• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• 대한수학교육학회지:학교수학
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• 제4권2호
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• pp.247-260
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• 2002

In recent elementary school mathematics a word 'stipulation' newly appears. The word is used instead of definition. However, there seems to be some differences between definition and stipulation. So, in this paper we investigate those differences through the concept 'function of definition'. In school mathematics textbooks there are definitions which carry out special functions In mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. Functions of definition are classified as, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in recent elementary school mathematics textbooks. As a result of analysing functions of definition we found that generally speaking, stipulation-function is excessively emphasized and the other functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding and the mathematics teachers should be aware of the functions of definitions. Finally, we comment that textbook author, teacher, and researcher should be careful in using the word 'stipulation' instead of definition, because, although there are various functions of definitions, students might ream only stipulation-function.

• 한국농촌건축학회논문집
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• 제5권3호
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• pp.34-43
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• 2003

This study attempts to understanding of outer space elements in a rural house through an analysis nouns for function definition phase in design value engineering. To choose main check objects, this study examines requests by rural dwellers and analyze function definition in design value engineering. The rural dwellers prefers that barrier free design, outdoor working space and security of calamity. Each selected elements are classified the nouns into a main noun by analysis function definition nouns at design VE phase. The nouns are reclassified into the main nouns as a distance, a space, and a form.

• 한국건설관리학회논문집
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• 제7권3호
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• pp.102-111
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• 2006

건설 VE Job plan의 진행단계 중 초기 단계인 기능분석에서 핵심이라 할 수 있는 기능정의의 정확성은 VE 성과와 직결된다. 그러나 현재 사용되고 있는 기능정의의 방법은 정확한 정의와 이해가 이루어지지 않거나 활용방법에 어려움이 따라 체계적으로 수행하지 못하는 경우가 많으며 VE 대상 선정에 있어 기능에 대한 정의가 명확하게 이루어지지 않아 기능정의 후 기능정리 단계에서 각 기능들간의 유기적 연결에 어려움이 발생하는 경우가 많다. 이에 본 연구에서는 기능정의를 보다 명확하게 하여 차후 기능정리에서 발생하는 문제점을 보완하여 보다 나은 기능분석 단계를 유도할 수 있도록 하기 위한 CAFAT(Combined Antithetic Function Analysis Technique)을 제안하고자 한다.

• East Asian mathematical journal
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• 제35권2호
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• 대한수학교육학회지:수학교육학연구
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• 제27권3호
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• pp.375-389
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• 2017

본 연구에서는 연속성 개념에 대한 학교수학에서의 정의와 학문수학에서의 정의 사이의 차별성과 상호연결성을 네 가지 관점에서 분석하고 있다. 이에 따르면, '한 점에서의 연속 불연속'의 정의가 학교수학에서는 극한 과정에 의존하고 있고, 학문수학에서는 정의역의 위상에 의존하고 있다. 학교수학에서는 정의역이 하나의 구간이나 구간들의 합집합인 함수에 한하여 연속함수인가를 판정할 수 있으나, 학문수학에서는 어떠한 함수에 대해서도 연속함수인가를 판정할 수 있다. 본 연구에서는 이러한 결과에 근거하여, 학교수학에서의 연속성 개념 취급과 관련하여 다음 두 가지 의견을 제시한다. 첫째, 극한 과정을 기반으로 한 학교수학에서의 국소적 연속성 개념으로 볼 때, 2009 개정 교과서에서 함수의 정의역에 속하지 않는 특정한 점에서 불연속을 취급하는 것은 적절하다. 이때 불연속점으로 무한 불연속점, 제거 가능한 불연속점과 도약 불연속점의 유형이 나타난다. 둘째, 일반적인 연속함수의 정의로 "함수 y = f(x)에서 정의역에 불연속점이 없으면, f을 연속함수라 한다."를 제안한다. 이 정의는 정의역에 속하지 않은 점에서의 불연속성의 판정을 허용하면서, 학문수학에서의 정의와 일관되게 연결된다.

• East Asian mathematical journal
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• 제39권2호
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• pp.119-139
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• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• 한국건설관리학회:학술대회논문집
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• 한국건설관리학회 2007년도 정기학술발표대회 논문집
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• pp.151-156
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• 2007

2006년부터 VE 대상프로젝트가 확대되고, 기본설계와 실시설계단계에 각 1회씩 설계VE를 적용토록 규정되어 설계단계별로 VE가 각각 적용되는 프로젝트가 늘어나고 있다. 그리고 원가절감과 성능향상으로 프로젝트 가치를 높인 설계VE 사례도 많아지고 있다. 하지만 기본설계와 실시설계단계의 조건에 적합한 VE 수행방안에 대한 연구가 미진하고 참여자들의 경험과 이해가 부족하여 단계별 설계VE를 효율적으로 수행하는데 많은 어려움이 있다. 본 연구에서는 기본설계단계와 실시설계단계로 나누어 VE를 수행한 실무사례를 분석하여 기능정의와 아이디어 창출간의 연관관계 및 각 설계단계에서 기능정의를 수행할 때 발생하는 문제점을 도출하였다. 문제점을 해결하고 효과적인 설계VE를 수행하기 위하여 다음과 같은 개선방안을 제시하였다. 첫째, 설계프로세스의 흐름에 맞추어 기본설계에는 공간기능에 대하여하고 실시설계에는 부위에 대하여 기능정의를 수행한다. 이때 상위의 레벨에는 하위의 레벨의 기능정의가 연계되는 기능분류체계 (FBS : Function Breakdown Structure)를 제안하였다. 둘째, 기본설계와 실시설계단계의 기능정의를 수행하는 프로세스 (FDP : Function Definition Process)를 제안하였다. 셋째, 실시설계단계에서는 부위별 요구 성능 평가 매트릭스 (EFM : Element Function Matrix)를 적용하여 기능정의와 아이디어 창출이 연계되도록 하였다. 설계VE의 주요 부분인 기능정의 과정에 대한 문제점을 도출하여 해결방안을 제시함으로써, 보다 효과적인 설계VE의 수행을 기대할 수 있다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.349-352
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• 2004

In this literature, the selection of data set among the universe set is carried out with the fuzzy entropy function. By the definition of fuzzy entropy, we have proposed the fuzzy entropy function and the proposed fuzzy entropy function is proved through the definition. The proposed fuzzy entropy function calculate the certainty or uncertainty value of data set, hence we can choose the data set that satisfying certain bound or reference. Therefore the reliable data set can be obtained by the proposed fuzzy entropy function. With the simple example we verify that the proposed fuzzy entropy function select reliable data set.

• 한국지능시스템학회논문지
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• 제14권5호
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• pp.655-659
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• 2004

In this literature, the selection of data set among the universe set is carried out with the fuzzy entropy function. By the definition of fuzzy entropy, the fuzzy entropy function is proposed and the proposed fuzzy entropy function is proved through the definition. The proposed fuzzy entropy function calculate the certainty or uncertainty value of data set, hence we can choose the data set that satisfying certain bound or reference. Therefore the reliable data set can be obtained by the proposed fuzzy entropy function. With the simple example we verify that the proposed fuzzy entropy function select reliable data set.