• Journal of Educational Research in Mathematics
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• v.11 no.2
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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.

• School Mathematics
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• v.4 no.2
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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.

• Journal of the Korean Institute of Rural Architecture
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• v.5 no.3
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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.

• Korean Journal of Construction Engineering and Management
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• v.7 no.3 s.31
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• pp.102-111
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• 2006

In the analysis of function, which is the core and early phase among the procedure of construction VE Job Plan, the accuracy of function definition directly connects to VE result. However, the method of defining function, which is currently used is not accurate and comprehended or is difficult to utilize it systematically. Also, there is not a clear definition about the function for selecting VE so that many difficulties occur in the organic connection between each of functions in the summarization of function after defining function. Therefore, this study cleared the definition of function and made up any counter measured problem occurred in FAST Diagram later on and suggested CAFAT(Combined Antithetic Function Analysis Technique) in order to induce better phase in functional analysis.

• East Asian mathematical journal
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• v.35 no.2
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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.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.375-389
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• 2017

The purpose of this study is to analyze the difference and inter-connectivity between the definition of continuity in school mathematics and the definition of academic mathematics in four perspectives. These difference and inter-connectivity have not analyzed in previous papers. According to this study, the definition of 'continuity and discontinuity at one point' in school mathematics depends on the limit processing but in academic mathematics it depends on the topology of the domain. The target function of the continuous function in school mathematics is a function whose domain is limited to an interval or a union of intervals, but the target function of the continuous function in academic mathematics is all functions. Based on these results, the following two opinions are given in relation to the concept of continuity in school mathematics. First, since the notion of local continuity in school mathematics is based on limit processing, the contents of 2009-revised textbooks that deal with discontinuity at special point not belonging to the domain is appropriate. Here the discontinuity appears as types of infinite discontinuity, removable discontinuity, and step discontinuity. Second, the definition of a general continuous function is proposed to "if there is no discontinuity point in the domain of a function y = f(x), we call the function f a continuous function." This definition allows the discontinuity at special point in non-domain, but is consistent with the definition in academic mathematics.

• East Asian mathematical journal
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• v.39 no.2
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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.

• Proceedings of the Korean Institute Of Construction Engineering and Management
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• 2007.11a
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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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.