• 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.

• Journal of The Korean Association of Information Education
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• v.12 no.4
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• pp.395-404
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• 2008

The shape learning of elementary mathematics should required a variety of activities to help student based on intuitive understanding. Learning three-dimensional shapes, it is effectively take advantage of actual object, but difficult to check a development figure or various forms of actual object, it is effectively utilizing computers semi-actual object. In addition, the computer to take advantage of even after school resources, the limits of learning something concrete to take advantage complement. This research developed the three-dimensional shapes application of elementary students shape learning to use of Flex and Flash. This application to take advantage of the free observation and causing an interesting and effective learning.

• School Mathematics
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• v.18 no.1
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• pp.159-173
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• 2016

In real educational field, there are cases that concrete problematic situations are introduced after abstract concepts are taught on the contrary to process that abstract from concrete contexts. In other words, there are cases that abstract knowledge has to be concreted. Freudenthal expresses this situation to antidogmatical inversion and indicates negative opinion. However, it is open to doubt that every class situation can proceed to abstract that begins from concrete situations or concrete materials. This study has done a comparative analysis in difference of mathematical thinking between a process that builds abstract context after being abstracted from concrete materials and that concretes abstract concepts to concrete situations and attempts to examine educational implication. For this, this study analyzed the mathematical thinking in the abstract process of concrete materials by manipulating AiC analysis tools. Based on the AiC analysis tools, this study analyzed mathematical thinking in the concrete process of abstract concept by using the way this researcher came up with. This study results that these two processes have opposite learning flow each other and significant mathematical thinking can be induced from concrete process of abstract knowledge as well as abstraction of concrete materials.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.99-120
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• 2001

The purpose of this thesis is to find the guiding direction of mathematical communication in lower grade students of elementary school and to present a new direction about the effect of using concrete material in communication. It is expected that mathematical communication increases when concrete material is used for the students of the lower grades, who are in concrete operational period. Therefore, this study ai s to investigate what characteristics there are in mathematical communication of second grade students and what effect concrete materials have on mathematical communication and learning. The analysis of the teaching record shows that the second grade students use alternative terms in the process of communication since they are not familiar with mathematical symbols or terms, which is a characteristic of communication in a mathematics class in which concrete material is used. In the process of teaming the students apply their living experiences to their teaming. Since a small number of students lead class, the interaction between students is also led by them. The direction of communication in a small group is not centered around solution of a problem, and most students show a more interest in finding answers than in the process of learning. The effect that concrete material has on communication plays an important role in promoting students' speaking activity; it allows students to identify and correct their errors more easily. It also makes students' activities more predictable, and it increases a small group activities through the medium of concrete material. However, it was also noticed that students' listening activities are not appropriately developed since they do not pay attention to a teacher who uses concrete material. The effects that concrete material has on mathematics class can be summarized as follows. Concrete material promotes students' participation in class by triggering their interest of learning of mathematics and helps them to understand the course of learning. It also helps the teaming and formation of concepts for children of low academic performance. And it makes a phased learning possible according to students' ability to use concrete material and to solve a problem. Based upon the results above mentioned, the use of concrete material is absolutely needed in mathematics classes of lower grade elementary school students since it increases communication and gives much influence on mathematics learning. Therefore, teachers need to develop teaching or learning method which can help increase communication, considering the characteristics of students' communication.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.11b
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• pp.716-719
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• 2002

이 연구의 목적은 근래에 초등학교 수학과 교육과정의 도형영역에 새로이 도입된 '공간감각'을 기르기 위한 웹 코스웨어를 개발하여 단순히 교과서에만 제시된 구체물 조작만으로는 기르기 힘든 공간감각을 기르는데 있다. 개발된 코스웨어는 학습내용을 수준별로 구성하고 있어 바로 학습 현장에 투입하여 수준별 학습, 개별화 학습을 실현할 수 있도록 하였다. 또한 초등학교 저학년에게 구체물로서는 조작할 수 없는 것들을 다양한 애니메이션 기법을 통하여 직접 조작해 볼 수 있도록 하고, 재미있는 놀이를 학습에 적절히 활용함으로써 학습 흥미도를 높이고자 하였다.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.701-722
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• 2010

Students have to investigate, experiment and inquire using the manipulative materials and real-world thing for studying Geometry. Manipulative materials activities encourage to understand mathematical concept and connection of symbol. Experiment activities using the computer focused the student's intuitive and inquisitive activities because of visualization of an abstract mathematics concept. This study developed a workbook through the use of manipulative materials and computer for operating and experimenting, and suggested a method for inquiry of geometrical properties and proved an effect. Manipulative materials-experiment activities was proven effective to middle level and lower level students in understanding the geometrical properties, and was proven effective to high level and lower level students when it comes to mathematical communication ability. When students operate, at first, they have to know about the feature and information of the materials, and the teacher has to make an elaborate plan and encourages the students to discuss about this.

• Korean Journal of Childcare and Education
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• v.10 no.2
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• pp.175-192
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• 2014

The purpose of this study was to investigate the differences in perceived importance of mathematical education (perceived importance) and mathematical interaction of 5-year-olds' mothers according to contents of mathematical education. Second, we intended to examine whether mothers' understanding of purpose of mathematical education predicted on their perceived importance and mathematical interaction. Third, we analyzed relative influence between mothers' perceived effectiveness of concrete materials and worksheets on their perceived importance and mathematical interaction. The subjects consisted of 151 mothers of 5-year-olds lived in D city and K province in Korea. The results were as follows: First, mothers' perceived importance and mathematical interaction were higher in 'number and arithmetic'. Second, mothers' understanding of purpose of mathematical education predicted their perceived importance in all contents and mathematical interaction in 'number and arithmetic', 'geometry', and 'algebra'. Third, mothers' perceived effectiveness of concrete materials predicted better in most contents of mathematical education. Meanwhile, in 'number and operation', mothers' perceived effectiveness of worksheets did a predictive role in their importance awareness. These results were discussed in terms of necessity of a parent education program to provide practical information about contents and methods of mathematical education for their 5-year-old children.

• 한국정보교육학회:학술대회논문집
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• 2008.01a
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• pp.192-197
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• 2008

초등학교 수학과 도형 학습은 매우 추상적인 분야로 직관적인 이해를 돕기 위해 다양한 구체적인 조작이 요구되는데, 그 중에서 컴퓨터를 활용한 도형 학습은 학생들의 구체물을 이용한 학습의 한계를 극복할 수 있는 장점이 있다. 특히 Flex와 Flash를 이용하면 입체도형의 가상물의 제작 및 동적인 학습은 물론 사용상의 제약이 적어 시,공간의 한계를 극복할 수 있다. 본 연구에서는 초등학교 수학과 제 7차 교육과정의 입체도형 영역을 분석하여 학습요소를 추출하고 플래시의 드로잉 메서드를 바탕으로 학습요소별로 속성과 메서드를 정의하고 클래스를 설계하여 입체도형 객체를 생성하고 플렉스의 컴포넌트로 구성된 학습 어플리케이션의 틀을 설계하여 입체도형 객체가 플렉스의 어플리케이션 내에서 사용이 가능하도록 설계 개발하였다. 본 연구가 갖는 의의는 첫째, 초등학교 수학과 수준에 맞는 속성과 메서드를 갖도록 개발한 입체도형 객체를 활용하여 학습자의 입체도형에 자유로운 탐구활동 기회를 제공하여 보다 직관적이고 구체적으로 도형학습을 할 수 있도록 돕는다. 둘째, 플렉스를 활용함으로서 학습자의 쉬운 접근을 돕고 학습 어플리케이션 틀을 활용하여 기존에 개발되어 있는 수학과 플래시 파일들을 활용한 다른 수학과 영역의 학습 어플리케이션 설계 및 개발의 시간과 노력을 단축시키는데 있다.

• 한국정보교육학회:학술대회논문집
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• 2004.08a
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• pp.475-484
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• 2004

공간 능력 및 공간 시각화 능력의 향상은 우리가 살고 있는 세계를 표현하고 설명하는데 도움을 주고 실생활과 직업에 관련된 문제해결 능력을 기를 수 있게 한다. 초등학교에서는 비형식적인 방법으로 일상생활에서 접하는 대상과 다른 구체적 자료를 사용한 조사, 실험, 탐구를 통하여 여러 위치에서 도형을 시각화하고, 그려보고, 비교하는 활동을 강조하고 있다. 제7차 수학과 교육과정에서 공간능력 및 공간 시각화 능력을 향상시키기 위한 학습으로 구체적 조작물과 학습지 사용을 병행하고 있다. 하지만 초등 기하는 공간적인 경험을 현실 상황이나 구체물 조작을 통하여 형성된 공간직관을 수학화하도록 하여야 하나, 실제 현장에서는 학교여건 등의 여러 실정으로 조작 자료들이 제대로 마련되어 있지 않거나 잘 사용하지 않고 있다. 3차원을 경험할 수 있는 공간 시각화 학습프로그램을 적극 활용하여 어떤 방향이든 상관없이 가상의 공간에서 물체를 옮기거나 회전시킬 수 있으며 시간적, 공간적 제약을 받지 않고 학습자들의 공간시각화 능력을 향상시킬 수 있는 학습 프로그램 개발이 필요하다. 이에 본 연구에서는 이런 요구에 의해 아동과의 상호 작용성과 접근성을 향상시킨 웹기반 가상현실 프로그램을 개발하고 그 효과 분석을 통해 웹 기반 가상현실 학습 프로그램에 대한 가능성을 진단해 보고자 한다.

• Journal of the Korean Electrochemical Society
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• v.17 no.2
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• pp.124-129
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• 2014

In this article, we report the fabrication and characterization of carbon sphere/$Fe_3O_4$ nanocomposite for Li/air batteries. $Fe_3O_4$ nanoparticles are dispersed homogeneously on the surface of carbon spheres in an attempt to enhance the low conductivity of oxide catalyst ($Fe_3O_4$). The carbon sphere/$Fe_3O_4$ nanocomposite could offer wide surface area of $Fe_3O_4$ and increased carbon/catalyst contact area, which lead to enhanced catalytic activity. The electrode employing carbon sphere/$Fe_3O_4$ nanocomposite presented relatively low overpotential and stable cyclic performance compared with the electrode employing carbon sphere.