• 대한수학회보
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• 제59권4호
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• 한국초등수학교육학회지
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• 제20권4호
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• pp.563-581
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• 2016

수학 문제해결에서의 메타정의에 대한 연구 관심은 인지-메타인지의 구조에 착안하여 정의적 요소 간에 유사한 구조 설정의 시도로부터 출발하였으나 메타인지에 대한 연구와 비교할 때 아직 연구의 명료성이나 통일성 또는 체계성 면에서 개선이 필요하다. 이에 본 연구는 수학 문제해결 과정에 작용하는 일련의 인지적, 정의적 요소의 연쇄 유형 중에 정의적 요소를 포함하는 경우로써 '메타정의'의 개념을 규정하여 수학 문제해결 과정에 나타날 수 있는 실제적인 메타정의의 각 경우를 논리적으로 유형화하였다. 이를 준거로 초등학생의 실제 수학 문제해결 과정에서 메타정의의 각 유형에 해당하는 실제 예를 관찰, 분석하였다. 이를 통해서 수학문제해결 과정에서 메타정의의 작동 메커니즘, 즉 메타정의의 각 유형별로 구체적 작동 원리와 특히 문제해결 과정에 생산적으로 작동하는 메타적 기능의 특성을 추출하였다. 이는 문제해결에서의 메타정의 분석 방법론의 효율성 제고와 수학 문제해결 교수-학습에서의 메타정의가 함의하는 교육적 시사점 제공이란 면에서 기여한다.

• 한국초등수학교육학회지
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• 제14권2호
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• pp.401-420
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• 2010

본 연구는 공간추론활동을 통한 기하학습이 수학적 문제해결력과 수학적 태도에 미치는 효과를 알아보는데 목적이 있다. 이러한 연구 목적을 규명하기 위하여 서울특별시 소재의 초등학교 6학년 2개 반을 연구대상으로 선정하여 실험집단에는 공간추론활동을 통한 기하학습을, 비교집단에는 일반적인 기하학습을 실시하였다. 학습내용은 6학년 1, 2학기 단원에서 선정하였으며 이를 바탕으로 실험집단과 비교집단에 적용할 지도안, 활동지를 작성하여 4주 동안 11차시를 적용하였다. 그 결과, 공간추론활동을 통한 기하학습을 한 실험집단과 일반적인 기하학습을 한 비교집단의 사후 수학적 문제해결력에서 통계적으로 유의미한 차이가 존재하였다. 수학적 태도에서는 유의미한 차이는 보이지 않았지만 실험 집단 내에서는 실험 전에 비하여 실험 처치 후에 수학적 태도가 유의미하게 향상되었음을 알 수 있었다. 이와 같은 결과로부터, 공간추론활동을 통한 기하학습은 학생들의 분석력, 공간감각능력, 논리력을 향상시켜 이를 종합적으로 발휘해야 해결할 수 있는 수학적 문제해결력을 신장시키고 수학적 태도에 긍정적인 영향을 미친다는 것을 알 수 있었다.

• 대한수학회논문집
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• 제34권4호
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• pp.1353-1364
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• 2019

Modified Lagrange functional for solving an elastic problem with a crack is considered. Two formulations of a crack problem are investigated. The first formulation concerns a problem where a crack extending to the outer boundary of the domain. In the second formulation, we consider a problem with an internal crack. Duality ratio is established for initial and dual problem in both cases.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.617-636
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• 1999

This study was executed with the intention of guiding ‘open education’ toward a desirable school innovation. The basic two directions of curriculum reconstruction essential for implementing ‘open education’ are one toward intra-subject (within a subject) and inter-subject (among subjects). This study showed an example of intra-subject curriculum reconstruction with a problem solving area included in elementary mathematics curriculum. In the curriculum, diverse strategies to enhance ability to solve problems are included at each grade level. In every elementary math textbook, those strategies are suggested in two chapters called ‘diverse problem solving’, in which problems only dealing with several strategies are introduced. Through this method, students begin to learn problem solving strategies not as something related to mathematical knowledge or contents but only as a skill or method for solving problems. Therefore, problems of ‘diverse problem solving’ chapter should not be dealt with separatedly but while students are learning the mathematical contents connected to those problems. Namely, students must have a chance to solve those problems while learning the contents related to the problem content(subject). By this reasoning, in the name of curriculum reconstruction toward intra-subject, this study showed such case with two ‘diverse problem solving’ chapters of the 4th grade second semester's math textbook.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제10권2호
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• pp.141-149
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• 2007

It is undeniably important to bring up a solution capability of arithmetic word problems in the elementary mathematical education. The goal of this study is to acquire the implication for remedial instruction on arithmetic word problems solving through surveying elementary school students' difficulties in the solving of arithmetic word problems. In order to do it, this study was intended to analyze the following two aspects. First, it was analyzed that they generally felt more difficulties in which field among addition, subtraction, multiplication and division word problems. Second, with the result of the first analysis, it was examined that they solved it by imagining as which sphere of the other word problems. Also, the cause of their error on the word problem solving was analyzed by the interview. From the foregoing analyses, the following implications for remedial instruction on arithmetic word problems solving are acquired. First, the accumulation of learning deficiency must be diminished through the remedial instruction. Second, it must help students to understand the given problem and to make of what the goal of problem is. Third, it must help students to form a good habit for reading the problem and to understand the context of problem. forth, the teacher must help students to review and reflect their problem-solving processes.

• 한국학교수학회논문집
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• 제1권1호
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• pp.111-119
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• 1998

So far the studies on mathematical problem-solving education have failed to realize the anticipated result from students. The purpose of this study is to examine the reasons from the metacognitional viewpoint, and to think of making meta-items which enables learners to study through making effective use of the meaning of problem-solving and through establishing a general, well-organized theory on metacognition related to mathematic teaching guiedance. Metacognition means the understanding of knowledge of one's own and significance in the situation that can be reflection so as to express one's own knowledge and use it effectively when was questioned. Mathematics teacher can help students to learn how to control their behaviors by showing the strategy clearly, the decision and the behavior which are used in his own planning, supervising and estimating the solution process himself. If mathematics teachers want their students to be learners not simply knowing mathematical facts and processes, but being an active and positive, they should develop effective teaching methods. In fact, mathematics learning activities are accomplished under the complex condition arising from the factors of various cognition activities. therefore, mathematical education should consider various factors of feelings as well as a factor as fragmentary mathematical knowledge.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제5권1호
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• pp.77-86
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• 2001

The purpose of this study is to examine a theoretical framework for the interactions of learning in a small group setting of mathematical problem solving. Many researchers already have described the theoretical background for the small group settings in problem solving. However, most of the literatures merely have reported findings of achievement and rising of test scores. They ignored the observation of process taken during the small group work and have not determined how various psychological, social and academic effects are created. As results of the study, two types, mutual collaboration and asymmetric collaboration, of interactions are observed as the interactions of learning, which are conceived as the cores of authentic mathematical activities.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.621-634
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• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• 한국산업정보학회논문지
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• 제14권4호
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• pp.198-204
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• 2009

수학적 사고의 입장에서 중등학생들이 수학적 문제해결에 논리적 사고와 직관적 사고가 어떻게 작용하는지를 연구하는 것은 수학교육에서 중요하고도 흥미로운 과제의 하나이다. 본 연구의 주된 목적은 중등학교 영재학생을 대상으로 이러한 문제를 조사하는 것이다. 특히 이들 중등영재학생들의 논리적 사고와 직관적 사고에 대한 선호도와 논리형 문제의 문제해결능력 사이의 관계를 로지스틱 회귀분석을 이용하여 조사한다.