• East Asian mathematical journal
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• v.31 no.4
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• Communications of Mathematical Education
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• v.25 no.3
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• pp.577-591
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• 2011

In this study, in order to use computer in mathematical learning effectively, we investigate application of computer shown textbooks in geometry unit of middle school mathematics. First, we analyzed about status of computer application and method of computer application in 27 textbooks. We presented concrete example of mathematics activity using computer that can be used by teachers. Also, we tried to find out the direction to use computer more effectively in teaching and learning geometry. Through this process, we do not simply use computer to play for interest but to use it more meaningfully.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.06a
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• pp.7-19
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• 2007

During the past 20 years, a small but potentially powerful initiative has established itself in the mathematics education landscape: Mathematics Across the Curriculum (MAC). This curricular reform movement was designed to address a serious problem: Not only are students unable to demonstrate understanding of mathematical ideas and their applications, but also they harbor misconceptions about the meaning and purpose of mathematics. This paper chronicles the brief history of the MaC movement. The sections of the paper correspond loosely tn the typical steps one might take to solve a mathematics problem. The Problem Takes Shape presents a discussion of the social and economic forces that led to the need for increased articulation between mathematics and other fields in the American educational system. Understanding the Problem presents the potential value of exploiting these connections throughout the curriculum and the obstacles such action might encounter. Devising a Plan provides an overview of the support systems provided to early MAC initiatives by government and professional organizations. Implementing the Plan contains a brief description of early collegiate programs, their approaches and their differences. Extending the Solution details the adoption of MAC principles to the K-12 sector and throughout the world. The paper concludes with Retrospective, a brief discussion of lessons learned and possible next steps.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.435-455
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• 2015

This study is aimed at analyzing the level change and features of mathematical communication in elementary students' expository writing. 20 students of 5th graders of elementary school in Seoul were given expository writing activity for 14 lessons and their worksheets was analyzed through four categories; the accuracy of the mathematical language, logicality of process and results, specificity of content, achieving the reader-oriented. This study reached the following results. First, The level of expository writing about concepts and principles was gradually improved. But the level of expository writing about problem solving process is not same. Middle class level was lower than early class, and showed a high variation in end class again. Second, features of mathematical communication in expository writing were solidity of knowledge through a mathematical language, elaboration of logic based on the writing, value of the thinking process to reach a result, the clarification of the content to deliver himself and the reader. Therefore, this study has obtained the conclusion that expository writing is worth keeping the students' thinking process and can improve the mathematical communication skills.

• School Mathematics
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• v.14 no.4
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• pp.553-564
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• 2012

Story corners in elementary school mathematics practice activity books are newly given for students not only to have interests in mathematics, but to solve story problems related to already learned mathematical contents. In this study, we investigate the story corners in third grade mathematics practice activity books to analyze the contents according to their utilizations. We also suggest their implications. Based on our analysis, we have the following results. First, there are cases where the contents of the story are not related to the corresponding learning contents. Second, there are cases where some the contents or the posed problems related to the story are hard to be understood by students. Third, there are cases where the posed problems are not related to the corresponding learning contents.

• Journal of the Korean School Mathematics Society
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• v.7 no.1
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• pp.121-138
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• 2004

For the efficient application of curriculum discretion activity, I developed the program, 'Let's go together', so that curriculum discretion activity can be applied in the classroom. The program consists of several experiences, which are <Man to man paired study>, <the learning materials for Mathematics in our lives>, <the cooperative study in the class> and <the variety experiences about Mathematics>. This study shows the following results: First, T-test about the students' learning attitude and interest in Mathematics, there was dramatic change in students' desire, interest and attitude for mathematics learning. Second, as the role of Baewomi & Dowomi in 'Man to man paired study', Baewomi & Dowomi provided students with confidence of mathematics learning. We were able to ensure this fact from students' essay after the class. Third, teachers found that the number of students who had positive attitude with Self-directed study increased. And students tried to solve mathematical problems by themselves and the time using self-directed learning experience was also increased. This study suggests that there needs more development for learning materials for mathematics in our lives.

• The Korean Journal of Physiology and Pharmacology
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• v.8 no.1
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• pp.33-41
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• 2004

We developed a cardiac cell model to explain the phenomenon of mechano-electric feedback (MEF), based on the experimental data with rat atrial myocytes. It incorporated the activity of ion channels, pumps, exchangers, and changes of intracellular ion concentration. Changes in membrane excitability and $Ca^{2+}$ transients could then be calculated. In the model, the major ion channels responsible for the stretch-induced changes in electrical activity were the stretch-activated channels (SACs). The relationship between the extent of stretch and activation of SACs was formulated based on the experimental findings. Then, the effects of mechanical stretch on the electrical activity were reproduced. The shape of the action potential (AP) was significantly changed by stretch in the model simulation. The duration was decreased at initial fast phase of repolarization (AP duration at 20% repolarization level from 3.7 to 2.5 ms) and increased at late slow phase of repolarization (AP duration at 90% repolarization level from 62 to 178 ms). The resting potential was depolarized from -75 to -61 mV. This mathematical model of SACs may quantitatively predict changes in cardiomyocytes by mechanical stretch.

• The Mathematical Education
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• v.47 no.1
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• pp.49-59
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• 2008

In this paper, we discuss two representations of a curve. One is a static representation as set of points, the other is a dynamic representation using time parameter. And we suggest needs of designing a computer microword where we can represent a curve both statically and dynamically. We also emphasize the importance of translation activity from a static representation to a dynamic representation. For this purpose, we first consider constructionism and 'computers and mathematics education' as a theoretical backgrounds. We focus the curve of a parabola in this paper since this is common in mathematics curriculum and is related to realistic situation such as throwing ball. And we survey the mathematics curriculum about parabola representation. And we introduce JavaMAL microworld that is integrated microworld between LOGO and DGS. In this microworld, we represent a parabola using a dynamic action, and connect this dynamic parabola action to recursive patterns. Finally, we remake a parabola for a realistic situation using this dynamic representation. And we discuss the educational meaning of dynamic representation and its computer microworld.

• East Asian mathematical journal
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• v.32 no.4
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• pp.425-441
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• 2016

In this study, we focused on the graphing calculator to support the activity-oriented mathematics instruction with considering the accessibility of technology. The purpose of this study was to investigate the direction of the education of mathematics teachers. For this, we gave the teacher training for mathematics using graphing calculators for secondary mathematics teachers, and then examined the recognition for that of teachers. Teacher training of the graphing calculator was carried out three times in two years, we conducted a survey immediately at the time that has passed and after the 8 months or more after the training. As a result, we have obtained the suggestions of the advantages of using a graphing calculator in the learning mathematics, the difficulties of use of the graphing calculator in the classroom and the form of teacher training they want.