• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.177-197
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• 2007

This study analyzes the theoretical background concerning problem solving, mathematization and real-life problems. Further it examines how middle school mathematics teachers and high school students of first grade recognize the real-life problems provides in textbooks concerning the area of geometry. Following those results found from this analysis, this paper reveals the issues and problems that we noticed through the analysis of real-life problems from textbooks, level 8 and level 9, Also we suggest the application of them along with the development of real-life problems for students' uplifting problem solving skills.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• Research in Mathematical Education
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• v.16 no.3
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• pp.195-206
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• 2012

We adopt a spirit of Problem based learning to the class of Multivariable Calculus in a school of scientifically talented students and observed effects of our teaching-learning method in the Spring Semester of 2010. Twelve students who enrolled in this class participated in this research. We have proceeded with classroom experiment for the half of semester after midterm exam so that the students could compare our teaching-learning method with usual traditional one in the subject of multivariable calculus. Especially, we investigated changes in the learning attitude and cognitive development of the students toward definition and theorem of mathematics. Each group of 4 students worked on a sheet of our well-designed structured problems of several steps in each class and presented how they understood the way of constructing new definition and related theorems. Instructor's role in this research was to guide students' activities as questioner so that students could attain the clear meanings of definitions and theorems by themselves. We firstly analyzed students' process of mathematization of definition through observing their discussions and presentations as well as their achievements in the quizzes and final exams. Secondly, we analyzed students' class-diaries collected at the end of each class in addition to pre/post surveys.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.231-236
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• 2012

This paper presents the MPPT(Maximum Power Point Tracking)control method of the PMSG wind generation system using the turbine model with a squirrel cage induction motor. The torque of squirrel cage induction turbine model is controlled by mathematization of speed characteristics of real blade. In this paper, maintenance and cost issues into consideration, except for previous method using information of the velocity of the wind speed sensor, the algorithm is presented. The algorithm is controlled by tracking the optimal point, the generator speed and maximum grid power. The vector controls of the generator side converter and the grid side converter are controlled respectively to obtain maximum torque and regulate unity power factor. With Psim simulations and experiments, the efficiency of squirrel cage induction turbine model and the validity of control algorithm are verified.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.123-140
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• 1997

Researchers have insisted that mathematics should be learned not as a product but as a process. Nevertheless school mathematics has chosen ‘top-down’ method and has usually instilled into the mind of students the mathematical concepts in the form of product. Consequently school mathematics has been teamed by students without the process of inquiring and mathematical thinking. According to Freudenthal, it is a major source of all problems of mathematics education. He suggested mathematising as the method for 'teaching to think mathematically' 'Teaching to think mathematically' through the process of mathematization, interpreting and analysing mathematics as an activity, is a means to embody the purpose of mathematics education.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.67-78
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• 2010

This paper aims to show the role of mathematics in the age of disciplinary convergence. Classifying disciplinary convergence into three levels by its degree, I claim that mathematics can contribute to disciplinary convergence in three aspects: theoretical, linguistical, and spiritual. Then I assert that there is a corresponding relationship between three levels of convergence and three contributing aspects.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Research in Mathematical Education
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• v.15 no.1
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• pp.15-30
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• 2011

We study to design educational Logo-based microworld environment equipped with 3D construction capability, 3D manipulation, and web-based communication. Extending the turtle metaphor of 2D Logo, we design simple and intuitive symbolic representation system that can create several turtle objects and operations. We also present various mathematization activities applying the turtle objects and suggest the way to make good use of them in mathematics education. In our microworld environment, the symbolic representations constructing the turtle objects can be used for web-based collaborative learning, communication, and assessments.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.125-136
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• 2008

There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.