 이미지에 차이점이 발견되지 않았지만 두 번째 과제에서는 분명한 차이를 드러내었다. 두 번째 과제에서 학생 B와 학생 C 모두 문제맥락에 대한 동적인 이미지를 가지고 있었지만 학생 B의 경우 양들 사이의 불변의 관계를 인식하지 못하였고 학생 C는 불변의 관계를 인식하는 잘 발달된 양적 구조를 가지고 있었다. 이에 따라 각 과제의 문제해결 성공 여부가 좌우되었는데, [과제1]에서는 문제 상황에서의 양들에 대한 동적인 이미지를 갖고 이론적 일반화 수준에 도달했는지의 여부에 의해서, [과제2]의 경우에는 문제 상황에서의 두 양에 대한 공변 추론 수준에 따라 학생들 간의 차이가 발생하였다.

• International Journal of Computer Science & Network Security
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• 제22권10호
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• pp.91-96
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• 2022

Article materials reflect the results of scientific research and generalization of experience concerning quality measurement of student's educational activities in the context of innovative development of the educational process, which is ensured by introducing educational innovations. The main point of monitoring of higher education students' activities and also phenomenon of education quality, particularly its results, are determined in the research. Guided by the scientific theory and personal experience of scientific and pedagogical activities, the attempt to single out the key components, important indicators and to introduce component indicator model of quality of higher education students' activities on the qualimetry base has been performed. Methodical solutions concerning the application of the developed model to determine the dynamics of pedagogical students' educational achievements by particular educational components in the process of innovative development of educational process are proposed. The advanced studies that relate to the development of methods for monitoring the quality of pedagogical higher education students' activities on the basis of systemic, competence and qualimetry approaches taking into account the levels of education and chosen specialties have been decided.

• 한국초등수학교육학회지
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• 제16권2호
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• pp.253-267
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• 2012

본 연구는 창의성이 발현되는 인지적 과정이 무엇인지에 대한 관점을 이론적으로 고찰한 후, 이를 토대로 수학적 창의성을 계발하고 측정하는데 바람직한 과제와 수업 방향을 제시하는 것을 목적으로 한다. 먼저, 창의성에 대한 영역-특수적 관점과 영역-일반적 관점을 이론적으로 고찰하였다. 창의성 발현에 대한 이 두 관점은 이론적 논의에 그치지 않고 수학적 창의성을 계발하고 신장시키기 위해 고안된 과제와 프로그램에 영향을 미친다. 창의성에 대한 교육학적 고찰에서는 수학적 창의성을 검사하고 계발하기 위한 과제와 수업 프로그램이 구비해야할 조건을 이론적으로 탐색한 후, 이를 바탕으로 실제 수학 수업에서 활용가능한 과제와 수업 사례를 제시하였다. 이 연구의 핵심적인 결론은 창의성의 발현되는 과정에 대한 연구는 수학적 창의성 연구의 핵심이 되어야 하며, 아울러 확산적 사고는 수학적 창의성 계발을 위한 필요조건이지만 충분조건은 될 수 없으므로, 수학적 창의성을 계발하기 위해서는 일반화, 추상화 등 다양한 수학적 추론과 수학적 지식을 고려할 필요가 있다.

• International Journal of Control, Automation, and Systems
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• 제2권4호
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• pp.463-474
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• 2004

Game theory is a method of mathematical analysis developed to study the decision making process. In 1928, Von Neumann mathematically proved that every two-person, zero-sum game with many pure finite strategies for each player is deterministic. In the early 50's, Nash presented another concept as the basis for a generalization of Von Neumann's theorem. Another central achievement of game theory is the introduction of evolutionary game theory, by which agents can play optimal strategies in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) as introduced by Maynard Smith in 1982. Keeping pace with these game theoretical studies, the first computer simulation of coevolution was tried out by Hillis. Moreover, Kauffman proposed the NK model to analyze coevolutionary dynamics between different species. He showed how coevolutionary phenomenon reaches static states and that these states are either Nash equilibrium or ESS in game theory. Since studies concerning coevolutionary phenomenon were initiated, there have been numerous other researchers who have developed coevolutionary algorithms. In this paper we propose a new coevolutionary algorithm named Game theory based Coevolutionary Algorithm (GCEA) and we confirm that this algorithm can be a solution of evolutionary problems by searching the ESS. To evaluate this newly designed approach, we solve several test Multiobjective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by the coevolutionary algorithm and analyze the optimization performance of our algorithm by comparing the performance of our algorithm with that of other evolutionary optimization algorithms.

• International Journal of Computer Science & Network Security
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• 제22권5호
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• pp.31-38
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• 2022

The article highlights the educational potential of information and communication technologies in the study of philological disciplines in higher education institutions. The study aims to analyze the didactic potential of ICT in the study of philological disciplines, as well as to check the scientific hypothesis that the use of ICT in HEIs in the study of philological disciplines will intensify and enhance the effectiveness of the learning process. To confirm the validity of the hypothesis, experimental testing was carried out and the results are illustrated in the article. The above-mentioned goal of the study determined the use of theoretical and empirical methods: analysis, synthesis, generalization, and systematization of pedagogical and scientific-methodological literature to clarify the state of research problem development and to identify pedagogical foundations on which the process of ICT use is based, comparison and prediction; questioning and testing of educational process participants to understand the effectiveness of ICT use in their training in HEIs. The research results showed positive changes in all analyzed criteria in the experimental group, which is due to the introduction of additional ICT tools into the educational process of the mentioned group. The scientific novelty of the study consists in highlighting the main characteristics and didactic functions of ICT in the learning process of philological students; in covering the classification of ICT, ICT tools, and typology of training sessions using ICT in the study of philological disciplines. In the conclusion it is summarized that the introduction of modern ICT in the educational process allows intensifying the learning process, implementation of a variety of ideas, increases the pace of classes and material assimilation, influencing the motivation for learning, increases the amount of independent work of students.

• International Journal of Computer Science & Network Security
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• 제24권5호
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• pp.165-171
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• 2024

The processes of society's informatization and digitalization necessitate the widespread use of new pedagogical technologies. Through these technologies, comprehensive disclosure of didactic functions of new methods of educational activity and the realization of the potential and creative potential. The use of information and computer multimedia technologies in teaching music art is especially relevant in the intensification of the development of interactive technologies, the transition to mixed forms of learning, and a period of socio-economic and sociopolitical upheavals. The study aims to substantiate the theoretical and applied principles of the analysis of multimedia technology learning musical art in modern conditions and assess the status and trends in their use in conducting educational activities. The study uses general scientific and unique methods of economic analysis, in particular, analysis and synthesis, analogy and comparison, generalization and systematization, and graphic ways. Regarding the results of the study of multimedia technologies for teaching musical art in current conditions, it was found that they contribute to the development of the seeker's creative, creative, and cognitive activity, have a positive impact on learning material, and diversify the educational process. Multimedia technologies such as presentations, programs for watching a video, listening to audio, music and singing karaoke, electronic encyclopedias, and Internet resources are proven to be the most used in music education. They have several qualitative and quantitative advantages, manifested in the possibilities of audio-visual presentation of educational material and significantly higher information density. It is suggested to strengthen the use of such computer programs as Microsoft Word, Ahead Nero, Finale, Adobe Audition, Sound Forge, and Microsoft PowerPoint for musical art classes.

• 대한수학교육학회지:수학교육학연구
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• 제24권4호
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• pp.607-622
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• 2014

이 논문의 목적은 삼각함수 개념의 역사적 발달과정을 분석하고, 이를 바탕으로 하여 교육적 함의를 논의하는데 있다. 역사적 분석의 결과는 다음의 두 가지이다. 첫째, 삼각함수 개념은 역사적으로 비를 측정하는 선분(호의 삼각선)에서, 비를 나타내는 수치(각의 함수)로 발달하였으며, 이 과정에서 기하, 산술, 대수, 해석이 통합되었다. 둘째, 실제적 계산에서 이론적 함수로 발달한 결과, 주기성으로 형식화되었으나 '삼각법'이 간과되었다. 그리고 교육적 함의는 다음의 두 가지이다. 첫째, 실제적 계산에서 간과된 삼각법을 닮음의 원리에 의해 관계적 구조적으로 다루어야 한다. 둘째, 삼각함수로의 개념적인 일반화는 인식론적 장애로 인정되어야 하며, 역사에서 드러난 통합을 강조하는 방향으로 개선되어야 한다. 이러한 연구결과는 학습 지도에 있어 유용한 시사점을 제공한다.