• School Mathematics
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• v.18 no.3
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• pp.441-455
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• 2016

The position as saying that the math learning needs to begin from what diversely presents concrete object or familiar situation is well known as a name dubbed CSA(Concrete-Semiconcrete-Abstract). Compared to this, a recent research by Kaminski, et al. asserts that learning an abstract concept first may be more effective in the aspect of knowledge transfer than learning a mathematical concept with concrete object of having various contexts. The purpose of this study was to analyze a class, which differently applied a guidance sequence of concrete object, semi-concrete object, and abstract concept in consideration of this conflicting perspective, and to confirm its educational implication. As a result of research, a class with the application of a concept starting from the concrete object showed what made it have positive attitude toward mathematics, but wasn't continued its effect, and didn't indicate significant difference even in achievement. Even a case of showing error was observed rather owing to the excessive concreteness that the concrete object has. This error wasn't found in a class that adopted a concept as semi-concrete object. This suggests that the semi-concrete object, which was thought a non-essential element, can be efficiently used in learning an abstract concept.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.547-563
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• 2005

There have been many papers reporting that the axiomatic approach in Abstract Algebra is a big obstacle to overcome for the students who are not trained to think in an abstract way. Therefore an instructor must seek for ways to help students grasp mathematical concepts in Abstract Algebra and select the ones suitable for students. Mathematics faculty and students generally consider Abstract Algebra in general and quotient groups in particular to be one of the most troublesome undergraduate subjects. For, an individual's knowledge of the concept of group should include an understanding of various mathematical properties and constructions including groups consisting of undefined elements and a binary operation satisfying the axioms. Even if one begins with a very concrete group, the transition from the group to one of its quotient changes the nature of the elements and forces a student to deal with elements that are undefined. In fact, we also have found through running abstract algebra courses for several years that students have considerable difficulty in understanding the concept of quotient groups. Based on the above observation, we explore and analyze the nature of students' knowledge about $Z_n$ that is the set of congruence classes modulo n. Applying the genetic decomposition method, we propose a model to lead students to achieve the correct concept of $Z_n$.

• Journal of Korean Medical classics
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• v.26 no.4
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• pp.43-70
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• 2013

Objective : analysis of words related with medical concept and context of paragraphs in Suwen of Huang Di Nei Jing based on concreteness and ideality. Method : First, I extract words having medical concept out of the whole sentence of Huang Di Nei Jing. and classifies them according to the type of medical concept. Second, I classify all sentence of it on the basis of analysing of the words. Result : 1. There are not an interrelationship between the abstract and concrete words from the perspective of cause and effect. Abstract words group are divided into two different parts according to the fundamental character. There are the concept being formed from pure idea and the concept being formed from material idea. The main words composed most important part of the oriental medicine have a combination mode with these two word groups. 2. We have several data about concreteness and ideality of Huang Di Nei Jing. Subjects and contents in provisions are concrete relatively. But the logical basis of sentences is remarkably ideational. Many kinds of abstract words are used dominantly to compose logics of these basis. It confirms that concrete words can not be used to make theories and concepts in Suwen. Conclusion : I analyzed words related with medical concept and context of paragraphs in Suwen of Huang Di Nei Jing based on concreteness and ideality and I found that the concept and logical system of Huang Di Nei Jing in the objective point of view.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.599-620
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• 2005

There can be two different approaches to introducing Abstract Algebra to undergraduate students: One is to introduce group concept prior to ring concept, and the other is to do the other way around. Although the former is almost conventional, it is worth while to take the latter into consideration in the viewpoint that students are already familiar to rings of integers and polynomials. In this paper, we investigated 16 most commonly used Abstract Algebra undergraduate textbooks and found that 5 of them introduce ring theory prior to group theory while the rest do the other way around. In addition, we interviewed several undergraduate students who already have taken an Abstract Algebra course to look into which approach they prefer. Then we compare pros and cons of two approaches on the basis of the results of the interview and the historico-genetic principle of teaching and learning in Abstract Algebra and suggest that it certainly be one of alternatives to introduce ring theory before group theory in its standpoint.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.41-47
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• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• Research in Mathematical Education
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• v.25 no.3
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• pp.227-244
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• 2022

The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

• Journal of the Korean Institute of Landscape Architecture
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• v.36 no.6
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• pp.1-11
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• 2009

This study focuses on Abstract Types in Contemporary Landscape Design. The formation and artistry of contemporary landscape design reveals many areas which Previously have not been able to be expressed in scenic landscape thanks to the deviation of the genre in contemporary landscape and the hybridization that has occurred among architecture, landscape and art genres. The focus of this study is basic research concerning "the abstract", which is used as a creative artistic theory in a variety of art fields such as landscape, architecture and painting. Through a theoretical establishment of "the abstract", its process of change, and the discovery of its contemporary principles, the relationship between each art field in landscapes and the formation of the abstract, abstract language, and abstract properties have been studied. The use of the abstract in contemporary landscape design can be classified in three ways: Inductive abstract representing conceptual transcendental symbols not logically but rather through intuition and transcendental cognition to display the inner expressions, ideas and minds of the artists. Second, a deductive abstract represents an expansive, logical model for the simplification of objects, distortion, exaggeration based on knowledge and logical reasoning about objective fact based on traditional realism. The complexity of the abstract is a concept that is bound to both the deductive & inductive abstract. As a major trend, the concept of "The abstract" in contemporary landscape has been putting forth ever-deeper roots. New trends like abstract works and landscape architecture reflecting the artist's inner expression, in particular, will provide fertile soil for landscape in the future. Further research about the concept of "the abstract" will also be necessary in the time to come.

• 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.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.10a
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• pp.11-18
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• 2000

No Abstract.See Full-text

• Bulletin of the Korean Space Science Society
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• 1994.04a
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• pp.30-30
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• 1994

No Abstract. See Full-text