• East Asian mathematical journal
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• 제29권4호
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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.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제16권3호
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• pp.285-301
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• 2013

본 연구는 초등학교 4학년 학생들의 수학 문제해결 과정에서 나타나는 시각적 표현이 어떠한지를 알아보고, 이를 바탕으로 수학 문제해결에 유용한 시각적 표현을 효과적으로 지도하기 위한 방안을 모색한 것이다. 연구문제 해결을 위해 서울D초등학교 4학년 1개 학급을 대상으로 학생들의 문제해결 과정에서의 시각적 표현이 어떠한지에 관한 검사를 실시하고 분석하였으며, 문제해결과정에서의 시각적 표현에 특징을 보이는 학생 4명을 선정 심층면담을 실시한 후 그 결과를 분석하였다. 학생들의 문제해결에 있어서 성취도와 문제해결과정에서의 시각적 표현의 활용사이에 깊은 관계가 있는 것으로 나타났다. 또한, 학생들이 문제해결과정에서 시각적 표현을 이용해 성공적인 문제를 해결하는 경험을 갖도록 함으로써 문제해결과정에서의 시각적 표현의 유용성을 인식할 수 있게 되었다.

• 대한수학회지
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• 제36권2호
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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.

• 대한수학회보
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• 제59권5호
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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.

• 정보교육학회논문지
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• 제5권2호
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• pp.185-196
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• 2001

초등학생들은 수식보다 문장으로 나타낸 문제를 더 어려워한다. 이것은 수학적인 계산 기능보다도 문제표상에 요인이 있는 것으로 생각할 수 있다. 수학 문장제 표상능력을 높이기 위해서는 문제의 요구를 정확히 이해하는 것이 요구된다. 이를 위해서는 멀티미디어 자료와 의사소통을 필요로 하는데, 웹은 멀티미디어 구현과 상호작용적 의사소통을 촉진할 수 있기 때문에 수학 문장제 표상학습을 위한 최적의 환경을 제공한다. 따라서 본 논문에서는 수학 문장제 표상능력 향상을 위한 웹 기반 시스템을 설계하여 초등학교 6학년을 대상으로 실험적으로 적용하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권4호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권1호
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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.

• 대한수학회보
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• 제51권4호
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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.

• 대한수학회지
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• 제38권2호
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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.

• 대한수학회논문집
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• 제11권3호
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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.