• Title/Summary/Keyword: function concept

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Mathematical and Pedagogical Discussions of the Function Concept

  • Cha, In-Sook
    • Research in Mathematical Education
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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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A Study on the instruction of function concept in school mathematics (학교수학에서의 함수 개념 지도 방법에 관한 고찰)

  • 강윤수;정성현;강덕심
    • Journal of Educational Research in Mathematics
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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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Phenomenology of the concept of functions (함수 개념의 현상학)

  • Yoo, Yoon-Jae
    • Journal for History of Mathematics
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    • v.23 no.3
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    • pp.75-90
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    • 2010
  • In this paper function concept is classified in the phenomenological aspect. According to the study, function concept is classified as causality, designation, operation, change, figure, morhism, variables, functional, and operator. This classifications are categorized as pre-level function, basic level function, and upper level function.

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

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

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

  • Yoon, Suk-Im
    • Communications of Mathematical Education
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    • v.21 no.4
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    • pp.575-596
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    • 2007
  • This study investigates preservice teachers' development of subject-matter knowledge and pedagogical content knowledge in teaching function concept. This development takes place in the pedagogical mathematics courses in which the theory of constructivism and cooperative learning theory are aligned. Pre and post courses test were administered to examine the development and the follow-up interviews were conducted to gain more details. Analysis of the written questionnaire results and interview transcripts reveal that their limited concept image can be extended and developed in depth through pedagogical mathematics courses that apply reformed teaching methods.

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

  • Kim, Yeon-Mi
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.417-444
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    • 2008
  • Many research papers on the college students' functional concept show they have poor understanding on this topic. To compare the results with that of Korean students, four interrelated topics are chosen: How do they understand the concept of function?; what are their misconceptions including epistemological obstacles?; How do the function concepts develop and are acquired? For this a survey has been conducted to 95 engineering students just before they start Calculus course. We have done research on other major areas including psychology, economics and statistics to see how function is defined in these areas. Function definitions from US math text books are also introduced. Based on the these and the survey, some suggestions are made on the new curriculum which treat function as a correspondence relation. Vertical line test should be added to the Algebra II/Pre calculus course to check the univalent property.

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

  • 이종희
    • Journal of Educational Research in Mathematics
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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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A Design of Economic CUSUM Control Chart Incorporating Quality Loss Function (품질손실을 고려한 경제적 CUSUM 관리도)

  • Kim, Jungdae
    • Journal of the Society of Korea Industrial and Systems Engineering
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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.

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

  • HwangBo, Hyun-Wook
    • Archives of design research
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    • v.19 no.1
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    • pp.39-48
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    • 2006
  • In recent marketing circumstances we passed the days just dealt with products sales and faced Sensitivity Marketing era concluded by merchandise, corporate and brand image. Especially although corporate commercial space is the important strategy factor performing immediate satisfaction, experience,sensitive stimulation and social relationship among customers, most of the domestic firms don't recognize its importance when looking into adopted graphic factors at spaces without consideration for a variety of space function, concept,merchandise and customer satisfaction. In addition the facade, which performs as visual information conveyance, boundaries of architecture and concluding space concept, merchandise image and incoming customer based on linkage between interior and exterior, is the important point. This research specializing the examples of facade design of corporate and brand commercial space including service, purchasing and advertising looks into reflected space identity through facade and theoretical factors for commercial space function, concept, merchandise and customers related facade design and makes alternative plans in order to make a better commercial space identity program.

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