• 한국수학교육학회지시리즈A:수학교육
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• 제49권4호
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• pp.437-462
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• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• 대한수학회보
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• 제36권2호
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• pp.403-409
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• 1999

In this paper we introduce the notions of expansive homeomorphism and its properties, and study the relation between countable compacta and ordinal numbers. Our results extend and improve those of T.Kimura and others.

• 대한수학회지
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• 제59권1호
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• 대한수학교육학회지:학교수학
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• 제15권1호
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• pp.137-158
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• 2013

발도르프 교육은 최근 대안교육계를 통해 활발히 국내에 소개되고 있는 상황이다. 이 논문에서는 1-1학기에 지도되는 0~10까지의 지도를 중심으로 우리나라 공교육과 발도르프 교육의 지도를 비교하였다. 연구방법으로는 문헌과 자료 분석을 택하였으며, 이를 위해 우리나라 교과서와 발도르프 교육 관련 자료들을 비교하여 주된 특징들을 각각 추출하였다. 먼저 우리나라 수학교과서에 나타난 주된 특징으로, 0~9까지와 10의 분리 지도, 집합수와 순서수의 의미 지도, '1 큰(작은) 수'의 지도, '이야기'의 활용 등을 들 수 있다. 발도르프교육 자료에서 나타난 주된 특징으로는 질적인 측면에서의 수의 지도, 이야기 들려주기, 리듬으로 수 만나기, 전체성에서 부분성으로 나아가기 등을 추출하였다. 결론적으로, 위와 같은 차이를 일으키는 근본적인 기제는, 상대적으로 우리나라 공교육에서는 수학적 구조나 개념이 주요한 요소로 작동하고 있다면, 발도르프 교육에서는 특정 연령에 있는 아이들의 발달적 특성을 주된 요소로 고려하여 지도하는 데 있는 것으로 보인다.

• Communications for Statistical Applications and Methods
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• 제15권4호
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• pp.517-530
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• 2008

본 논문은 시간의 흐름에 따라 일정한 간격으로 관측된 시계열자료에 대한 통계적인 관계를 추정하기 위하여 삼각퍼지수를 이용한 퍼지시계열모형을 소개한다. 모든 관측치를 포함하는 전체집합을 분할하는 구간을 자료의 빈도수에 따라 결정하고 연속되는 두 시점에서 퍼지수가 일치하는 경우에는 관측된 자료의 차에 대한 정보를 이용하여 제안된 퍼지시계열모형을 추정한다. 예제를 이용하여 제안된 퍼지시계열모형의 정확성을 일반적인 시계열모형과 여러 가지 방법으로 추정된 퍼지시계열모형과 비교한다.

• 한국수학사학회지
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• 제12권1호
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• pp.32-44
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• 1999

This paper is a sequel to [8]. Development of modern logic was initiated by Boole and Morgan. Boolean logic is one of their completed works. Cantor created the set theory along with cardinal and ordinal numbers. His theory on infinite sets brought about a remarkable development on modern mathematical theory, but generated many paradoxes (e.g. Russell Paradox) that in turn motivated mathematicians to solve them. Further, mathematicians attempted to construct sound foundations for Mathematics. As a result three important schools of thought were formed in relation to fundamentals of mathematics for the resolution of paradoxes of set theory, namely logicism developed by Russell and Whitehead, intuitionism lead by Brouwer and formalism contended by Hilbert and Bernays. In this paper, we examine the logic for intuitionism which is originated by Brouwer in 1908 and study Heyting algebra.

• 한국문헌정보학회지
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• 제23권
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• pp.33-62
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• 1992

The purpose of this is to evaluate the contents through the anal us is of the merits and demerits, and its special quality of the Cutter-Sanborn Three-figure Author Table. table. The abstract of this study is as follows : With the results of the analysis of Cutter-Sanborn's Tabls, several advent-age were found in the area of enumerative-ordinal numbering system, mixed notation, and information retrieval. A defect is that each corporate author and serials and reference book's titles are difficult to be numbered, and there is serious diviation in percentages of the numbers assigned to each letter because each letter apportion rate was applied without any criteria. Such phenomenon decrease the effectiveness as author notation in several letters. The separation of headings are seriously unbalanced because the separation of heading is not consistent with actual publishing trends. This phenomenon made difficult individualization of materials in several letters.

• 대한간호학회지
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• 제52권2호
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• pp.144-156
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• 2022

Purpose: This study aimed to investigate the influence of social capital on the depression of older adults living in rural areas. Methods: Data sets were obtained from the 2019 Korea Community Health Survey. The participants were 39,390 older adults over 65 years old living in rural areas. Indicators of social capital included trust, reciprocity, network, and social participation. Depression-the dependent variable-was measured using the Patient Health Questionnaire-9 (PHQ-9). Hierarchical ordinal logistic regression was conducted to identify factors associated with depression after adjusting the data numbers to 102,601 by applying the Synthetic Minority Oversampling Technique (SMOTE). Results: The independent variables-indicators of social capital-exhibited significant association with the depression of older adults. The odds ratios of depression were higher in groups without social capital variables. Conclusion: To reduce depression, we recommend increasing social capital. Factors identified in this study need to be considered in older adult depression intervention programs and policies.