• East Asian mathematical journal
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• 제35권2호
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• pp.115-139
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• 2019

In problem solving education, sentence problems are a tool for comprehensive evaluation of mathematical ability. The sentence problems refer to the problem expressed in sentence form rather than simply a numerical representation of mathematical problems. In order to solve sentence problems with a mixture of mathematical terms and general language, problem-solving ability including the ability to understand the meaning of sentences as well as the mathematical computation ability is required. Therefore, it is important to analyze syntactic elements from the linguistic aspects in sentence problems. The purpose of this study is to investigate the complexity of sentence problems in the length of sentences and the grammatical complexity of the sentences in the depth of the sentences by analyzing the 51 sentence problems presented in the $4^{th}$ grade mathematics textbook(2015 revised curriculum). As a result, it was confirmed that it is necessary to examine the length and depth of the sentence more carefully in the teaching and learning of sentence problems. Especially in elementary mathematics, the sentence problems requires a linguistic understanding of the sentence, and therefore it is necessary to consider syntactic elements in the process of developing and teaching sentence problems in mathematics textbook.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권3호
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• pp.139-170
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• 2013

We extend a p-hierarchical decomposition of the second degree finite element space of N$\acute{e}$d$\acute{e}$lec for tetrahedral meshes in three dimensions given in [1] to meshes with hexahedral elements, and derive p-hierarchical decompositions of the second degree finite element space of Raviart-Thomas in two dimensions for triangular and quadrilateral meshes. After having proved stability of these subspace decompositions and requiring certain saturation assumptions to hold, we construct a local a posteriori error estimator for fem and bem coupling of a time-harmonic electromagnetic eddy current problem in $\mathbb{R}^3$. We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권4호
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• pp.389-403
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• 2020

본 연구는 수학과 교과역량으로서의 정보처리 능력이 어떻게 해석, 적용되고 있는지 교과서 분석을 통해 탐구하였다. 중학교 1-3학년 10종 30권 교과서의 191개 과제를 정보처리 능력 하위요소에 따라 분석한 결과, 하위요소별, 교과서별로 차이가 컸으며 공통적으로 '공학적 도구 및 교구 활용'에 매우 치우쳐 있었다. 과제 유형별로도 해석과 적용 방법의 다양성이 발견되었다. 본 연구 결과를 바탕으로 정보처리 능력 함양을 위한 개선 방향과 시사점을 논의하였다.

• 대한수학교육학회지:학교수학
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• 제6권1호
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• pp.91-118
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• 2004

1988년 개인용 컴퓨터를 활용하는 교육용 컨텐츠가 개발되기 시작한 이래 우리나라의 교육용 컨텐츠의 수는 엄청나게 늘어났다. 그러나 이러한 컨텐츠들이 교육과정이 바뀔 때마다 각 교과의 학습 주제가 재편성됨으로 인해 지속적인 사용이 어려워지고 있다. 그러므로, 교과별로 변하지 않는 학습 요소를 정립한다면 교육과정이 변하더라도 자료를 재분류하지 않고도 기존에 만들어진 질 높은 자료들을 충분히 사용할 수 있을 것이다. 이러한 취지에 따라, 작년(2003년)에 교육인적자원부 및 한국교육학술정보원 측에서는 수학 교과를 시범 교과로 두어 현 교육과정을 지원하되 교육과정 개정에도 유연하게 대처할 수 있는 분류 방법(틀)을 마련하고자 하였다. 결과적으로, 이 연구에서는 그들의 요청에 따라 교육과정이 개정되더라도 수학 교과에서 나뉘거나 바뀌어 다뤄지지 않을, 즉 하나의 독립적이면서도 중요한 수학 내용을 '단위'라 칭하고, 이를 선정하는데 초점을 두었다. 이 연구에서 마련한 단위는 총 339개이고, 각 단위의 구체적인 내용을 이해하기 위하여 마련한 요소는 총 1191개이었다.

• 대한수학회지
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• 제53권1호
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• pp.115-126
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• 2016

Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

• 대한수학회논문집
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• 제6권1호
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• pp.93-95
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• 1991

• 대한수학회보
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• 제48권1호
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• pp.115-127
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• 2011

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

• 한국수학사학회지
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• 제33권2호
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• pp.103-114
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• 2020

In 1607, Matteo Ricci and Xu Guangqi translated Euclid's 《Elements》 and published 《Jihe yuanben, 幾何原本》. Though 《Elements》 consists of 13 volumes (or 15 volumes according to its editions), they translated only the first 6 volumes on the plane geometry. Why did they do so? This paper discusses about the three questions which naturally arise: What might be the motive of the translation of the 《Elements》? What method did they adopt for the translation? And why did they translate the 6 volumes, especially, the first 6 volumes, not completing the whole?

• East Asian mathematical journal
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• 제38권2호
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• pp.165-185
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• 2022

The six core competencies have been emphasized in the mathematics curriculum revised in 2015. In particular, the communication is very important for students' representing their own thinking and enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of the communication such as the understanding of mathematical representation, development and transition of mathematical representation, the representation of his own thinking, the understanding of the others' thinking. And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the communication competency were shown in each textbook.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.