DOUBLY NONLINEAR PARABOLIC EQUATIONS RELATED TO THE LERAY-LIONS OPERATORS: TIME-DISCRETIZATION

신기연,강수진 영남수학회 2010 East Asian mathematical journal Vol.26 No.3

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

초등수학 기하문제해결에서의 시각화 과정 분석

윤여주,김성준,Yun, Yea-Joo,Kim, Sung-Joon 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

각뿔과 각뿔대의 부피에 대하여 산학서("산학정의(算學正義)(상편(上編))", "구장술해(九章術解)")와 한국.중국수학교과서와의 내용 비교연구

박영식,최길남,Park, Young-Sik,Choi, Kil-Nam 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

In this paper, we investigate the methodology to calculate the volume of the pyramid and frustum of the pyramid that is found in Gu Jang Sel Hae and San Hak Jeong Ui(The first volume)text. Comparing and analyzing content in Korean and Chinese mathematics education textbooks that uses as a foundation the aforementioned methodology, it is proposed that in future development of mathematics education curriculum the area of solid geometry be taught in greater depth in basic study guides.

동화를 활용한 문제 만들기 활동이 수학적 태도와 학업성취에 미치는 영향

오동근,김상룡,Oh, Dong-Geun,Kim, Sang-Lyong 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

This study will contribute to improve intimacy and interests of students in mathematics and to cultivate their abilities and attitudes to continuously learn through problem posing activities using fairy tales. An experimental study was carried out two classes of the fifth grade (total 60 of students, each group 30 os students) in G elementary school located in Daegu Metropolitan City. This experiment was performed for thirteen weeks. For this study, using two examination devices for measuring mathematical attitude and learning achievement, pre- and post-tests were carried out. As a result, it was found that two groups are identical groups. Problem posing activities with fairy tales had significant effect on mathematical attitudes of children and learning achievement of children.

삼각함수의 Mathematization에 관한 연구

김부윤,정영우,Kim, Boo-Yoon,Chung, Young-Woo 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.

GSP를 활용한 도형학습이 수학학업성취도 및 추론 능력에 미치는 영향

김진호,김인경,Kim, Jin-Ho,Kim, In-Kyung 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

The purpose of this paper is to investigate if the instruction using GSP to 4th graders for them to explore 'rectangles and making them' have an influence of understanding and retention of the knowledge, generation of the knowledge which is not dealt with during experimental treatment, and if they can reason based on what they have learned about it and about what has not been learned. According to the result from the data gained, learners in the experiment group show that they can retain, generate, reason better than ones in the comparison group.

LOGO와 함께 곡선 만들기 - 다각형 패턴의 관점에서

김화경,송민호,Kim, Hwa-Kyung,Song, Min-Ho 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

Papert [17] introduced the LOGO environment in which we make a curve using LOGO commands (FORWARD, ROTATE). We call this geometry as turtle geometry. This environment has influenced many researchers and designers of computers and mathematics education. But the curve that we can make using LOGO command is elementary or too difficult. Polygon and circle is elementary and making other curves is difficult. In this paper, we introduce the method of drawing some other curves mediating new command. First, we study epicycloid and hypocycloid in the historical and the physical context. And we introduce the method of making epicycloid and hypocycloid using vector addition. Next we study the polygon patterns of this curve. Finally, we extend the method for making more general curve and we improve the computer environment using this metaphor.

화이트헤드의 철학과 수학 교육

유충현,김혜경,Yu, Chung-Hyun,Kim, Hye-Kyung 영남수학회 2009 East Asian mathematical journal Vol.25 No.3

Whitehead's philosophy is evaluated as an applicable philosophy and an accurate, logical explanation system about the world through mathematics. Whitehead's ideological development can be divided into mathematical research, critical consciousness about sciences and philosophical exploration. Although it is presented as a whole unified conceptual framework to understand nature and human beings which is based on modern mathematics and physics in the 20th century, Whitehead's philosophy has not been sufficiently understood and evaluated about the full meaning and mathematics educational values. In this paper, we study relations of Whitehead's philosophy and the mathematical education. Moreover, we study implicity of mathematical education.

(예비)교사를 위한 완비성의 학습과 지도에 관한 소고

이병수,Lee, Byung-Soo 영남수학회 2010 East Asian mathematical journal Vol.26 No.4

In this paper, the author focuses on the teaching-level and learning-level of the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics, which is usually introduced in the class of real analysis of university mathematics. Firstly the author considers the properties of the completeness axiom and its 19 equivalent theorems, next he deals with its importances in the school mathematics and finally he suggests the teaching and learning of the concepts on the completeness axiom and its applications on [0,1] and $\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}$, $\mathbb{R}{\times}\mathbb{R}{\times}\mathbb{R}$ by (expected) teachers in the school mathematics.

교구를 활용한 학습활동이 각과 각도의 개념이해에 미치는 영향

백종림,최재호,Baek, Jong-Rim,Choi, Jae-Ho 영남수학회 2010 East Asian mathematical journal Vol.26 No.2

The purpose of this paper was to develop manipulative materials to teach the angle concepts and construct a teaching-learning program by using that. Furthermore, this study analyzed how does the program affect students understanding of the angle concepts. To check the effects of learning activities with manipulative materials on the understanding of an angle concepts, applied observation during class and write a mathematics journal writing, a description of students impressions at the end of the class and analyzed before and after test paper. We find that students approached the subject more friendly and knew well about the mathematical concepts by using materials. Furthermore, this activity helped that way to solve add and subtract of the angle, estimate ability, round angle concept, positive response in mathematics learning.