• School Mathematics
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• v.8 no.2
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• pp.123-138
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• 2006

The fraction concept consists of various meanings and is one of the more abstract and difficult in elementary school mathematics. This study intends to analyze the fraction concept from historical and psychological viewpoints, to examine the current elementary mathematics textbooks by these viewpoints and to seek the direction for improvement of it. Basic ideas about fraction are the partitioning - the dividing of a quantity into subparts of equal size - and about the part-whole relation. So these ideas are heavily emphasized in current textbooks. However, from the learner's point of view, situations related to different meanings of fraction concept draw qualitatively different response from students. So all the other meanings of fraction concept should be systematically represented in elementary mathematics textbooks. Especially based on historico-genetic principle, the current textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction as a unit.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.7
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• pp.801-806
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• 2015

Recently, retro music is popular in the domestic music industry. Even in the movie industry, remake or retro movies are made continuously. In this paper, we consider the reason of remake in the viewpoint of mathematics and show that there is a maximum number of lyrics, pictures, music, and movies that human can make due to the characteristics of digital contents. The time that human cannot make new lyrics, new pictures, new music, and new movies any more will be estimated. Therefore, artists will have difficulties to make new contents in the future, and human have to listen and see the previous lyrics, movies, music, or pictures in the future. This study will give a deep philosophical insight for contents industry.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.77-94
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• 2011

This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.217-228
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• 1999

The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. first, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.135-152
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• 2013

The purpose of this study is to navigate to the desired direction for the figure of number line through the extensive analysis of number line in middle school textbooks and literatures. For the efficient achievement of this purpose, three research questions were posed as follows: First, we compare the figures of number line in textbooks of Korea and other countries. Korean math textbooks mark the arrow on both sides of number line. But, however, coordinate plane was marked with arrow on only positive direction of number line. In contrast, the majority of secondary school textbooks in several foreign countries has the arrow only on positive direction. Second, the change in the figure of number line has been analyzed historically from two perspectives. From the first to 2007-revised curriculum, math textbooks of Korea were analyzed. Since the 6th curriculum, the number of textbooks with arrows on both sides has increased sharply. That is, textbooks with one arrow almost have disappeared. It is strange that any explanation for this abrupt change can't be found. The following analysis was also performed on published foreign literatures since Descartes. There was no arrow in the early figures of number line. But after 19th century, number lines with one arrow have begun to appear. Third, based on the previous study, we propose a reasonable way for the figure of number line. In fact, we claim that, in terms of linguistic symbols, the number line should be with only one arrow on positive side.

• Proceedings of the Speleological Society Conference
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• 1993.07a
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• pp.129-145
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• 1993

상근에 있는 자연과학관으로 3층건물이다. 1층은 관광코너로 자연의 아름다움과 이 풍부한 상근의 관광자원을 슬라이드 사진등으로 전시하고 있으며 하이킹코오스 기념사진관코너등을 마련하고 있다. 1층의 관광코너는 전시장에 있는데 하쯔네 화산의 함원과 지질, 암석, 온천등의 전시와 지질관측의 실제상황을 설명하고 있다. 이층 전시장에는 상근의 지형과 모든 지리적인 분포등을 알 수 있는 종합모형, 기상관측과 지구의 역사의 모습 등이 전시되고 있다. 한편 3층에는 생물사회 즉, 삼림과 습지. 계곡 그 부근에 있는 소, 호의 모습과 이들의 고장에서 서식하는 동식물의 모습을 입체적으로 전시하고 있는데 물론 박제품들로 전시되고 있다. 이 자연과학관은 최근에 설립된 것으로 부토산 소, 호를 한눈으로 전망할 수 있는 곳에 세워진 수학여행, 자연관찰, 임간학교등의 관찰코오스로서 가장 적당하다.(중략)

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.2
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• pp.101-107
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• 1997

고전제어와 현대제어의 이론을 선형제어론을 중심으로 각각의 특징을 간략히 살펴보았다. 21세기의 문턱에 서 있는 현재, 과학의 발전은 급진전하고 있음은 주지하는 바이며, 이러한 시점에서 천학비재한 필자가 제어계의 미래를 전망한다는 것은 대단히 어려운 일이지만, 현재 상황으로 볼 때 짧은 기간의 미래에는 강인성에 중점을 둔 제어기의 설계에 관한 연구가 계속 되어지리라고 본다. 그리고 컴퓨터 기술의 발달과 더불어 복잡한 제어 알고리즘도 쉽게 실현될 수 있으므로 뉴럴네트워크 및 인공지능에 의한 제어 기술도 크게 발전될것으로 생각된다. 한편 일반적인 제어기의 설계 순서는 대상으로 하는 플란트의 동특성을 고려하여 플란트를 수학적으로 모델링하고, 모델링된 공칭모델을 기초로 하여 제어기를 설계한 다음, 시뮬레이션 및 실험을 통하여 설계된 제어계의 타당성을 검토하여 불만족스러운 경우는 제어계를 재설계하거나, 나아가 모델링을 다시 하는 것이 통상적으로 이용되어온 설계 순서였다. 이 경우는 플란트의 모델링 과정과 제어기 설계 과정이 완전히 독립적으로 이루어졌다. 그러나 최근 모델링과 제어기 설계의 불가분(나눌수 없음) 성이 제기되면서, 시스템의 동정(identification)과 보상기(compensator)의 통합화 설계기법이 제안되고 있으며, 앞으로 이 연구 테마도 흥미있는 한 분야가 될 것으로 생각된다.

• Journal of Information Management
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• v.31 no.3
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• pp.21-34
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• 2000

In recent year, much progress has been made in understanding the application of the chaos in the engineering. In the electrical engineering, electronics, communication, mechanical, chemistry as well as mathematics, physics, there are extended to the application of chaos. In this review, I explained chaos engineering application and future application possibility.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.05a
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• pp.1049-1052
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• 2013

저자들은 1980 년대 후반부터 역사학적 논쟁들을 통계적 수학적 방법을 이용하여 분석해보고자 하는 시도들을 하여 왔다. 최근에는 역사학의 논쟁점 중이 하나인 화랑세기의 진위 여부를 분석하기 위한 일련의 연구를 시도하였다. 이러한 일련의 시도의 일환으로 이 연구는 기획되었다. 이 글에서는 일본의 고대 기년 추정 방법을 참고하면서 세대 평균치와 재위 평균치의 추정이라는 방법을 통하여 "삼국사기" 초기 기년 문제에 대한 해명을 시도해 보고자 한다. 종래에는 세대 평균치라는 개념을 사용하지 않아서 편차가 심한 왕별 재위기간 평균치만 사용하여 재위기간 추정의 오차가 컸다. 또한 여러 가지 추론들이 주관적인 판단에 의지한 부분이 많아서 폭넓은 지지를 얻지 못한 경우가 많았다. 따라서 세대 평균치와 재위 평균치는 반드시 일치하지 않는다는 점을 분명히 하는 한편, 양자를 결합한 추정 방안을 마련해 볼 것이다.