• 한국수학교육학회지시리즈C:초등수학교육
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• 제26권4호
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• pp.257-275
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• 2023

본 연구는 초등학교 5학년 학생들을 대상으로 수학적 논증을 강조한 수업을 설계 및 구현하여 수업의 실제를 분석하였다. 문헌 연구를 통해 수학적 논증을 강조한 수업을 1) 패턴 주목하기, 2) 추측 분명히 나타내기, 3) 시각적 모델로 표현하기, 4) 표현에 근거한 논증하기, 5) 비교 및 대조하기 5단계로 구성한 다음, 연속된 홀수의 합은 제곱수임을 주제로 수업을 설계하였다. 그리고 실제 수업 과정에서 수학적 논증을 강조한 수업이 어떻게 구현되는지 수업의 흐름을 단계별로 분석하였다. 본 연구의 결과를 바탕으로 초등학교에서 수학적 논증을 강조한 수업의 시사점을 논의하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제27권2호
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• pp.157-173
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• 2024

Researchers continue to emphasize the centrality of proof in the context of school mathematics and the importance of proof to student learning of mathematics is well articulated in nationwide curricula. However, researchers reported that students' performance in proving tasks is not promising and students are not likely to see the need to prove a proposition even if they learned mathematical proof previously. Research attributes this issue to students' tendencies to accept an empirical argument as proof for a mathematical proposition, thus not being able to recognize the limitation of an empirical argument as proof for a mathematical proposition. In Korea, there is little research that investigated high school students' views about the need for proof in mathematics and their understanding of the limitation of an empirical argument as proof for a mathematical generalization. Sixty-two 11^th graders were invited to participate in an online survey and the responses were recorded in writing and on either a four- or five-point Likert scale. The students were asked to express their agreement with the need of proof in school mathematics and to evaluate a set of mathematical arguments as to whether the given arguments were proofs. Results indicate that a slight majority of students were able to identify a proof amongst the given arguments with the vast majority of students acknowledging the need for proof in mathematics.

• 한국수학교육학회지시리즈A:수학교육
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• 제52권4호
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• pp.549-565
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• 2013

To help students understand the deduction system in the proof, we analyzed the textbook on mathematics at first. As results, we could find that the textbook' system of deduction is similar with the Euclid' system of deduction. The starting point of deduction is different with each other. But the flow of deduction match with each other. Next, we searched for the example of circular argument and analyzed. As results, we classified the circular argument into two groups. The first is an internal circular argument which is a circular argument occurred in a theorem. The second is an external circular argument which is a circular argument occurred between many theorems. We could know that the flow of deduction system is consistent in internal-external dimension. Lastly, we proposed the desirable teaching direction to help students understand the deduction system in the proof.

• 대한수학회지
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• 제41권4호
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• pp.747-754
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• 2004

In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.

• 대한수학회지
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• 제34권2호
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• pp.427-436
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• 1997

In the present paper, we invetigate some argument properties of certain analytic functions and the integral preserving properties in a sector. Our results include several previous results as special cases.

• 대한수학회논문집
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• 제15권2호
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• pp.263-274
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• 2000

The object of the present paper is to obtain some argu-ment properties of certain mermorphic functions in the punctured open unit disk. Furthermore, we investigate their integral preserving properties in a sector.

• 논리연구
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• 제18권1호
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• pp.39-64
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• 2015

수학적 플라톤주의자가 해결해야 할 가장 큰 문제는 바로 베나세라프가 제기하고 필드가 재정식화한 인식론적 문제라고 할 수 있다. 최근에 밸러궈는 자신의 독특한 형태의 수학적 플라톤주의인 FBP 즉 "혈기 왕성한 플라톤주의"는 이 인식론적 문제를 해결할 수 있다는 논의를 전개했다. 필자는 이 논문에서 그런 논의가 얼마나 성공적인가를 평가하면서 그의 논변이 지닌 문제점들을 살핀다. 우선 필자는 밸러궈 특유의 수학적 플라톤주의가 인식론적 문제를 해결한다는 논변을 형식적 측면에서 비판적으로 분석한다. 그리고 밸러궈의 논변과 전략에 대해 마녀주의의 사례를 통해 보다 본격적 반론을 전개한다. 마지막으로 밸러궈가 유비 논변에 기초해 자기 입장을 옹호하려는 대응을 무력화시키기 위한 논의를 펼친다.

• 대한수학회논문집
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• 제7권2호
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• pp.313-324
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• 1992

• 대한수학회보
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• 제52권1호
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• pp.159-172
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• 2015

This paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

• 대한수학회보
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• 제38권2호
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• pp.237-260
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• 2001

The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.