• School Mathematics
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• v.19 no.2
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• pp.229-248
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• 2017

This study investigated the factors that should be considered when teaching proportional expression and proportional distribution through literature review. Based on these results, we analyzed and compared Korean and foreign mathematics textbooks on proportional expression and proportional distribution longitudinally and horizontally to search for desirable methods of organizing the unit of proportional expression and proportional distribution in mathematics textbooks. For longitudinal analysis, we took the mathematics textbooks according to the national curriculum since the 5th one. For horizontal analysis, we selected the mathematics textbooks of Japan, Singapore, and China. In each textbook, the contents and the order in relation to proportional expression and proportional distribution, the definitions of terminology, and the contexts and the visual representations for introducing related concepts are selected as the analysis framework. The results of analysis revealed many characteristics and the differences in ways of dealing contents about proportional expression and proportional distribution. Based on these results, we suggested some implications for writing the unit of proportional expression and proportional distribution in elementary mathematics textbooks.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.05a
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• pp.1049-1052
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• 2013

저자들은 1980 년대 후반부터 역사학적 논쟁들을 통계적 수학적 방법을 이용하여 분석해보고자 하는 시도들을 하여 왔다. 최근에는 역사학의 논쟁점 중이 하나인 화랑세기의 진위 여부를 분석하기 위한 일련의 연구를 시도하였다. 이러한 일련의 시도의 일환으로 이 연구는 기획되었다. 이 글에서는 일본의 고대 기년 추정 방법을 참고하면서 세대 평균치와 재위 평균치의 추정이라는 방법을 통하여 "삼국사기" 초기 기년 문제에 대한 해명을 시도해 보고자 한다. 종래에는 세대 평균치라는 개념을 사용하지 않아서 편차가 심한 왕별 재위기간 평균치만 사용하여 재위기간 추정의 오차가 컸다. 또한 여러 가지 추론들이 주관적인 판단에 의지한 부분이 많아서 폭넓은 지지를 얻지 못한 경우가 많았다. 따라서 세대 평균치와 재위 평균치는 반드시 일치하지 않는다는 점을 분명히 하는 한편, 양자를 결합한 추정 방안을 마련해 볼 것이다.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.4
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• pp.319-326
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• 2015

Recently in the fields o f stochastic optimal control ( SOC) and reinforcemnet l earning (RL), there have been a great deal of research efforts for the problem of finding data-based sub-optimal control policies. The conventional theory for finding optimal controllers via the value-function-based dynamic programming was established for solving the stochastic optimal control problems with solid theoretical background. However, they can be successfully applied only to extremely simple cases. Hence, the data-based modern approach, which tries to find sub-optimal solutions utilizing relevant data such as the state-transition and reward signals instead of rigorous mathematical analyses, is particularly attractive to practical applications. In this paper, we consider a couple of methods combining the modern SOC strategies and approximate inference together with machine-learning-based data treatment methods. Also, we apply the resultant methods to a variety of application domains including financial engineering, and observe their performance.

• Journal of Gifted/Talented Education
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• v.21 no.2
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• pp.269-286
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• 2011

The purpose of this thesis is to examine difficulties students face in the inquiry activities of quadratic surface throughout mathematically gifted students' analogical inference and the influence of Cabri 3D in students' inquiry activities. For this examination, students' inquiry activities were observed, data of inferring quadratic surface process was analyzed, and students were interviewed in the middle of and at the end of their activities. The result of this thesis is as following: First, students had difficulties to come up with quadratic surfaced graph in the inquiry activity of quadratic surface and express the standard type equation. Secondly, students had difficulties confirming the process of inferred quadratic surface. Especially, students struggled finding out the difference between the inferred quadratic surface and the existing quadratic surface and the cause of it. Thirdly, applying Cabri 3D helped students to think of quadratic surface graph, however, since it could not express the quadratic surface graph in a perfect form, it is hard to say that Cabri 3D is helpful in the process of confirming students' inferred quadratic surface.

• Journal of Radiation Protection and Research
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• v.19 no.2
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• pp.109-120
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• 1994

A method for estimating the effectiveness of each protective action against a nuclear accident has been proposed using the fuzzy set theory. In most of the existing countermeasure models in actions under radiological emergencies, the large variety of possible features is simplified by a number of rough assumptions. During this simplification procedure, a lot of information is lost which results in much uncertainty concerning the output of the countermeasure model. Furthermore, different assumptions should be used for different sites to consider the site specific conditions. Tn this study, the diversity of each variable related to protective action has been modelled by the linguistic variable. The effectiveness of sheltering and evacuation has been estimated using the proposed method. The potential advantage of the proposed method is in reducing the loss of information by incorporating the opinions of experts and by introducing the linguistic variables which represent the site specific conditions.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.385-403
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• 2018

Fraction division can be categorized as partitive division, measurement division, and the inverse of a Cartesian product. In the contexts of quotitive division and the inverse of a Cartesian product, the multiply-by-the-reciprocal algorithm is drawn well out. In this study, I analyze the potential and significance of the method of using $1{\div}$(divisor) as an alternative way of developing the multiply-by-the-reciprocal algorithm in the context of quotitive division. The method of using $1{\div}$(divisor) in quotitive division has the following advantages. First, by this method we can draw the multiply-by-the-reciprocal algorithm keeping connection with the context of quotitive division. Second, as in other contexts, this method focuses on the multiplicative relationship between the divisor and 1. Third, as in other contexts, this method investigates the multiplicative relationship between the divisor and 1 by two kinds of reasoning that use either ${\frac{1}{the\;denominator\;of\;the\;divisor}}$ or the numerator of the divisor as a stepping stone. These advantages indicates the potential of this method in understanding the multiply-by-the-reciprocal algorithm as the common structure of fraction division. This method is based on the dual meaning of a fraction as a quantity and the composition of times which the current elementary mathematics textbook does not focus on. It is necessary to pay attention to how to form this basis when developing teaching materials for fraction division.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.177-196
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• 2005

In the Korean curriculum, students learn the concept of sample, sampling and other concepts related to sample and sampling, when they have reached the 10th grade of high school. But before the 10th grade, they have an activity about data collection, data analysis and the formulation of conclusion. We then investigated and analyzed the informal knowledge of students before they receive formal instructions. The results enabled the identification of the maximum response rate for each question that each student agreed or disagreed with. In particular, it didn't agree with how students consider the characteristic of population in the process of sampling, and the students agreed on a sampling process without considering the characteristic of the population or the components that consist the population. It showed that 5th grade students didn't investigate the data connected with sampling, and didn't understand the validity of sample survey process. While, 6th grade students equally understood sample size, sampling process, the reliance of data acquired through sample survey that applied to the source of judgment. But in details, it revealed that student had a misconception, or stayed at a subjective judgment level. The significant point is that many high school students didn't adequately understood a sample size with sampling. Though statistics instruction has traditionally been delayed until upper secondary education, this inquiry convinced us that this delay is unnecessary.

• School Mathematics
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• v.15 no.2
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• pp.289-314
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• 2013

Achievement profile by attribute in Korean students' mathematics was analyzed by applying cognitive diagnostic model, which is the newest measurement theory, to 2011 NAEA(National Assessment of Educational Assessment) results. The results are as follows. As the level of school is higher from 6th grade, 9th grade to 11th grade, the percentage of students mastering cognitive attribute 9(expressions using picture, table, graph, formula, symbol, writing, etc) drastically declined from 78%, 35% to 26%. It is necessary to have learning strategies to reinforce their abilities of expressing table, graph, etc. that higher graders in mathematics are more vulnerable to. Next, the property of mastering cognitive attributes according to gender, multi-cultural family was analyzed. In terms of mathematics, the percentage of girls mastering most of the attribute generally is higher than that of boys from 6th grade to 9th grade, however, boys show higher mastery in almost attributes than girls in the 11th grade. Compared to boys, the part where girls have the most trouble is attribute 9 in mathematics(expressions using picture, table, graph, formula, symbol, writing, etc). As international marriage, influx of foreign workers, etc. increase, the number of students from Korea's multi-cultural families is expected to be higher, therefore, identifying the characteristics of their educational achievement is significant in reinforcing Korea's basic achievement. In mathematics, gap of mastery level of attributes between multi-cultural group and ordinary group is more severe in higher grade and the type of multi-cultural group that needs supports for improving achievement most urgently changed in 6th grade, 9th grade and 11th grade respectively. In the 6th and 11th grade, migrant students from North Korea show the lowest level of mastering attributes, however, in the 9th grade, the mastery rate of immigrant students is lowest. Therefore, there is an implication that supporting plans for improving achievement of students from multi-cultural family should establish other strategies based on the characteristics of school level.

• The Journal of the Korea Contents Association
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• v.11 no.3
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• pp.460-466
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• 2011

Kameun temple was constructed in A.D. 682 after 46 year after Chumsungdae was constructed. This paper discusses the scientific implication of Taegeuk stone rods of Kameun temple site through the geometric analysis of their engraved figures. So we can estimate that the west Taegeuk of Kameun temple site has 2 circles comparing the path of the moon with that of the sun leading to the asymmetry in its emblem(Taegeuk) and the east Taegeuk of Kameun temple site has 1 circle representing the path of the sun. The Taegeuks along with around 30 equilateral triangles representing the north latitude $35.8^{\circ}$ give the explicit information of period of the orbit of the moon and the sun. These mathematical methods can explain some relics structure of antiquity with a few historical expounds.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.865-871
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• 2009

In this paper, a novel feedback linearization is proposed for discrete-time nonlinear systems described by discrete-time T-S fuzzy models. The local linear models of a T-S fuzzy model are transformed to a controllable canonical form respectively, and their T-S fuzzy combination results in a feedback linearizable Tagaki-Sugeno fuzzy model. Based on this model, a nonlinear state feedback linearizing input is determined. Nonlinear state transformation is inferred from the linear state transformations for the controllable canonical forms. The proposed method of this paper is more intuitive and easier to understand mathematically compared to the well-known feedback linearization technique which requires a profound mathematical background. The feedback linearizable condition of this paper is also weakened compared to the conventional feedback linearization. This means that larger class of nonlinear systems is linearizable compared to the case of classical linearization.