• Journal of the Korean Geographical Society
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• v.35 no.4
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• pp.503-518
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• 2000

분수계는 지형적 실체이며, 지역의 지형 연구 분야에서 자연적 경계로서 설정된다. 분수계는 수계, 산계, 유역등의 지형 요소들과 연관된다. 분수계의 지형 형성과 기능은 경사의 법칙, 구조의 법칙, 그리고 계층의 법칙으로 설명될 수 있다. 분수계는 구조적 형성과정과 기후적 삭박과정을 통하여 변화한다. 지형분수계는 능선분수계, 하천 분수계, 폐쇄 분수계, 세탈 분수계, 문턱 분수계, 세포형 분수계 등으로 유형화 될 수 있다. 지하수 분수계는 대개 지형의 기복을 반영하지만, 지역의 지질구조, 암서, 파쇄대 등으로 인하여 지형 분수계와 일치하지 않을 수 있다. 분수계의 법칙의 예외로서 설명되는 분수계의 일반적 단면은 선형이 아닌 대상 혹은 지대로서 나타난다. 분수계를 물의 흐름을 분리하는 곳으로 볼 때, 지형분수계는 지표면의 고도에 의해서 결정되며, 지하수 분수계는 지형, 지질 구조, 선구 조적 지형 요소들의 배열, 지층의 방향을 고려하여 결정된다.

• Communications of Mathematical Education
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• v.15
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• pp.71-76
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• 2003

학생들의 분수 나눗셈에 대한 이해는 개념적 이해를 바탕으로 수행되어야 함에도 불구하고 분수 나눗셈은 많은 학생들이 기계적인 절차적 지식으로 획득할 가능성이 높은 내용이다. 이것은 학생들이 학교에서 분수 나눗셈을 학습할 때에 일상생활에서의 경험과 선행 학습과의 연결이 잘 이루어지지 못하고 있는 것에 큰 원인이 있다고 본다. 본 연구에서는 학생들의 분수 나눗셈의 개념적 이해를 돕기 위하여 경험적 지식과의 연결 관계를 활용한 교수 방안을 실험 교수를 통해 조사하였다. 결과로서 번분수를 활용한 수업은 분수 나눗셈의 표준 알고리즘이 수행되는 이유를 알 수 있게 하는데 도움이 되나 여러 가지 절차적 지식이 뒷받침되어야 하며 분수 막대를 직접 잘라 보는 활동을 통한 수업은 분수 나눗셈에서의 나머지를 이해하는데 효과가 있다는 것을 알았다. 결론적으로, 학생들의 경험과 학교에서 이미 학습한 분수 나눗셈들의 관련 지식들을 적절히 연결하도록 한다면 수학적 연결을 통해 분수 나눗셈의 개념적 이해를 이끌 수 있다.

• School Mathematics
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• v.8 no.2
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• pp.123-138
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• 2006

The fraction concept consists of various meanings and is one of the more abstract and difficult in elementary school mathematics. This study intends to analyze the fraction concept from historical and psychological viewpoints, to examine the current elementary mathematics textbooks by these viewpoints and to seek the direction for improvement of it. Basic ideas about fraction are the partitioning - the dividing of a quantity into subparts of equal size - and about the part-whole relation. So these ideas are heavily emphasized in current textbooks. However, from the learner's point of view, situations related to different meanings of fraction concept draw qualitatively different response from students. So all the other meanings of fraction concept should be systematically represented in elementary mathematics textbooks. Especially based on historico-genetic principle, the current textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction as a unit.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.663-682
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• 2016

This study conducted an analysis of strategies that the 3rd to 6th grade elementary students used when they were solving problems of comparing the size of the fractions with like and unlike denominators, and unit fractions. Although there were slight differences in the students' use of strategies according to the problem types, students were found to use the 'part-whole strategy', 'transforming strategy', and 'between fractions strategy' frequently. But 'pieces strategy', 'unit fraction strategy', 'within fraction strategy', and 'equivalent fraction strategy' were not used frequently. In regard to the strategy use that is appropriate to the problem condition, it was found that students needed to use the 'unit fraction strategy', and the 'within fraction strategy', whereas there were many errors in their use of the 'between fractions strategy'. Based on the results, the study attempted to provide pedagogical implications in teaching and learning for comparing the size of the fractions.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.307-332
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• 2022

This action research was carried out to help students learn fractions computation by making and using semi-concrete fraction manipulatives that can be used continuously in math classes. For this purpose, the researcher and students made semi-concrete fraction manipulatives and learned how to use these through reviewing the previously learned fraction contents over 4 class sessions. Afterward, through the 14 classes (7 classes for learning to reduce fractions and to a common denominator, 7 classes for adding and subtracting fractions with different denominators) in which the principle inquiry learning model was applied, students actively engaged in learning activities with fraction manipulatives and explored the principles underneath the manipulations of fraction manipulatives. Students could represent various fractions using fraction manipulatives and solve fraction computation problems using them. The achievement evaluation after class found that the students could connect the semi-concrete fraction manipulatives with fraction representation and symbolic formulas. Moreover, the students showed interest and confidence in mathematics through the classes using fraction manipulatives.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.291-302
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• 2005

학생들이 분수 개념을 이해하기 위하여 분수 개념에 대한 표상과 현행 교과서에 기술되고 있는 분수 개념에 대한 실제를 살펴보았다. 그리고 5학년 남학생 3명과 여학생 3명을 대상으로 동치분수의 개념과 모델링이 동치분수를 이해하는데 어떤 역할을 하는지를 살펴보고자 하는 것이 본 연구의 목적이다.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.83-102
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• 2014

The purpose of this study was to explore students' understanding on units embedded in multiple interpretations of fractions: (a) part-whole relationships, (b) measures, (c) quotients, (d) ratios, and (e) operators. A total of 150 sixth graders in elementary schools were surveyed by a questionnaire comprised of 20 tasks in relation to multiple interpretations of fractions. As results, students' performance on units varied depending on the interpretations of fractions. Students had a tendency to regard the given whole as the unit, which led to incorrect answers. This study suggests that students should have rich experience to identify and operate various units in the context of multiple fractions.

• Education of Primary School Mathematics
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• v.23 no.3
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• pp.117-134
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• 2020

Based on the current curriculum, students learn the concept of fraction in the 3rd grade for the first time. At that time, fraction is introduced as whole-part relationship. But as the idea of fraction expands to improper fraction and so on, fraction as measurement would be naturally appeared. In that situation where fraction as whole-part relationship and fraction as measurement are dealt together, it is necessary for students to get experiences of understanding and exploring unit and whole adequately in order to fully understand the concept of fractions. Therefore, the purpose of this study is to analyze how to deal with unit fractions, how to implement activities to find the standard of reference from the part, and what visual representations were used to help students to understand the concept of fractions in elementary mathematics textbooks from the 7th to the 2015 revised curriculum. And we analyzed 60 3rd graders' understanding of finding and drawing the whole by looking at the part. Several didactical implications for teaching the concept of fractions were derived from the discussion according to the analysis results.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.707-734
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• 2009

The purpose of the study was to investigate how children understand addition and subtraction of fractions and how their understanding influences the solutions of fractional word problems. Twenty students from 4th to 6th grades were involved in the study. Children's understanding of operations with fractions was categorized into "joining", "combine" and "computational procedures (of fraction addition)" for additions, "taking away", "comparison" and "computational procedures (of fraction subtraction)" for subtractions. Most children understood additions as combining two distinct sets and subtractions as removing a subset from a given set. In addition, whether fractions had common denominators or not did not affect how they interpret operations with fractions. Some children understood the meanings for addition and subtraction of fractions as computational procedures of each operation without associating these operations with the particular situations (e.g. joining, taking away). More children understood addition and subtraction of fractions as a computational procedure when two fractions had different denominators. In case of addition, children's semantic structure of fractional addition did not influence how they solve the word problems. Furthermore, we could not find any common features among children with the same understanding of fractional addition while solving the fractional word problems. In case of subtraction, on the other hand, most children revealed a tendency to solve the word problems based on their semantic structure of the fractional subtraction. Children with the same understanding of fractional subtraction showed some commonalities while solving word problems in comparison to solving word problems involving addition of fractions. Particularly, some children who understood the meaning for addition and subtraction of fractions as computational procedures of each operation could not successfully solve the word problems with fractions compared to other children.

• Proceedings of the Korean Information Science Society Conference
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• 2008.06b
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• pp.135-140
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• 2008

최근 주변에서 다양한 음악분수를 찾아볼 수 있다. 음악분수의 연출을 위해서는 음악과 동기화되는 물의 움직임을 정의하는 음악분수 시나리오가 요구된다. 하지만 일반적으로 이러한 시나리오는 전문가들에 의하여 생성되기 때문에, 비용적인 문제로 인하여 다양한 음악에 대한 시나리오가 생성되지 못하고 있는 현실이다. 본 논문에서는 예제 기반 방식을 이용하여 자동으로 음악 분수의 시나리오를 생성하는 방법을 제안한다. 즉 기존에 전문가들에 의하여 생성되었던 음악분수의 시나리오를 분석하여 데이터베이스화 시킨 후, 이를 새롭게 합성하여 시나리오를 생성한다. 또한 음악분수 시나리오 생성에서 중요하게 요구되는 음악과 물 모양의 동기화를 위하여 본 논문에서는 임의의 음악이 들어왔을 때, 이 음악의 비트를 추출한 후 비트를 단위로 시나리오를 합성하게 된다. 사용자 실험결과 본 기술에 의하여 자동 생성된 시나리오는 전문가가 생성한 시나리오와 큰 차이가 나지 않음을 알 수 있었다. 본 기술을 이용하면 음악분수 시나리오를 생성할 때 요구되는 시간을 크게 줄일 수 있으며, 이로 인해 음악분수의 유지비용을 크게 절감할 수 있다.