• Title/Summary/Keyword: concept definition

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A Study on Teaching and Learning of the Limit Concept in High School (고등학교에서의 극한개념 교수.학습에 관한 연구)

  • 박임숙;김흥기
    • Journal of Educational Research in Mathematics
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    • v.12 no.4
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    • pp.557-579
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    • 2002
  • The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

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A study on understanding of continuity concept of function (함수의 연속 개념 이해에 대한 연구)

  • Oh, Hye-Young
    • 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.

An Analysis and Criticism on the Definition of the Similarity Concept in Mathematical Texts by Investigating Mathematical History (수학사 고찰을 통한 교과서의 닮음 정의에 대한 분석과 비판)

  • Choi, Ji-Sun
    • Journal of Educational Research in Mathematics
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    • v.20 no.4
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    • pp.529-546
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    • 2010
  • This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

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A Study on the Definition of a Circumcenter and an Incenter of Triangle (삼각형의 외심, 내심의 정의에 관한 고찰)

  • Jun, Young-Bae;Kang, Jeong-Gi;Roh, Eun-Hwan
    • Journal of the Korean School Mathematics Society
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    • v.14 no.3
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    • pp.355-375
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    • 2011
  • This paper was designed for the purpose of helping the functional comprehension on the concept of a circumcenter and an incenter of triangle and offering the help for teaching-learning process on their definitions. We analysed the characteristic of the definition on a circumcenter and an incenter of triangle and studied the context, mean and purpose on the definition. The definition focusing on the construction is the definition stressed on the consistency of the concept through the fact that it is possible to draw figure of the concept. And this definition is the thing that consider the extend of the concept from triangle to polygon. Meanwhile this definition can be confused because the concept is not connected with the terminology. The definition focusing on the meaning is easy to memorize the concept because the concept is connected with the terminology but is difficult to search for the concept truth. And this definition is the thing that has the grounds on the occurrence but is taught in a made-knowledge. The definition focusing on both the construction and meaning is the definition that the starting point is vague in the logical proof process. We hope that the results are used to improve the understanding the concept of a circumcenter and an incenter of triangle in the field of mathematical education.

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Independence in probability, The conflicts between its intuitive concept and formal definition (확률 영역에서의 독립성, 그 직관적 개념과 형식적 정의의 갈등)

  • Cho, Cha-Mi;Park, Jong-Youll
    • The Mathematical Education
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    • v.47 no.3
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    • pp.373-386
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    • 2008
  • In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.

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An analysis on concept definition and concept image on quadrangle of middle and high school students (중·고등학생의 사각형에 대한 개념 정의 이해와 개념 이미지 분석)

  • Chang, Hyun Suk;Kim, Myung Chang;Lee, Bongju
    • The Mathematical Education
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    • v.61 no.2
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    • pp.323-338
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    • 2022
  • The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9th graders and 65 10th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.

A study on the Problems and Improvement Proposals on Legal Definitions in Regards to Herbs, Herbal Drugs, Crude Drugs and Natural Products (한약, 한약재, 생약과 천연물의 법규상 개념 및 정의의 문제점과 개선안)

  • Eom, Seok-Ki
    • Journal of Korean Medical classics
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    • v.27 no.2
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    • pp.77-95
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    • 2014
  • Objectives : This study was to analyze the definitions of herbs, herbal drugs, crude drugs and natural products in the relevant laws and regulations, understand the related problems, and propose directions for improvement. Methods : I analyzed the legal definitions in respect of herbs, herbal drugs, crude drugs and natural products in relevant laws and regulations since 1945, explained the problems, and suggested the solution-considering the academic stance of Traditional Korean Medicine and the dualistic medical and pharmaceutical system. Results : Herbs are defined as "refined things that are cut and dried in their most original state". The definition of crude drugs includes herbs and the "cell contents, secretion, extracts, minerals and other parts of animals and plants that are used medicinally". The concept of natural products is expanded to adding tissue cultures to the definition of crude drugs. Conclusions : The definition of herbs should at least include all products that are "processed, extracted and prepared" as well as contents that consist of various forms of hospital-prepared herbs. The term "herbal drug" corresponds to a traditional term of "drug", and this should be established as a concept to explain "drugs in raw materials that are used to prepare herbs and/or manufacture herbal medicine". The legal definition of herbs should include the concept of crude drugs. Herbal drug preparations and crude drugs should be included in the definition of herbal drugs.

Researches on Fire in Traditional Chinese Medicine (중의학(中医学) "화(火)" 더변석(的辨析))

  • Li, Hai-Yu;Pan, Gui-Juan
    • Journal of Korean Medical classics
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    • v.22 no.4
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    • pp.255-259
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    • 2009
  • The origin of "Fire" in Traditional Chinese Medicine is summed up based on observation and knowledge of natural fire, followed by abstract thinking, of which the outcomes are best symbolized in the character Fire[火]. Because it is an abstract concept, it is hard to give a single and strict definition. Naturally, it would be necessary to analyze and illustrate the origin of 'Fire' from different angles such as broad definition, multi-definition, levels, classifications and effects. The concept of 'Fire' has four meanings in the aspect of the broad definition: first, natural fire; second, the physiological conception of fire; third, the medical conception of fire; fourth, general concept related to fire. In Traditional Chinese Medicine, fire mainly indicates physiologic fire, pathological fire, the fire in the six kinds of natural climate and the fire as one of the properties and the flavors of herbs.

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System Requirement Definition Process from Operational Concept and The Application Case-Study of ATACMS (운용 개념에서 시스템 요구사항을 정의하는 프로세스의 개발 및 특정 유도무기(ATACMS) 적용 사례)

  • 이중윤;박영원
    • Journal of the Korea Institute of Military Science and Technology
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    • v.6 no.3
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    • pp.22-35
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    • 2003
  • This paper describes system technical requirement development process from operational concept using computer-aided Systems Engineering tool(CASysE Tool-CORE). The army tactical missile system-ATACMS's technical requirements are developed by the process as a case-study The scope of the work is context analysis and requirement definition process. The proposed process is as follows. At first, an integrated architecture could be developed from the operational concept. From the integrated architecture a capability needs, which includes KPPs, are generated. And the capability needs expanded according to the Mil-Std-961D format. Lastly, a system technical requirement could be generated automatically from the CASysE Tool-CORE.

High School Textbook Definition and Students' Understanding of Continuity of Functions (연속함수에 대한 고등학교 교과서의 정의와 고등학생들의 이해)

  • Park, Dal-Won;Hong, Soon-Sang;Shin, Min-Young
    • Journal of the Korean School Mathematics Society
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    • v.15 no.3
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    • pp.453-465
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    • 2012
  • In this paper, we first analysis definition of continuity of functions in high school textbooks, the mathematics high school curriculum and university mathematics textbooks. We surveyed what was causing the students to struggle in their concept image of continuity of functions. We arrived at that students' concept for errors in images of continuity of function were caused by definition of continuity of functions in high school textbooks.

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