• East Asian mathematical journal
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• 제14권1호
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• pp.99-106
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• 1998

We establish a version of Fernique lemma for Gaussian processes which plays an important role in studying their moduli of continuity properties and related limit theorems.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.175-181
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• 2000

The purpose of this to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods .

• Korean Journal of Mathematics
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• 제15권1호
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• pp.79-85
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• 2007

We study codes over the polynomial ring $\mathbb{F}_q[D]$ and introduce the notion of basic codes which play a fundamental role in the theory.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제2권1호
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• pp.15-26
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• 1998

Teachers beliefs for the mathematics can have a powerful impact on how children go about learning mathematics, and theirs mathematical beliefs and abilities. In this study, \circled1 to divided teacher's mathematical beliefs into three - absolutism, progressive absolutism, constructivism - and to search into a theoretical characteristic, \circled2 to analyze and criticize the problems of the behaviorism and to investigate a point of basic view of the constructivism on mathematics education, \circled3 to suggest teacher's a role in mathematics learning be based on the constructivism perspective .

• 대한수학교육학회지:수학교육학연구
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• 제20권3호
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• pp.293-303
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• 2010

이 연구의 목적은 인식론 분석을 통해 수학사의 세 가지 역할을 분류하는 것이다. 무한과 극한에 대한 수학사를 바탕으로 네 가지의 다른 인식론들을 통해 "잠재적 무한"과 "실제적 무한" 담화를 묘사한다. 무한과 극한 개념의 상호 의존성을 또한 제시한다. 이러한 분석들을 이용하여 무한과 극한에 대한 수학사의 세가지 다른 사용을 보이고자 한다 : 과거, 현재, 그리고 미래사용.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.555-566
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• 2014

In this paper, we formulate two chemostat type models of phytoplankton and zooplankton population dynamics with instant nutrient recycling to study the role of viral infection on phytoplankton. The infection is transmitted only among phytoplankton population and it makes them more vulnerable to predation by zooplankton. It is observe that the chemostat system is very stable in the absence of viral infection but the presence of viral infection make the chemostat system sensitive with respect to the grazing rate of infected-phytoplankton by zooplankton. Further, if the grazing rate is less than certain threshold the system remain stable and exhibits Hopf-bifurcation after crossing it.

• 한국수학사학회지
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• 제15권1호
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• pp.115-134
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• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제19권4호
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• pp.247-265
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• 2015

Mathematics textbook plays a significant role in shaping students' learning of mathematics. Logic, rigor and abstraction as typical features of the formalization of mathematics, dominate mathematics textbooks around the world, which is regarded as one of the important origins of students' learning difficulties in mathematics. An innovative series of Chinese mathematic textbooks is presented in this paper. Supported by the supplementary materials excerpts from the textbooks, it gives a comprehensive theoretical analysis of the principles of design and implementation of this series of mathematics textbooks. The effectiveness of this series of textbooks is demonstrated by student achievement and secondary research data. It shows that series of Chinese mathematic textbooks has largely decreased students' learning difficulties in mathematics and enhance classroom teaching efficiency. It suggests that prioritizing the essence of mathematics and reducing abstraction is an important notion for mathematics textbook design and implementation.

• 한국수학교육학회지시리즈A:수학교육
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• 제63권3호
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• pp.573-591
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• 2024

본 연구는 AI 기반 수학 교수·학습에 대한 문헌을 체계적, 종합적으로 고찰하여 연구 동향을 탐색하고자 수행되었다. 이를 위해 최근 10년 간의 수학교육 문헌 중 문헌선정기준에 부합하는 57개의 문헌을 연구 대상, 연구 방법, 연구 목적, 학습 내용, AI의 유형, AI의 역할, 교사의 역할 측면에서 체계적 문헌 고찰하였다. 연구 결과, 연구 대상 중 학생을 대상으로 한 연구가 51%로 가장 많은 비중을 차지했으며, 연구 방법 중 양적 연구의 비중이 49%로 가장 높았다. 연구 목적은 효과 분석 44%, 이론적 논의 35%, 수업 사례 탐색 21%로 분포했다. 학습 내용으로 '수와 연산'과 '문자와 식'이 가장 많이 다루어졌고, AI 유형 중 지능형 튜터링 시스템(ITS)이 가장 많이 사용되었다. AI의 역할은 학습자 교수의 비중이 40.4%로 가장 높았으며, 교수자 지원 22.8%, 학습자 지원 21%, 시스템 지원 15.8% 순으로 분포하였다. 교사의 역할은 초기 연구일수록 'AI 수용자'로서의 역할이, 최근 연구일수록 'AI와의 건설적 파트너'로서의 역할이 부각되었고, 각 역할이 교육학적, AI-기술적, 내용적 측면에서 탐색되었다. 이를 통해 국내 수학교육 후속 연구의 방향이 제안되었고, AI 기반 수학 교수·학습에서의 교사가 갖추어야 할 소양이 논의되었다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제23권3호
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• pp.165-179
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• 2020

In this article, the author's intent is to begin a conversation centered on the question: How was the integration of digital technology into elementary mathematics classrooms framed? In the first part of the discussion, the author provides a historical perspective of the development of theoretical perspectives of the integration of digital technology in learning mathematics. Then, the author describes three theoretical perspectives of the role of digital technology in mathematics education: microworlds, instrumental genesis, and semiotic mediation. Last, based on three different theoretical perspectives, the author concludes the article by asking the reader to think differently.