• Communications of Mathematical Education
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• v.26 no.1
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• pp.51-69
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• 2012

The cognition of an intrinsic attribute play an important role in the process of theoretical generalization. It is the aim of this paper to study how the theoretical generalization is made. First of all, we suggest the What-if-only-strategy(WIOS) which is the strategy helping the cognition of an intrinsic attribute. And we propose the process of the theoretical generalization that go on the cognitive stage, WIOS stage, conjecture stage, justification stage and insight into an intrinsic attribute in order. We propose the process of generalization adding the concrete process cognizing an intrinsic attribute to the existing process of generalization. And we applied the proposed process of generalization to two mathematical theorem which is being managed in middle school. We got a conclusion that the what-if-only strategy is an useful method of generalization for the proposition. We hope that the what-if-only strategy is helpful for both teaching and learning the mathematical generalization.

• East Asian mathematical journal
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• v.40 no.2
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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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• v.22 no.8
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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).

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.129-158
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• 2020

In this study, we presented two geometric tasks to three 11th grade students to identify the characteristics of the images that the students had at the beginning of problem-solving in the problem situations and investigated how their images changed during problem-solving and effected their problem-solving behaviors. In the first task, student A had a static image (type 1) at the beginning of his problem-solving process, but later developed into a dynamic image of type 3 and recognized the invariant relationship between the quantities in the problem situation. Student B and student C were observed as type 3 students throughout their problem-solving process. No differences were found in student B's and student C's images of the problem context in the first task, but apparent differences appeared in the second task. In the second task, both student B and student C demonstrated a dynamic image of the problem context. However, student B did not recognize the invariant relationship between the related quantities. In contrast, student C constructed a robust quantitative structure, which seemed to support him to perceive the invariant relationship. The results of this study also show that the success of solving the task 1 was determined by whether the students had reached the level of theoretical generalization with a dynamic image of the related quantities in the problem situation. In the case of task 2, the level of covariational reasoning with the two varying quantities in the problem situation was brought forth differences between the two students.

• International Journal of Computer Science & Network Security
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• v.22 no.10
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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.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.2
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• pp.253-267
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• 2012

In this paper, we primarily focus on the perspectives about creative process, which is how mathematical creativity emerged, as one aspect of mathematical creativity and then present a desirable task characteristic to measure and program characteristics to develop mathematical creativity. At first, we describe domain-generality perspective and domain-specificity perspective on creativity. The former regard divergent thinking skill as a key cognitive process embedded in creativity of various discipline domain involving language, science, mathematics, art and so on. In contrast the researchers supporting later perspective insist that the mechanism of creativity is different in each discipline. We understand that the issue on this two perspective effect on task and program to foster and measure creativity in mathematics education beyond theoretical discussion. And then, based on previous theoretical review, we draw a desirable characteristic on instruction program and task to facilitate and test mathematical creativity, and present an applicable task and instruction cases based on Geneplor model at the mathematics class in elementary school. In conclusion, divergent thinking is necessary but sufficient to develop mathematical creativity and need to consider various mathematical reasoning such as generalization, ion and mathematical knowledge.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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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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• v.22 no.5
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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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• v.24 no.5
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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.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.