• 제목/요약/키워드: function concept

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Mathematical and Pedagogical Discussions of the Function Concept

  • Cha, In-Sook
    • 한국수학교육학회지시리즈D:수학교육연구
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    • v.3 no.1
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    • pp.35-56
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    • 1999
  • The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

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학교수학에서의 함수 개념 지도 방법에 관한 고찰 (A Study on the instruction of function concept in school mathematics)

  • 강윤수;정성현;강덕심
    • 대한수학교육학회지:수학교육학연구
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    • v.8 no.1
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    • pp.381-403
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    • 1998
  • As a researcher engaged in the mathematical education, mathematics teachers are interested in instructional methods. While it is unlikely that the viewpoints of individual mathematics teachers are reflected in making decisions on instructional purposes and instructional contents, a good many parts of instructional methods on mathematical facts are decided by individual teachers. This means that the role of mathematics teachers is given much weight in the mathematical education. Therefore, the mathematics teachers must not be excluded in all parts of the study of mathematical education. We studied the instructional methods of function concept, a central topic in school mathematics from the following perspectives. First, we examined the characteristics of the three(correspondence-centered, middle, dependence centered) viewpoints about the essence of function concept. And we should that which of them should be the viewpoint of instruction of function concept in school mathematics. Second, we investigated the questions regarding the process of function instruction in school mathematics and presented alternative instruction methods of function concept to solve the questions. Third, we postulated the importance of polynomial function, relating college mathematics in order to present the reason why the polynomial function is importantly treated in functional instruction of school mathematics.

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함수 개념의 현상학 (Phenomenology of the concept of functions)

  • 유윤재
    • 한국수학사학회지
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    • v.23 no.3
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    • pp.75-90
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    • 2010
  • 함수 개념을 실제로 사용되고 있는 측면에서 분석하면 인과, 명명, 연산, 변화, 도형, 형태, 변수, 범함수, 작용소 등 적어도 9가지의 양상이 존재한다. 이러한 분석을 통하여 함수 개념은 현재 3단계로 성장해 왔다는 것이 밝혀졌다.

우리 나라 제 7 차 수학과 교육과정의 7-가 단계 내용 중 함수 부분에 관한 비판적 고찰 (A Critical Contemplation on the Contents of Function in 7-first Stage of the 7th Mathematics Curriculum in Korea)

  • 박교식
    • 대한수학교육학회지:학교수학
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    • v.1 no.2
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    • pp.401-415
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    • 1999
  • In this paper, 'relations of proportion are used in the introduction of function concept' in 7-first stage of 7th mathematics curriculum is focused. Under the assumption that above statement means dependence-centered view in the teaching of function, the contents of function In 7-first stage is interpreted. Some issues are critically contemplated, And, finally, statement of using relations of proportion in the introduction of function concept is interpreted as dependence-centered view in the teaching of function. Conclusions are as follows: (1) symbol y= f(x) is not inevitable. (2) Term 'codomain' must not be used. (3) Term 'range of x' and 'range of y' must be used. (4) Term 'independent variable' and 'dependent variable' must be used.

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관계적 이해를 위한 수업 도구로서의 소프트웨어 활용에 관한 사례 연구 - 고등학교 1학년 함수 단원을 중심으로 - (Using computer software as an instructional tool for enhancing relational understanding of function concept : three case studies)

  • 최윤녕;권오남;황혜정
    • 대한수학교육학회지:학교수학
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    • v.1 no.2
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    • pp.637-660
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    • 1999
  • Although ‘to understand mathematics’ is an important educational purpose, most student do not have a relational understanding of the basic concept of mathematics but have a instrumental understanding. This paper will investigate the possibility of using computers for enhancing relational understanding. In the ‘Qualitative case study’, three students who are in the first grade at E-High school took part in 7 activities during four weeks, and were later interviewed and engaged in informal discussion and were observed. This is the result of this study. 1. The three students were passive participants in mathematics problem solving situation at school. Therefore, student B just applied formulas which she had memorized, and student C would forgot the formulas occasionally. These common students needed to participate actively in doing mathematics. 2. The activities utilized two software healing with connection between graphs and function, giving the students the opportunity to plan, practice, and test by themselves. As a result, they understood the mathematical formulas and rules more deeply through their own trial and error, and then they gained thinking abilities necessary for doing mathematics. In addition, the activities boosted their confidence. 3. The understanding type of students was slightly different. Student A who received a high score, understood the most relationally, but student B who received a very high score, understood instrumentally and so couldn't app1y her knowledge to solving problems related to function concept. Student C who received a middle score lacked knowledge of mathematics but thought more creatively. The result is that students need an opportunity to think rotationally regardless of score. Therefore, this study concludes that using computer software will provide a positive effect for relational understanding in loaming function concept.

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함수개념의 교수.학습과정에서 나타난 subject-matter knowledge와 pedagogical content knowledge 능력의 발전에 관한 연구 (The Development of Subject-matter Knowledge and Pedagogical Content Knowledge in Function Instruction)

  • 윤석임
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • v.21 no.4
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    • pp.575-596
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    • 2007
  • 본 논문은 예비교사들이 함수교육과 관련된 subjective-matter knowledge와 pedagogical content knowledge를 어떻게 효율적으로 의미있게 학습하고 발전시키는 가에 대하여 조사하였다. 함수의 기본개념과 원칙, 그리고 그들이 어떻게 조직되었는지를 이해하는 능력과 의미있는 함수학습이 가능하도록 그들을 표현하고 구성하는 능력을 증진시키기 위하여 본 연구에서는 구성주의와 협동학습에 기반 한 학습방법을 채택하였다. 사전, 사후테스트와 인터뷰를 통하여 평가한 결과 소그룹 구성원들과의 상호작용 결과를 전체 구성원과의 토론을 통하여 학습하는 과정에서 보다 깊이 있고 확장된 subject-matter knowledge와 다양한 pedagogical content knowledge를 획득하게 되는 결과를 얻게 되었다.

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공과대학 신입생들의 함수개념 연구와 함수 영역의 교육과정에 대한 제안 (The Function Concept in Korean Engineering Freshmen and Some Suggestions on the Curriculum in the Function Area)

  • 김연미
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • v.22 no.4
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    • pp.417-444
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    • 2008
  • 본 논문에서는 세 가지 관련된 분야의 연구를 통하여 우리나 대학 신입생들의 함수 개념을 조사하였다. 대학 신입생들은 함수를 어떻게 이해하고 있는가?; 인식론적 장애를 포함한 오 개념에는 어떤 것들이 있는가?; 함수 개념은 어떤 경로를 거쳐서 획득되는가? 등이다. 이와 함께 대학의 여러 분야에서 함수가 어떻게 정의되고 쓰이는지를 살펴보고, 미국의 교과서들에 나타난 함수 정의와 도입을 살펴보았다. 설문조사와 이들을 토대로 함수를 대응의 관점에서 도입하는 새로운 교육과정에 대하여 수직선 테스트의 도입을 포함한 몇 가지 제언을 하였다.

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함수 개념의 역사적 발달과 인식론적 장애 (Historical Development and Epistemological Obstacles on the Function Concepts)

  • 이종희
    • 대한수학교육학회지:수학교육학연구
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    • v.9 no.1
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    • pp.133-150
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    • 1999
  • In this study, we tried to make histo-genetic analyses necessary to identify epistemological obstacles on the function concepts. Historical development on the function concept was analysed. From these analyses, we obtain epistemological obstacles as follows: the perception of changes in the surrounding world, mathematical philosophy, number concepts, variable concepts, relationships between independent variables and dependent variables, concepts of definitions.

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품질손실을 고려한 경제적 CUSUM 관리도 (A Design of Economic CUSUM Control Chart Incorporating Quality Loss Function)

  • 김정대
    • 산업경영시스템학회지
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    • v.41 no.4
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    • pp.203-212
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    • 2018
  • Quality requirements of manufactured products or parts are given in the form of specification limits on the quality characteristics of individual units. If a product is to meet the customer's fitness for use criteria, it should be produced by a process which is stable or repeatable. In other words, it must be capable of operating with little variability around the target value or nominal value of the product's quality characteristic. In order to maintain and improve product quality, we need to apply statistical process control techniques such as histogram, check sheet, Pareto chart, cause and effect diagram, or control charts. Among those techniques, the most important one is control charting. The cumulative sum (CUSUM) control charts have been used in statistical process control (SPC) in industries for monitoring process shifts and supporting online measurement. The objective of this research is to apply Taguchi's quality loss function concept to cost based CUSUM control chart design. In this study, a modified quality loss function was developed to reflect quality loss situation where general quadratic loss curve is not appropriate. This research also provided a methodology for the design of CUSUM charts using Taguchi quality loss function concept based on the minimum cost per hour criterion. The new model differs from previous models in that the model assumes that quality loss is incurred even in the incontrol period. This model was compared with other cost based CUSUM models by Wu and Goel, According to numerical sensitivity analysis, the proposed model results in longer average run length in in-control period compared to the other two models.

Space Identity를 위한 기업 상업공간 파사드 디자인 연구 (The Design Research on Facade in Corporate Commercial Space Identity)

  • 황보현욱
    • 디자인학연구
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    • v.19 no.1
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    • pp.39-48
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    • 2006
  • 현재 마케팅 환경은 과거의 가격 위주 전략의 제품판매 시대를 지나 상품, 기업, 브랜드 이미지를 통한 감성마케팅 시대로 접어들었다. 특히 고객의 직접 대면 장소인 기업 상업 공간 Space Identity는 직접 체험, 감각적 자극, 즉시 만족, 사회적 관계 형성을 할 수 있는 중요한 전략 요소임에도 불구하고 대부분의 국내 기업이 CI 기본 시각 시스템을 그대로 대입하는 2차원적 디자인 고려에만 머무르고 있으며 상업공간의 다양한 기능성, 컨셉, 상품과 고객 만족에 대한 고려는 부족한 것이 현실이다. 특히 공간과 고객의 최초 대면 접점인 파사드는 시각적 정보전달, 물리적 경계 역할과 더불어 내외부 공간의 연결성을 통해 공간의 컨셉과 기업과 상품 이미지, 정보 전달 및 고객 유입 정도를 결정하는 중요한 요소이다. 본 연구는 판매, 서비스, 홍보 등이 중심이 된 기업의 상업공간 파사드를 통해 상업 공간 전반에 적용된 Space Identity 적용 사례를 조사하여 상업 공간의 기능에 따른 상품, 고객 유입을 위한 이론 연구 바탕을 마련하고, 이론적 배경과 사례에서 지적된 문제점 개선을 위한 발전된 디자인을 위한 제안을 한다.

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