• School Mathematics
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• v.6 no.1
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• pp.91-118
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• 2004

Since 1998 year, many educational software and its contents have been developed by individuals and public institutes. However, it is not easy to re-use the contents effectively and consistently, because they should be changed and reorganized whenever a curriculum is changed. Therefore, it is important for each subject to establish new system in which the contents or their teaching-learning elements are not changed although new curriculum appears. In this respect, in last year(2003 year), while setting mathematics as a representative subject, KERIS executed a study on developing a system(or method) of classifying teaching-learning materials in mathematics using computers, based on future-oriented curriculum including the current mathematics curriculum. Finally, for this study, the most essential and basic teaching-teaming 'units' were developed and the total number of units were 339. Also, in addition to the development of 'units', the 'elements' were developed for understanding more concrete contents included in each 'unit' and the total number of elements were 1191.

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.87-99
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• 2003

As the development of computer science discrete mathematics has been developed accordingly. Discrete mathematics is one of the vital element for the development of the computer and IT technologies since it is the theoretical basis for these field of technologies. Currently, according the Seventh Curriculum Standards in Mathematics, high school students may participate in the class of discrete mathematics as one of their optional curriculum. However, discrete mathematics is a new to the most students in high school. Therefore, the teaching methods for the class of discrete mathematics must be carefully designed so that students acknowledge the importance of this new subject. For this purpose, we first show that why the algorithm is needed and then analyze the problem involved in the method of the traditional matrix multiplications. Finally, we suggest two matrix multiplication algorithms which are more efficient than the traditional method.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.139-146
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• 1991

A generalization of an earlier diffusion model for system subject to continuous wear is presented. It is assumed that the state of the system is modelled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a stationary renewal process and increases the state of the system by a random amount if the state does not exceed a threshold. Various properties of this model are investigated including the distribution of the state of the system at time t, the first passage time to state 0 and the probability that the state of the system exceeds a certain level throughout a specified interval.

• The Mathematical Education
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• v.39 no.2
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• pp.145-150
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• 2000

In this paper, we study the subject-matter knowledge related to the problem about rational exponent with negative bases. From the school mathematics point of view, we first investigate the meaning of the extensions of the number systems. We analyze the intrinsic meaning involved in the (-8)$^{1}$ 3) through the natural interpretation of rational exponent with negative bases by the complex number. we explain why it is important for a teacher to have the subject-matter knowledge in order to detect and correct student\`s mistake and misunderstanding.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.141-147
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• 1995

A diffusion model for a system subject to random shocks is introduced. It is assumed that the state of system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. It is also assumed that the shocks coming to the system according to a Poisson process decrease the state of the system by a random amount. It is further assumed that a repairman arrives according to another Poisson process and repairs or replaces the system i the system, when he arrives, is in state zero. A forward differential equation is obtained for the distribution function of X(t), the state of the systme at time t, some boundary conditions are discussed, and several interesting characteristics are derived, such as the first passage time to state zero, F(0,t), the probability of the system being in state zero at time t, and F(0), the limit of F(0,t) as t tends to infinity.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.201-204
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• 1992

After this discovery of lower bounds by Stark and Odlyzko, some people searched for number fields with relatively small discriminants. Also some others studied algorithms which will produce number fields with the smallest absolute value of the discriminant for a fixed degree n. However, this algorithmic approach does not work well if the extension degree n is greater than seven or eight. And it is not clear whether current computers can finish those algorithms in a reasonable amount of time for large n. So we are justified in our approach for this subject. In this paper we will report the results of our computations. Some number fields we found are better than previously known examples. Others are rediscoveries of known examples. However, there is theoretically nothing new in our approach to this subject.

• The Mathematical Education
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• v.47 no.3
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• pp.291-310
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• 2008

This article is based on an international collaborative study that aimed to investigate mathematical preparation of prospective elementary teachers in several selected education systems in East Asia. This article reports the Korean portion of the study. A survey instrument was developed to explore not only prospective teachers' knowledge of elementary mathematics curriculum and their beliefs in their preparation and mathematics instruction but also their subject matter knowledge and pedagogical content knowledge on the topic of fraction division. A total of 291 seniors in 3 universities participated in the survey. The results reveal these prospective teachers' strengths and weaknesses with regard to their knowledge of fraction division, and suggest that content-specific pedagogical knowledge needs to be emphasized in the teacher preparation program.

• The Mathematical Education
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• v.42 no.2
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• pp.247-258
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• 2003

In this study, total 486 articles in the journal of the Korea Society of Mathematical Education Series A are classified and analyzed by MSC2000 and ZDM classification. The results are as follows: 1) 2000 Mathematics Subject Classification : (number of articles) 1) 2000 Mathematics Subject Classification : (number of articles) 97- : (31), 97A : (7), 97B : (40), 97D : (229), 97U(105) 2) ZDM classification : (number of articles) A : (36), B (45), C : (57), D : (145), E : (19), F : (27), G : (37) H : (7), I : (19), K : (18), M (4), N : (12), U : (60) 3) Some remarks and suggestions are proposed.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.57-72
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• 2000

In this paper, in order to explicate how mathematics education can contribute to humanity education, I enquired in which position mathematics occupy in Froebel's For this, I examined Froebel's theory of humanity education, his theory of mathematics education, and the applicational problem of his thoughts to nowaday education. Froebel's educational theory is based on the concept of the Divine Unity which is relevant to the notion of 'The Absolute' of Fichte, Schelling, Hegel. He claims that from inanimate objects to human being, all is subject to the eternal law, which is presided by God. So the world itself is the representation of this law of the Divine Unity and education consists in leading man to conscious and free representation of it. The revealing process of the inner law of the Divine Unity can be attained through the awareness of the divinity which resides in the self. And this process of self-consciousness is dialectical movement of the two opposites, i.e. 'inner' and 'outer' Froebel suggests that mathematics is the mediator between the inner and outer world, i.e. he suggests that since both human being and nature are the representations of the Divine Unity, mathematics is both the pure human spirits and the law of nature. Having such a role, mathematics becomes the main discipline in education. Though there are some criticism on Froebel's educational thoughts on mathematics discussed in this paper, it can provide a typical answer to the question about how mathematics education contributes to humanity education.