• 대한수학회보
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• 제58권6호
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• pp.1327-1340
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• 2021

In this paper, we investigate hereditary and semihereditary representations of quivers over an arbitrary ring. As consequences hereditary and semihereditary category of representations of quivers over an arbitrary ring are characterized.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권1호
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• pp.123-134
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• 2007

In the article, representations useful in mathematics education are introduced and show how they are related in the context of mathematics education. They are classified in three categories: representations in mind, representations for understanding and problem solving, and mathematical representations.

• 대한수학회지
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• 제34권3호
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• pp.673-693
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• 1997

In this work, the irreducible complex representations of degree 4 of $B_4$, the braid group on 4 strings, are classified. There are 4 families of representations: A two-parameter family of representations for which the image of $P_4$, the pure braid group on 4 strings, is abelian; two families of representations which are the composition of an irreducible representation of $B_3$, the braid group on 3 strings, with a certain special homomorphism $\pi : B_4 \longrightarrow B_3$; a family of representations which are the tensor product of 2 irreducible two-dimensional representations of $B_4$.

• 대한수학회지
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• 제51권6호
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• pp.1177-1187
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• 2014

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

• 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.

• 한국초등과학교육학회지:초등과학교육
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• 제27권2호
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• pp.158-169
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• 2008

The purpose of this study was to analyze the uses of the external representations in the $3{\sim}6th$ grade science textbooks developed under the 7th National Curriculum on the basis of the theories and the research results on learning with the multiple representations. The results showed that the frequencies of the macroscopic external representations were higher than those of the symbolic external representations. The external representations with drawing and/or writing, especially writing, were used more frequently than those without drawing and/or writing. However, the most of the external representations were rarely used according to the principles and/or the theories (e.g., personalization principle, dual coding theory, cognitive load theory, and social constructivism theory) for effective uses of the multiple external representations in the science textbooks. The present study provides the guideline to establish the effective uses of the external representations in the science textbooks that not only meet learners but also teachers.

• 한국과학교육학회지
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• 제40권1호
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• pp.61-75
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• 2020

이 연구에서는 2015 개정 교육과정 7학년 과학의 물질 영역인 '기체의 성질'과 '물질의 상태 변화' 단원에 제시된 외적 표상을 분석하여 표상을 활용한 과학교육을 위한 시사점을 도출하고자 하였다. 표상의 유형, 표면적 특성의 해석, 본문과의 관련성, 캡션의 존재와 특성, 복합적 표상에서 표상 간 관련성, 표상의 기능의 여섯 가지 범주로 구성된 분석틀을 이용하여 다섯 종의 교과서에 나타난 표상의 특성을 분석하였다. 또한, '기체의 성질'과 '물질의 상태 변화' 단원의 성취기준을 설명하는 각 교과서에 제시된 대표적인 표상의 특징을 분석하였다. 연구의 결과는 다음과 같다. 먼저 표상의 유형에서는 거시적 표상이 가장 높은 빈도로 나타났으며, 표면적 특성의 해석 범주에서는 명시적 특성을 가진 표상의 빈도가 가장 높았다. 본문과의 관련성 범주의 분석 결과, 대부분의 표상이 완전한 연관성과 연결 또는 완전한 연관성과 비연결에 해당하여 표상과 본문 내용은 일관성 있게 연관되어 있는 것으로 나타났다. 캡션의 존재와 특성 범주에서는 적절한 캡션이 존재하는 표상의 빈도가 가장 높았고, 복합적 표상에서 표상 간의 관련성은 충분히 연결된 표상이 대부분이었다. 표상의 기능 범주에서는 완성형이 가장 높은 빈도를 보였으나 탐구 활동에 제시된 표상에서는 미완성형이 높은 빈도를 나타냈다. 성취기준과 관련된 대표적인 표상을 분석한 결과, 표상의 유형, 표상에 제시된 정보및 기호의 사용 등에서 교과서별로 차이를 나타냈다. 연구의 결과로부터 7학년 물질 영역의 표상 활용과 관련된 교육적 시사점을 논의하였다.

• 대한가정학회지
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• 제50권5호
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• pp.91-100
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• 2012

The purpose of this study was to examine the effects of children's representations of mothers and peer competence on preschool adjustment. 102 preschoolers (47 boys and 55 girls, aged 4-5) participated in this study. The data were analyzed using descriptive statistics and structural equation modeling analysis. The results were as follows: Firstly, children's representations of mothers had a direct effect on peer competence. Secondly, peer competence had a direct effect on preschool adjustment. Thirdly, children's representations of mothers did not directly affect preschool adjustment, but their representations of mothers did indirectly affect preschool adjustment, through peer competence. In conclusion, children's representations of mothers and peer competence influence preschool adjustment.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• 대한수학회지
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• 제36권6호
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• pp.1021-1031
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• 1999

In this paper we introduce matrix representations of polygroups over hyperrings and show such representations induce representations of the fundamental group over the corresponding fundamental ring. We also introduce the notion of a polygroup hyperring generalizing the notion of a group ring. We establish homo-morphisms among various polygroup hyperrings.