• 대한수학회보
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• 제57권1호
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• pp.1-30
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• 2020

In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots admit Dehn surgery yielding either Seifert-fibered spaces or graph manifolds at a surface slope. We show that middle/hyper doubly Seifert twisted torus knots admit the latter, that is, non-Seifert-fibered graph manifolds whose decomposing pieces consist of two Seifert-fibered spaces over the disk with two exceptional fibers.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.163-176
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• 2019

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.287-293
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• 2023

In this paper, the Augmented graph Es(τ) of the inverse graph Gs(τ) of a cyclic group (τ,◦) was studied. The Augmented inverse graph was constructed by applying the method of Mycielski's construction. The dimension of Augmented inverse graph and different properties of the graph were investigated. Later the chromatic number of Augmented inverse graph was discussed and the relation between the maximum degree of the graph and the chromatic number was established. In the Mycielski's construction, the properties of the key node 'u' in Es (τ) were established based on cardinality of the cyclic group (τ,◦) and also proved that the Augmented inverse graph Es(τ) was a triangle free graph.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.353-366
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• 2024

A total coloring of a graph G is an assignment of colors to both the vertices and edges of G, such that no two adjacent or incident vertices and edges of G are assigned the same colors. In this paper, we have discussed the total coloring of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n) and also obtained the total chromatic number of M(T_n), M(D_n), M(DT_n), M(AT_n), M(DA(T_n)), M(Q_n), M(AQ_n).

• East Asian mathematical journal
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• 제30권4호
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• pp.451-474
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• 2014

The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.403-414
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• 2012

A voltage assignment on a graph was used to enumerate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph $K_{m,n}$ is surprisingly the ($m,n$) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph $K_{m,n}$ for which voltage assignments are either -1 or 1 and that every link is the boundary of a complete bipartite graph $K_{2,n}$ for which voltage assignments are either -1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권3호
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• pp.197-210
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• 2012

In this study, we will develop and implement the teaching program of 'Function', on the subject of "Poster-Making utilizing the Graph Art" in the Math Camp for middle-school students. And we will examine the didactical significance through student's activities and products. The teaching program of 'Function' utilizing the Graph Art can be promoted self-directly the understanding of 'Function' concept and the ability for handling 'Function'. In the process of drawing up the graph art, in particular, this program help students to promote the ability for problem-solving and mathematical thinking, and to communicate mathematically and attain the his own level. Ultimately, this program have a positive influence upon cognitive and affective and areas with regard to mathematics.

• 대한수학회보
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• 제53권1호
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• pp.273-301
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• 2016

In this paper, we classify all twisted torus knots which are doubly middle Seifert-fibered. Also we show that all of these knots possibly except a few admit Dehn surgery producing a non-Seifert-fibered graph manifold which consists of two Seifert-fibered spaces over the disk with two exceptional fibers, glued together along their boundaries. This provides another infinite family of knots in $S^3$ admitting Dehn surgery yielding such manifolds as done in [5].

• 한국과학교육학회지
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• 제39권5호
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• pp.655-668
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• 2019

이 연구에서는 중학생들의 과학 그래프 구성 과정을 문제 해결의 관점에서 심층적으로 조사하였다. 중학교 3학년 학생 10명이 연구에 참여하였으며, 이들은 앙금 생성 반응을 묘사한 그림 자료를 바탕으로 과학 그래프를 구성하였다. 학생들이 그래프를 구성할 때 거치는 사고 과정을 심층적으로 조사하기 위하여 발성사고법을 활용하였고, 그래프 구성 과정에 대한 녹화 및 반구조화된 면담을 실시하였다. 연구 결과, 학생들의 과학 그래프 구성 유형은 사용한 문제 해결 전략과 활용한 표상의 수준에 따라 네 가지 유형으로 구분할 수 있었다. 구조적 전략을 사용한 학생들은 그래프의 목표 개념에 대한 명제적 지식을 바탕으로 자료를 분석하고 경향성을 파악함으로써 활용한 표상의 수준과 무관하게 과학 그래프 구성에 성공하였다. 임의 전략-고차원 표상 유형의 학생들은 다양한 표상을 활용해 자료의 특징을 체계적으로 분석하고 자신이 구성한 그래프의 의미를 과학적 맥락에서 검토하는 과정을 거치며 과학 그래프 구성에 성공할 수 있었다. 반면, 임의전략-저차원 표상 유형의 학생들은 단순히 점을 연결하는 방식으로 그래프를 구성하였고, 과학적 맥락에 대한 고려 없이 그래프 구성 과정만을 점검하는 수준에 머물며 올바른 과학 그래프 구성에 실패하였다. 연구 결과를 바탕으로 학생들의 과학 그래프 구성 능력을 효과적으로 함양하는 방안을 제안하였다.

• 한국학교수학회논문집
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• 제1권1호
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• pp.151-163
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• 1998

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.