• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.425-437
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• 1998

The difference between "open" mathematics education and education of "open mathematics" arises from the difference of tearcher's understanding on the meaning of "teaching and learning mathematics" in the paper. Discusses the agreements and the worries of the researchers, the teachers, the students in korea, about open educationism, firstly, Three practical cases in mathematics lesson in korea are reviewed and analyzed in the respect of learning principles, secondly. Thirdly, the paper examines how to be modified two main learning principles, individualised learning and self-regulation of learning by teachers in the process of instruction. Finally, open mathematics advocated by Fisher(1984) and closed mathematics are compared especially in the probability unit. It concludes that the open approaches in mathematics lessons in korea need to improve with respect to teacher's attitude for didactic contents or mathematical knowledge. It is argued that teacher's open or flexible understanding of mathematical knowledge is no less important than that of their pupils.ant than that of their pupils.

• 한국수학사학회지
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• 제34권2호
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• pp.75-87
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• 2021

Hirabayashi Ichiei has sought theoretical improvement of educational studies in mathematics from the standpoint that educational studies in mathematics should be practical. His beliefs and subsequent attempts have many implications for Korean educational studies in mathematics. In this regard, it is meaningful to examine his theory of mathematics education. But he is not well-known in Korean community of educational studies in mathematics today. For this reason, His life and theory of mathematics education are outlined.

• 한국초등수학교육학회지
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• 제21권1호
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• pp.73-92
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• 2017

표는 자료 정리의 효과적 수단이지만, 그래프에 비해 시각적 한계가 뚜렷해서 수학교육분야에서 독립적인 연구주제로서의 위상을 차지하지는 못하고 있다. 그러나 표가 초등학교 수학과 교육과정에 명시적으로 포함된 만큼 표에 대한 체계적 연구와 합리적인 논의는 필요하다. 이 연구는 표를 다양한 용도로 적극적으로 활용하고 있는 핀란드 초등학교 수학교과서를 채택하여, 수학교과서에서 표가 어떤 의미로 어떻게 활용될 수 있는지 분석하였다. 연구결과 표는 통계영역 뿐만 아니라 수와 연산, 도형, 측정, 비와 비율 등의 수학내용을 전개하기 위한 유용한 수단이 될 수 있음을 확인하였다. 그 외에도 표의 외양이나 표를 구성하는 자료의 소재나 크기 등에 있어 의미 있는 시사점을 도출하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권6호
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• pp.2497-2517
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• 2020

For compressed sensing (CS) applications, it is significant to construct deterministic measurement matrices with good practical features, including good sensing performance, low memory cost, low computational complexity and easy hardware implementation. In this paper, a deterministic construction method of bipolar measurement matrices is presented based on binary sequence family (BSF). This method is of interest to be applied for sparse signal restore and image block CS. Coherence is an important tool to describe and compare the performance of various sensing matrices. Lower coherence implies higher reconstruction accuracy. The coherence of proposed measurement matrices is analyzed and derived to be smaller than the corresponding Gaussian and Bernoulli random matrices. Simulation experiments show that the proposed matrices outperform the corresponding Gaussian, Bernoulli, binary and chaotic bipolar matrices in reconstruction accuracy. Meanwhile, the proposed matrices can reduce the reconstruction time compared with their Gaussian counterpart. Moreover, the proposed matrices are very efficient for sensing performance, memory, complexity and hardware realization, which is beneficial to practical CS.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권2호
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• pp.159-179
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• 2011

This paper reports on the learning journeys in mathematical problem solving of 21 teachers enrolled on a Masters of Education course entitled Discrete Mathematics and Problem Solving. It draws from the reports written by these teachers on their personal journeys: the commonalities and differences among them in terms of how they look at their own problem solving experiences, what language they employ in talking about problem solving, and what impact the course has on their views about problem solving. One particular aspect of problem solving instruction, a pedagogical innovation called the Practical Worksheet, is addressed in some detail. These graduate students are full-time mathematics teachers with at least two years of classroom experience. They include primary and secondary teachers.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권9호
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• pp.4645-4664
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• 2019

It is significant to construct deterministic measurement matrices with easy hardware implementation, good sensing performance and good cryptographic property for practical compressed sensing (CS) applications. In this paper, a deterministic construction method of bipolar chaotic measurement matrices is presented based on binary sequence family (BSF) and Chebyshev chaotic sequence. The column vectors of these matrices are the sequences of BSF, where 1 is substituted with -1 and 0 is with 1. The proposed matrices, which exploit the pseudo-randomness of Chebyshev sequence, are sensitive to the initial state. The performance of proposed matrices is analyzed from the perspective of coherence. Theoretical analysis and simulation experiments show that the proposed matrices have limited influence on the recovery accuracy in different initial states and they outperform their Gaussian and Bernoulli counterparts in recovery accuracy. The proposed matrices can make the hardware implement easy by means of linear feedback shift register (LFSR) structures and numeric converter, which is conducive to practical CS.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.891-900
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• 2011

In this paper, we study the impulsive dynamic systems on time scales with initial time difference. By employing cone-valued Lyapunov functions, some comparison theorems and several practical ${\phi}_0$-stability criteria for impulsive system on time scales with initial time difference are obtained.

• 한국수학교육학회지시리즈A:수학교육
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• 제38권2호
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• pp.95-103
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• 1999

Russia is a country which is interested in mathematics education for gifted students for a long time. Some aspect of education for the gifted students in Russia(for example, mathematics curriculum, contents and activities of study, and selection of students in Russian physio-mathematics school) has already been studied. The purpose of this work was to introduce system of the mathematics education by correspondence for gifted students in Russia. In order to achieve this goal, we analyzed Russian literatures and articles published by the various physio-mathematics correspondence schools for gifted students. In this article, we gave some characteristics of the physio-mathematics correspondence schools for gifted students: various types of mathematics education by correspondence, curriculum, practical materials for mathematics education by correspondence.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.461-482
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• 1999

Russia is a country which is interested in mathematics education for the gifted students for a long time. Some aspect of education for the gifted students in Russia (for example, mathematics curriculum of the Russian physio-mathematics school, mathematics education by correspondence for sifted students etc.) has been partially studied. The purpose of this work is to introduce various systems of the mathematics education for the gifted students in Russia, and to draw significant conclusion for systematizing gifted education in Korea. In order to achieve this goal, we analyzed Russian literatures and articles published in Russia by the physio-mathematics school, ministry of education, and etc. In this article, we gave some characteristics of the various types of gifted education in Russia, and the practical curriculum for the gifted education.