• 한국수학교육학회지시리즈A:수학교육
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• 제21권3호
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• pp.43-45
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• 1983

• East Asian mathematical journal
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• 제27권2호
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• pp.223-242
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• 2011

The fact that Herbart's education has realized in the educational context the Kant's theory of transcendental education by applying Kant's transcendentalism to education is of great significance for education. It also provides an implication for mathematics education that Herbart's education of mathematics education can be applied to mathematics education through an attempt to combine a practical ethics education and an aesthetic emotion education with mathematics education. Both Kant and Herbart clearly show that an only practical, aesthetic education would not exist as a solely theoretical mathematics education cannot. Therefore, these multi-dimensional aspects of mathematics education should be always considered as a whole although there could be a difference in importance among those aspects. It implies that, regardless of the environments for mathematics education, mathematics teachers and students must do mathematics education activities that take into consideration the humanity in its entirety. The theory of mathematics education based on Herbart's education reveals that the entireness of human being should not be neglected in any case. In this regard, Herbart's theory of education shows that mathematics education is an all-inclusive theory of mathematics education that embraces both phenomenon and transcendence.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권2호
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권2호
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권4호
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• pp.349-377
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• 2009

In this work we present a study undertaken with in-service mathematics teachers of primary and secondary school where we describe and analyze the didactical competences needed to implement an innovative design in geometry applying Van Hiele's models. The relationship between such competences and an ideal teacher profile is also studied. Teachers' epistemology is established in terms of didactical competences and we can see that this epistemology is an element that helps us understand the difficulties that teachers face in practice when implementing an innovative curriculum, in this case, geometry based on the Van Hiele theory.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제7권1호
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• pp.59-67
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• 2003

In linear algebra course, the theory of vector space is usually presented in a very formal setting, which causes severe difficulties to many students. In this study, the effect of teaching the theory of vector space in linear algebra from the geometrical point of view on students' learning was investigated. It was found that the teaching of the theory of vector space in linear algebra from the geometrical point of view increases the meaningful loaming since it increases the visualization.

• 한국수학사학회지
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• 제14권1호
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• pp.73-82
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• 2001

In this article we studied one of the greatest mathematicians and pedagogues, A.N. Kolmogorov. He wrote about five hundreds o( books and articles in the fields of pure mathematics and mathematics education. In this paper we in detail introduced Kolmogorov's history of mathematics education and his theory of mathematical abilities, and elaborated this theory. In addition, we suggested some materials which are aimed to develop mathematical abilities in correspondence to the theory of Kolmogorov.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제38권3호
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• pp.331-351
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• 2024

본 연구의 목적은 수학교과교육론 강좌 수강이 예비교사의 수학적 신념에 미치는 영향을 살펴보는 것이다. 이를 위해 2021년도 1학기와 2022년도 1학기에 「수학교과교육론」 강좌를 운영하였고 예비교사들에게 수학적 신념 설문과 수학 수업 장면에 대한 이미지 검사 및 포커스 그룹 면담을 시행하여 자료를 수집하였다. 이를 분석한 결과, 예비교사들의 수학적 신념 설문 검사에서 수학 본질의 '탐구의 과정'과 수학 학습의 '적극적인 참여' 범주에 대한 사전, 사후 검사 결과가 통계적으로 유의미한 차이가 나타났다. 더불어 수학 수업 장면에 대한 이미지 검사에서는 사전 검사보다 사후 검사 결과에서 학생 중심의 수업 이미지 비율이 증가한 반면, 교사 중심의 수업 이미지 비율은 감소한 것으로 나타났다. 이는 수학교과교육론 강좌에서 제공한 다양한 학습 기회가 예비교사들의 명제적 지식에 기반한 실천적 지식의 구성을 촉진시켰고, 이러한 일련의 학습 과정이 예비교사들의 수학적 신념을 학습자 중심의 신념으로 변화시키는 데 기여한 것으로 추측할 수 있다.

• 충청수학회지
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• 제36권1호
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• pp.9-11
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• 2023

Intuitionistic Zermelo-Fraenkel (IZF) set theory is a set theory without the axiom of choice and the law of excluded middle (LEM). The weak excluded middle law (WEM) states that ¬𝜑∨¬¬𝜑 for any formula 𝜑. In IZF we show that LEM is equivalent to WEM plus the condition that any set not equal to the empty set has an element.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.575-586
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• 2006

Both theory and experiment are very important parts in sciences. Especially in mathematics, theory seems to be very important, but experiment or practice doesn't. Numerical analysis of many parts in mathematics needs practice in computer. In this paper, I suggest that computer-practicing in teaching power method, inverse power method and deflation to calculate eigenvalues and eigenvectors is good in understanding the theory. It also makes students sure that mathematics is helpful.