• 대한수학회보
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• 제46권2호
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• 충청수학회지
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• 제21권4호
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• 한국초등수학교육학회지
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• 제16권1호
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• pp.1-19
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• 2012

칸트는 "순수이성비판"에서 수학적 인식과 철학적 인식의 차이를 개념에 의한 인식과 개념의 구성에 의한 인식의 차이로 설명한다. 이 논문에서는 칸트가 주장한 수학적 인식의 특성인 '개념의 구성'의 의미를 "순수이성비판"에 나타난 감성과 지성에 관한 칸트의 이론을 바탕으로 고찰한다. 개념의 구성은 개념을 직관에 나타내는 것으로, 상상력의 종합에 의해 개념의 역동적인 도식을 형성하는 과정이다. 개념의 구성에 관한 칸트의 이론은 수학적 개념 학습 지도에서 경험에서의 추상화를 통한 개념 형성을 넘어 주어진 표상을 개념의 도식으로 보는 관점의 형성을 요청하는 것으로 해석될 수 있다.

• 영재교육연구
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• 제18권3호
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• pp.465-496
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• 2008

21세기 지식기반사회에서 창의성은 리더십 및 전문성과 더불어 인재의 핵심가치로 부각되고 있다. 창의성은 영재성의 주요한 요소이며, 영재교육에서 창의성 계발은 프로그램의 핵심이다. 특히 고차원의 사고력과 이해를 요구하는 수학영역에서의 창의성은 사고의 융통성을 잴 수 있는 척도로 창의성 연구의 기초 도구로 쓰인다. 그러나 수학 창의성에 대한 이론적 연구는 많지 않다. 본 논문에서는 Sternberg와 Lubart가 제안한 6가지의 창의성 접근, 즉 신비주의적 접근, 실용주의적 접근, 심리-역등적 접근, 심리-측정적 접근, 인지적 접근, 사회-성격적 접근에 따라 수학 창의성을 분석하였다. 이는 수학 창의성을 여러 측면에서 고찰해봄으로써 수학 창의성 개념과 최근 연구를 이해하는데 도움을 주고자 한다.

• 대한수학회논문집
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• 제11권3호
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• pp.539-546
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• 1996

The purpose of this paper is to show that the Noetherian semi-local property of the underlying ring enables us to develope a setisfactory concep of the theory of reduction of ideals in a commutative Noetherian ring.

• 대한수학회보
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• 제32권2호
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• pp.139-144
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• 1995

Two subgroups U and V of a finite group G are called to be p-conjugate for a prime p if a Sylow p-subgroup of U is conjugate to a Sylow p-subgroup of V. This concept of p-conjugacy also makes sense for some infinite groups with a reasonable Sylow theory.

• 충청수학회지
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• 제5권1호
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• pp.23-34
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• 1992

This is an extension of results of Wiener's nonlinear noise theory from noises generated by the Wiener process to noises generated by processes with stationary Gaussian increments. In particular, using Nisio's Approach, we show that every measurable ergodic noise can be approximated in law by Gaussian process-presentable noise.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.87-95
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• 2011

The existence of T-periodic solutions for a general class of p-Laplacian equations is investigated. By using coincidence degree theory, some existence and uniqueness results, which generalize some earlier works on this topic, are presented.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권1호
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• pp.13-25
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• 2011

The Goals of mathematics education for the lower grades of primary school is to shape the basic concepts and the skills of mathematics. To achieve this goal, it is necessary an assessment which is able to help the students' learning activities by precisely diagnosing their basic mathematical capability. It should lend the students an assistance in diagnosing and revising their problems throughout teacher's cognitive participation in the process of mathematical problem solving. I would like to suggest the dynamic assessment as one of these kinds of approaches. In order to prove the utilities of this way, it was examined the necessity of dynamic assessment on the basis of the Vygotsky's theory after looking into the characteristics of the contents and methods of the mathematics education for the lower grades of primary school. Next, I researched the principles of the dynamic assessment and embodied the assessment tool to evaluate the mathematical achievement of the lower grades of the primary school. Lastly, it was provided the examples of the dynamic assessment tool in order to assist the practice of it.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권3호
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• pp.215-229
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• 2018

Despite the importance of learning to do mathematical proofs, researchers have reported that not only secondary school students but also undergraduate students have difficulties in learning proofs. In this study, we introduced a new toll for learning proofs and explored the reliability and the validity of peer assessment on proofs. In the course of a university in Seoul, students were given weekly proof assignments prior to class. After solving the proofs, each student had to assess other students' proofs. The inter-rater reliabilities of weekly peer assessment was higher than .9 over 90 percent of the observed cases. To examine the validity of peer assessment, we check whether students' assessments were similar to expert assessment. Analysis showed that the equivalence has been quite high throughout the semester and the validity was low in the middle of the semester but rose by the end of the semester. Based on these results, we believe instructors can consider the application of peer assessment on proving tasks as a tool to help students learn.