• 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.

• 한국수학교육학회지시리즈A:수학교육
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• 제48권4호
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• pp.365-385
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• 2009

Recently, mathematical modeling has been attractive in that it could be one of many efforts to improve students' thinking and problem solving in mathematics education. Mathematical modeling is a non-linear process that involves elements of both a treated-as-real world and a mathematics world and also requires the application of mathematics to unstructured problem situations in real-life situation. This study provides analysis of literature review about modeling perspectives, case studies about mathematical modeling, and textbooks from the United States and Korea with perspective which mathematical modeling could be potential and meaningful to students even in elementary school. Further, teaching method with mathematical modeling was investigated to see the possibility of application to elementary mathematics classroom.

• 대한수학교육학회지:학교수학
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• 제19권1호
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• pp.1-18
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• 2017

본 연구는 초등 예비교사의 수학적 문제제기 활동을 관찰하여 그 특징을 파악하고 문제제기 과정이 예비교사에게 제공하는 학습 기회를 분석하였다. 예비교사들의 문제제기 과정은 문제 조건 변형, 문제 성립 조건 탐구, 문제 구조 이해, 문제에서 생성된 개념탐구로 구성되었고, 각 단계에서 문제제기와 수학적 탐구가 결합하면서 다음 단계로 이어졌다. 탐구와 결합된 문제제기를 통해 예비교사들은 기존 개념을 재해석하고 새로운 수학적 대상을 발견하면서 수학적 개념들 사이의 연결성을 이해할 수 있었다. 예비교사들은 수학교육에서 문제제기의 중요성을 인식하였으며, 문제제기는 예비교사들에게 토론과 협력의 기회를 제공하였다.

• East Asian mathematical journal
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• 제30권4호
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• pp.475-491
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• 2014

We can easily see the 'cycloid slide' in the many mathematics and science museums. The educational materials, however, do not give us any mathematical principle. For this reason, we, in this thesis, first study the brachistochrone problem in the history of mathematics, and suggest a method of how to teach the principle using 'the dynamic geometry software GSP5' in order to help students understand the idea that the cycloid is the brachistochrone. Secondly, we examine the origin of the calculus of variations and apply it to prove the brachistochrone problem in order to build up the teachers' background knowledge. This allows us to increase the worth of history of mathematics and recognize how useful the learning is which uses technological tools or materials, and we can expect that the learning which makes use of cycloid slide will be meaningful.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제24권3호
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• pp.255-278
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• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

• 호남수학학술지
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• 제32권4호
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.

• 대한수학회보
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• 제36권4호
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.749-757
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• 2015

In this paper, we prove existence of radial positive solutions for the following boundary value problem

• 대한수학회논문집
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• 제10권3호
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• pp.751-758
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• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.

• 대한수학회논문집
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• 제13권1호
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• pp.37-59
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• 1998

We prove that solutions $u^\epsilon$ for the mixed hyperbolic-elliptic system of conservation laws with the viscosity term are total variation bounded uniformly in $\epsilon$ and that the solution $u^\epsilon$ converges to the solution for the mixed hyperbolic-elliptic Riemann problem as $\epsilon \to 0$.