• Title, Summary, Keyword: mathematical induction

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Comparative Study on Teaching of 'Mathematical Induction' in South and North Korea (교과서에 나타난 '수학적 귀납법'에 대한 남.북한 비교)

  • 박문환
    • Journal of Educational Research in Mathematics
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    • v.12 no.2
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    • pp.181-192
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    • 2002
  • There are various methods of proving a proposition. Among these, 'mathematical induction' is treated in school mathematics weightly. But many students have difficulty with the proof by 'mathematical induction'. To solve this problem, analysis needs to be attempted in various aspects This study attempts to compare the teaching methods of 'mathematical induction' in South and North Korea and to acquire the implication. In fact, many differences between South and North Korea are found. These differences are caused by epistemological and psychological premise. Therefore this study investigates the epistemological and psychological aspects in North Korea and compares the textbooks in South and North Korea. Through this study, some implications are found. First, the sequence of introducing the 'mathematical Induction' needs to be considered. Second, the rich context of applying the 'mathematical induction' is needed. Finally, disagreement between curriculum and textbook in South Korea needs to be reconsidered.

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The Role of Regression in the History of Mathematical Induction and Its Didactical Implications (수학적 귀납법의 역사에서 하강법의 역할 및 교수학적 논의)

  • Park, Sun-Yong;Chang, Hye-Won
    • Journal for History of Mathematics
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    • v.20 no.4
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    • pp.23-48
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    • 2007
  • This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

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On the Students' Understanding of Mathematical Induction (수학적 귀납법에 대한 학생들의 이해에 관하여)

  • Hong, Jin-Kon;Kim, Yoon-Kyung
    • Journal of Educational Research in Mathematics
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    • v.18 no.1
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    • pp.123-135
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    • 2008
  • This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

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Investigation of Present State about Mathematical Reasoning in Secondary School -Focused on Types of Mathematical Reasoning- (학교 현장에서 수학적 추론에 대한 실태 조사 -수학적 추론 유형 중심으로-)

  • 이종희;김선희
    • The Mathematical Education
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    • v.41 no.3
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    • pp.273-289
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    • 2002
  • It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

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Abduction As A Mathematical Resoning. (수학적 추론으로서의 가추법)

  • 김선희;이종희
    • Journal of Educational Research in Mathematics
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    • v.12 no.2
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    • pp.275-290
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    • 2002
  • This Study takes Peirce' abduction which is Phenomenology' first reasoning mode, as a part of mathematical reasoning with deduction and induction. Abduction(retroduction, hypothesis, presumption, and originary argument) leads a case through a result and a rule, while deduction leads a result through a rule and a case and induction leads a rule through a case and a result. Polya(1954) involved generalization, specialization, and analogy within induction, but this paper contain analogy in abduction. And metaphors and metonymies are also contained in abduction, in which metaphors are contained in analogy. Metaphors and metonymies are applied to semiosis i.e. the signification of mathematical signs. Semiotic analysis for a student's problem solving showed the semiosis with metaphors and metonimies. Thus, abductions should be regarded as a mathematical reasoning, and we must utilize abductions in mathematical teaming since abductions are thought as a natural reasoning by students.

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Analysis on Types and Roles of Reasoning used in the Mathematical Modeling Process (수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석)

  • 김선희;김기연
    • School Mathematics
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    • v.6 no.3
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    • pp.283-299
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    • 2004
  • It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

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A Study on Dynamic Characteristics of Induction Motor System (유도전동기 시스템의 동특성 연구)

  • Lee Hyoung-Woo
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.5
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    • pp.128-136
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    • 2006
  • To predict the noise and vibration characteristics of induction motor system, it is necessary to develop the mathematical model including all the mechanical elements such as shaft, blower, rotor, fan, bearing, case and mounting parts. Coupling effect between case-mount system and rotor- shaft system including shaft, blower, rotor, fan and bearing is examined. Impact exciting experimentation was done in order to verify vibration model of the induction motor system. From experimental results, we can appreciate that the natural frequencies of induction motor system are in good agrements with analysis.

Mathematical Model of Two-Degree-of-Freedom Direct Drive Induction Motor Considering Coupling Effect

  • Si, Jikai;Xie, Lujia;Han, Junbo;Feng, Haichao;Cao, Wenping;Hu, Yihua
    • Journal of Electrical Engineering and Technology
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    • v.12 no.3
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    • pp.1227-1234
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    • 2017
  • The two-degree-of-freedom direct drive induction motor, which is capable of linear, rotary and helical motion, has a wide application in special industry such as industrial robot arms. It is inevitable that the linear motion and rotary motion generate coupling effect on each other on account of the high integration. The analysis of this effect has great significance in the research of two-degree-of-freedom motors, which is also crucial to realize precision control of them. The coupling factor considering the coupling effect is proposed and addressed by 3D finite element method. Then the corrected mathematical model is presented by importing the coupling factor. The results from it are verified by 3D finite element model and prototype test, which validates the corrected mathematical model.