• School Mathematics
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• v.18 no.3
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• pp.647-666
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• 2016

This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

• School Mathematics
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• v.19 no.2
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• pp.319-343
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• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.63-82
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• 2016

Mathematical notation is the main means to realize the power of mathematics. Under this perspective, this study analyzed the difficulties of learning an irrational number concept in terms of notation. I tried to find ways to overcome the difficulties arising from the notation. There are two primary ideas in the notation of irrational number using root. The first is that an irrational number should be represented by letter because it can not be expressed by decimal or fraction. The second is that $\sqrt{2}$ is a notation added the number in order to highlight the features that it can be 2 when it is squared. However it is difficult for learner to notice the reasons for using the root because the textbook does not provide the opportunity to discover. Furthermore, the reduction of the transparency for the letter in the development of history is more difficult to access from the conceptual aspects. Thus 'epistemological obstacles resulting from the double context' and 'epistemological obstacles originated by strengthening the transparency of the number' is expected. To overcome such epistemological obstacles, it is necessary to premise 'providing opportunities for development of notation' and 'an experience using the notation enhanced the transparency of the letter that the existing'. Based on these principles, this study proposed a plan consisting of six steps.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.237-246
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• 2007

According to 7-th curriculum, irrational number should be introduced using non-repeating infinite decimals. A rational number is defined by a number determined by the ratio of some integer p to some non-zero integer q in 7-th grade. In 8-th grade, A number is rational number if and only if it can be expressed as finite decimal or repeating decimal. A irrational number is defined by non-repeating infinite decimal in 9-th grade. There are misconceptions about a non-repeating infinite decimal. Although 1.4532954$\cdots$ is neither a rational number nor a irrational number, many high school students determine 1.4532954$\cdots$ is a irrational number and 0.101001001$\cdots$ is a rational number. The cause of misconceptions is the definition of a irrational number defined by non-repeating infinite decimals. It is a cause of misconception about a irrational number that a irrational number is defined by a non-repeating infinite decimals and the method of using symbol dots in infinite decimal is not defined in text books.

• The Mathematical Education
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• v.62 no.1
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• pp.35-55
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• 2023

The purpose of this study is to examine not only students' cognition in the mathematical error-finding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, error-finding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher's questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Bulletin of the Society of Naval Architects of Korea
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• v.34 no.4
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• pp.53-61
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• 1997

1. 가시적인 PM(Product Model)의 구조와 자료구조의 미존재로 PM의 실체가 아직 개념적 수준에 머무르고 있다. 2. Physical통합 PM보다 Logical 통합 PM이 요구된다. 3. 광의의 PM 보다 협의의 PM개념에 의한 시스템 개발이 요구된다. :Step by Step 4. PM이 반드시 문제해결의 만병통치약은 아니다. 5. 설계.생산.관리의 각 부문별 고유특성을 살리고 무리한 단일 PM개발보다 Interface 가능을 갖는 중간자의 개발(경우에 따라서 직접 Access 할 수도 있음.) 을 통해 각 부문별 정보의 PM으로의 표현을 용이하게 하여야 한다. 6. 기존의 시스템, 개발중인 시스템, 개발예정 시스템등을 무리없이 순조롭게 통합하기 위해서는 현실적인 정보통합수단으로서의 PM 설계가 요구된다. 7. 생산현장의 각 공정별 자동화 설비 및 운용 소프트웨어, 이것으로부터 생성되는 각종 정보등을 관리할 수 있는 공정 별 생산정보시스템은 필수적으로 요구되는 시스템이다. 8. 자동화된 생산시스템에서의 PM과 생산현장의 POP(Point of Porduction)시스템과의 연계는 필수적이다.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.375-396
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• 2022

In this paper, to provide an idea for the 2022 revised mathematics curriculum by restructuring the content of the 2015 mathematics curriculum, the content elements of recurring decimals of textbooks, which showed differences in the curriculum of Korea and Japan, were analyzed. As a result of this study, in Korea, before the introduction of the concept of irrational numbers, repeating decimals were defined in the second year of middle school, and the relationship between repeating decimals and rational numbers was dealt with. In Japan, after studying irrational numbers in the third year of middle school, the terminology of repeating decimals is briefly dealt with. Then, when learning the concept of limit in the high school <Mathematics III> subject, the relationship between rational numbers and repeating decimals is dealt with. Based on the results of the study, in relation to the optimization of the amount of learning in the 2022 curriculum revision, implications for the introduction period of the circular decimal number, alternatives to the level of its content, and the teaching and learning methods were proposed.

• 한국경영정보학회:학술대회논문집
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• 2008.06a
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• pp.478-485
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• 2008

고객 만족과 납기 충족율을 최대화하기 위하여, 정확하고 실용적인 납기회답 시스템(ATP)은 매우 중요한 역할을 한다. 그러나 복잡한 공급사슬관리 환경 하에서 조달, 제조, 분배 등을 모두 고려한 정확한 ATP 수량 할당은 매우 어려운 업무이고, 때문에 많은 연구들이 이루어져 왔다. 지금까지 기존의 선행 연구에서 시도되었던 ATP 모형들은 공통적으로 정수배의 시간 단위만 고려해 왔고, 이는 실제 산업 현장의 ATP 프로세스를 정확하게 반영하지 못하고 있는 비현실적인 가정이라 할 수 있다. 본 논문에서는 SCM을 위하여 비정수 타임 랙을 사용한 ATP 시스템을 고려한다. 기존 연구들에서 이산형의 무리한 가정으로 표현되어 왔던 시간 단위를 동적 생산 함수(dynamic production function) 개념을 통하여 비음의 실수 범위에서의 자유롭게 나누어 고려할 수 있도록 하였다. 이를 통하여 기존 ATP 연구들의 무리한 가정을 제거하였으며, 보다 더 현실에 가까운 ATP 모델을 제안한다. 본 논문에서는 특히 공급 사슬(Supply Chain) 전체의 재고와 생산, 운송을 모두 고려하며 고객 주문에 대응하는 통합 ATP 시스템을 설계하였고, 기존 연구들이 미처 고려하지 못한 시간 흐름의 연속성에 중점을 두고 선형 계획(LP) 문제의 형태로 비정수 타임랙(non-integer time lag)을 갖는 ATP 시스템을 모델링하였다.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.1448-1452
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• 2010

최근 기상변동성 증가 및 기후변화 영향으로 수문순환과정이 과거와는 다른 양상으로 전개되고 있으며 전반적으로 극치사상의 빈도 및 강도의 증가현상이 지배적이다. 이러한 영향을 정량적으로 검토하기 위해서 경향성분석 방법 등이 도입되어 극치수문사상의 변동경향을 평가하는데 이용되고 있다. 대표적인 방법으로 선형회귀분석, Mann-Kendall 경향성 분석 등이 있으나 기본적인 가정(assumption)의 제약으로 극치수문자료 계열의 특성을 효과적으로 분석하는데 무리가 있다. 대표적이고 일반적으로 적용되는 선형회귀분석의 경우 자료가 정규분포(normal distribution)의 특성을 가질 때 유효한 방법으로서 극치수문자료와 같이 Heavy Tail를 가지는 분포특성을 표현하는 데는 무리가 따른다. 이밖에도 기존 선형회귀분석을 극치수문자료에 적용할 경우 추정된 결과를 수자원설계의 관심사항인 빈도해석 등에 직접적으로 연계시켜 해석할 수 없는 단점이 있다. 이는 자료계열의 분포특성을 정규분포로 가정하기 때문에 발생하는 문제로서 극치수문자료계열의 분포 특성을 반영할 수 있는 방법론의 개발이 필요하다. 본 연구에서는 이러한 점을 개선하기 위해서 극치분포(extreme distribution)를 선형회귀분석에 적용하는 비정상성빈도해석(nonstationary frequency analysis) 방법론의 개념을 제시하고자 한다. 비정상성빈도해석을 위해서 Bayesian 기법이 도입되며 Bayesian 기법의 특성상 관련변수들이 사후분포(posterior distribution)로 귀결되기 때문에 경향성에 대한 정량적이고 확률적인 분석이 가능한 장점이 있다. 본 연구를 통해 개발된 방법론은 국내외 주요 강수지점에 대해서 적용되며 경향성, 분포특성, 빈도별 강수량에 대한 체계적인 분석이 이루어진다.