• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Korean Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.1-19
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• 1996

Non-manifold topological representations can provide a single unified representation for mixed dimensional models or cellular models and thus have a great potential to be applied in many application areas. Various boundary representations for non-manifold topology have been proposed in recent years. These representations are mainly interested in describing the sufficient adjacency relationships and too redundant as a result. A model stored in these representations occupies too much storage space and is hard to be manipulated. In this paper, we proposed a compact hierarchical non-manifold boundary representation that is extended from the half-edge data structure for solid models by introducing the partial topological entities to represent some non-manifold conditions around a vertex, edge or face. This representation allows to reduce the redundancy of the existing schemes while full topological adjacencies are still derived without the loss of efficiency. To verify the statement above, the storage size requirement of the representation is compared with other existing representations and present some main procedures for querying and traversing the representation. We have also implemented a set of the generalized Euler operators that satisfy the Euler-Poincare formula for non-manifold geometric models.

• Korean Journal of Child Studies
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• v.38 no.1
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• pp.17-31
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• 2017

Objective: The purpose of this research was to examine the effects of parents' childhood attachment representations and parenting behavior in developing early childhood self-regulation, a developmental skill. Methods: This research was conducted with 171 preschoolers, 171 parent couples, and 22 teachers of 5-year-old classes in kindergartens and children's houses in Seoul. Results: First, there was significant correlation among parental childhood attachment representations, parenting behavior, and child self-regulation. Second, parental attachment representations and parenting behavior were shown to affect self-monitoring, a subvariable of self-regulation, and were influenced by maternal independence-oriented parenting behavior, maternal attachment representation, and parental attachment representation. As factors affecting self-control, a subvariable of self-regulation, they were influenced by maternal attachment representation, and maternal and paternal affectionate parenting behavior. Lastly, as factors affecting self-control, they were influenced by attachment representation to parents of origin, maternal affectionate parenting behavior, and maternal independence-oriented parenting behavior. Conclusion: This research revealed that parental childhood attachment representations and parenting behavior are important variables affecting the development of self-regulation in preschoolers. This finding can be used as basic data for parent education content to help preschoolers grow healthier and happier and as basic data for a program to improve parent-child attachment.

• ETRI Journal
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• v.46 no.1
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• pp.82-95
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• 2024

As automated essay scoring (AES) has progressed from handcrafted techniques to deep learning, holistic scoring capabilities have merged. However, specific trait assessment remains a challenge because of the limited depth of earlier methods in modeling dual assessments for holistic and multi-trait tasks. To overcome this challenge, we explore providing comprehensive feedback while modeling the interconnections between holistic and trait representations. We introduce the DualBERT-Trans-CNN model, which combines transformer-based representations with a novel dual-scale bidirectional encoder representations from transformers (BERT) encoding approach at the document-level. By explicitly leveraging multi-trait representations in a multi-task learning (MTL) framework, our DualBERT-Trans-CNN emphasizes the interrelation between holistic and trait-based score predictions, aiming for improved accuracy. For validation, we conducted extensive tests on the ASAP++ and TOEFL11 datasets. Against models of the same MTL setting, ours showed a 2.0% increase in its holistic score. Additionally, compared with single-task learning (STL) models, ours demonstrated a 3.6% enhancement in average multi-trait performance on the ASAP++ dataset.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.365-386
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• 2005

Let L be the free Lie superalgebra generated by a $Z_2$-graded vector space V over C. Suppose that g is a Lie superalgebra gl(m, n) or q(n). We study the g-module structure on the kth homogeneous component Lk of L when V is the natural representation of g. We give the multiplicities of irreducible representations of g in Lk by using the character of Lk. The multiplicities are given in terms of the character values of irreducible (projective) representations of the symmetric groups.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.55-72
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• 2000

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.639-645
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• 2013

We aim at presenting certain integral representations for the Riemann Zeta function ${\zeta}(s)$ at positive integer arguments by using some known integral representations of log ${\Gamma}(1+z)$ and ${\psi}(1+z)$.

• East Asian mathematical journal
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• v.33 no.1
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• pp.45-52
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• 2017

Motivated by the problem of determining all right ideals of a group algebra FG for a finite group G over a finite field F, we explicitly determine the faithful irreducible representations of some finite metacylic groups over finite fields. By using that result, we determine the structure of all right ideals of the group algebra for the symmetric group $S_3$ over a finite field F, as an example.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.29-43
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• 2006

The article deals with the problem of extending representations of a closed normal subgroup H to a topological group G. We show that the standard technique using group cohomology to solve the problem in the case of finite groups can be generalized in the category of topological groups if G/H is discrete.