• East Asian mathematical journal
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• v.29 no.4
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• pp.449-466
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• 2013

This paper started from a question: Can it help a student solve the problem to give supports in point of view of a teacher knowing the solution. We performed a case study to get an answer for the question. We analysed a case which students do not make full use of data in the mathematical problem from this point of view of the mental representation. We examined closely the cause for not making full use of data. We got that the wrong mental representation which the students get from data in the problem lead to not making full use of data. We knew that it is insufficient to present the data not making use of. To help a student truly, it is necessary to give a aid based on a student's mental representation. From the conclusion of study, We got that figuring out student's mental representation is important and hope that many investigation about student's mental representation for various problem occur with frequency.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.285-301
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• 2013

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.421-430
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• 1999

In this paper we investigate representation groups of wreathed 2-groups and explicitly determine all the linearly inequivalent irreducible projective representations of wreathed 2-groups.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• Journal of The Korean Association of Information Education
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• v.5 no.2
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• pp.185-196
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• 2001

Elementary school students feel more difficult the mathematical word problems than the numberical formula. I think that this reason isn't the ability of mathematical calculation but the problems representation. It is demanded exactly understanding about the requirements of problem for improving ability of the mathematical word problem representation. It is necessary that we take multimedia data and communication for this, because web advances multimedia materialization and promotes mutual communication, then it gives us with the most environment for word problem representation learning. According to, this thesis is designed web-based system to improve ability of the mathematical word problem representation, applied the sixth grade it experimentally.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.627-651
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• 2005

This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.933-942
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• 2014

We give a representation of the component of solutions with characteristic multiplier 1 in a periodic linear inhomogeneous continuous system. It follows from this representation that asymptotic behaviors of the component of solutions to the system and to its associated homogeneous system are quite different, though they are similar in the case where the characteristic multiplier is not 1. Moreover, the representation is applicable to linear discrete systems with constant coefficients.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.297-309
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• 2001

White noise distribution theory over the complex Gaussian space is established on the basis of the recently developed white noise operator theory. Unitarity condition for a white noise operator is discussed by means of the operator symbol and complex Gaussian integration. Concerning the overcompleteness of the exponential vectors, a coherent sate representation of a white noise function is uniquely specified from the diagonal coherent state representation of the associated multiplication operator.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.547-555
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• 1996

In this paper, we shall study the generalized covering group which plays a role for Schur multiplier. We discuss the lifting property over covering group and product of covering groups.