• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.451-454
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• 2002

본 논문에서는 개인의 적성을 판단하는 문제를 처리하기 위한 가중치 퍼지추론 알고리즘을 제시하고, 지식표현을 위해 퍼지 집합 이론과 퍼지 생성 규칙들을 이용하였다. 거리척도에 서는 퍼지값이 높은 구간의 척도를 낮은 구간의 척도에 비례하여 유사성을 구하였다. 또한, 가중치를 정량화한 값과 척도값을 연산하여 유사성을 나타냈고, 추출된 항목과 규칙과의 가능성을 구하였다. 여기서, 결과는 수검자들이 응답한 값들에 따라 임의의 직업군이 적당한 지를 나타내기 위해 확신도로 해석하였다.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.39-43
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• 2000

분산 추정 및 신뢰구간 추정의 한 방법으로 널리 쓰이고 있는 붓스트랩 방법을 복합표본에 적용하는 방법에 대해 알아보았다. 복합 표본은 유한 모집단에서 추출되고 추출확률이 다르기 때문에 i.i.d. 표본에 기초하여 개발된 전통적인 붓스트랩 방법을 직접 적용하면 추론의 오류가 발생할 수 있다. 본 연구에서는 복원 확률비례표본과 랜덤그룹표본에 붓스트랩을 적용하는 방법을 알아보았다.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.237-260
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• 2018

This study investigated the models of four countries' elementary mathematics textbooks in Ratio and Rate and identified how multiplicative perspectives on proportional relationships and the structure of proportion situations are reflected in the textbooks. For this, textbooks of 5th and 6th grade textbooks in Korea Japan, Singapore and U.S. are compared and analyzed. As a result, we can find multiplicative perspectives on proportional relationships and the structure of proportion situations on pictorial models, ratio tables, double number lines and double tape diagrams. Also, the development of Japanese textbooks from multiple batches perspectives to variable parts perspectives and the examples of the use with two models together implied the connection and union of two multiplicative perspectives. Based on these results, careful verification and discussion for the next textbook is needed to develop students' proportional reasoning and teach some effective reasoning strategies. And this study will provide the implication for what kinds of and how visual models are presented in the next textbook.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.352-355
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• 2006

본 논문에서는 스팸 대응 시스템의 특징 추출 방법들을 비교한다. 실험 결과는 퍼지추론 방법이 정보획득량, 카이제곱 통계량, 상호정보 방법에 비하여 정확률과 재현율의 결합 척도인 F-척도면에서 월등한 성능을 보여주지는 않는다. 하지만 제안된 퍼지추론 방법은 사용된 특징들의 수에 비례하여 성능이 증가하므로 좋은 특징 추출 방법으로 간주된다. 따라서 본 연구는 무수한 스팸 메일로 고통 받는 전자우편 사용자들을 위한 스팸 메일 필터링 시스템 개발에 도움을 줄 수 있다.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.

• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.331-352
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• 2012

The purpose of the study is to verify what cognitive variables have significant effect on proportional problem solving. For this aim, the study classified proportional problem into well-structured, moderately-structured, ill-structured problem by the level of structuredness, then classified the cognitive variables as well into factual algorithm knowledge, conceptual knowledge, knowledge of problem type, quantity change recognition and meta-cognition(meta-regulation and meta-knowledge). Then, it verified what cognitive variables have significant effects on 6th graders' proportional problem solving abilities through multiple regression analysis technique. As a result of the analysis, different cognitive variables effect on solving proportional problem classified by the level of structuredness. Through the results, the study suggest how to teach and assess proportional reasoning and problem solving in elementary mathematics class.

• 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.

• School Mathematics
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• v.14 no.4
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• pp.565-577
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• 2012

In this study, we investigated the process of constructing the geometrical solutions to quadratic equation, through proportions between lengths of similar triangles in a dynamic environment. To do this, we provided one task to 4 ninth grades students and observed the process of the students' activities and strategies. As a result of this pilot lesson study, our research shows the advantage and possibility of geometrical method in learning and teaching quadratic equation.

• The Mathematical Education
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• v.46 no.3
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• pp.315-329
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• 2007

The concepts of ratio, rate, and proportion are used in everyday life and are also applied to many disciplines such as mathematics and science. Proportional reasoning is known as one of the pivotal ideas in school mathematics because it links elementary ideas to deeper concepts of mathematics and science. However, previous research has shown that it is difficult for students to recognize the proportionality in contextualized situations. The purpose of this study is to understand how the mathematical concept in the middle school mathematics curriculum is connected with ratio, rate, and proportion and to investigate the characteristics of proportional reasoning through analyzing the concept including ratio, rate, and proportion on the middle school mathematics curriculum. This study also examines mathematical concepts (direct proportion, slope, and similarity) presented in a middle school textbook by exploring diverse interpretations among ratio, rate, and proportion and by comparing findings from literature on proportional reasoning. Our textbook analysis indicated that mechanical formal were emphasized in problems connected with ratio, rate, and proportion. Also, there were limited contextualizations of problems and tasks in the textbook so that it might not be enough to develop students' proportional reasoning.