• Title, Summary, Keyword: 분수의 개념

### 수학학습부진아를 대상으로 분수의 개념적 이해에서 분수의 덧셈으로의 전이 가능성 연구

• Ha, Bo-Geum
• Proceedings of the Korea Society of Elementary Mathematics Education
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• pp.89-103
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• 2010

### A Case Study on the Effects of the Primary Concepts of Division and Fraction upon Relational Understanding of Decimals (나눗셈과 분수의 1차적 개념이 소수의 관계적 이해에 미치는 영향에 대한 사례연구)

• Kim, Hwa Soo
• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.353-370
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• 2015
• This study was conducted as a qualitative case study that explored how gifted 3rd-grade elementary school children who had learned the primary concepts of division and fraction, when they studied contents about decimal, formed the transformed primary concept and transformed schema of decimal by the learning of accurate primary concepts and connecting the concepts. That is, this study investigated how the subjects attained relational understanding of decimal based on the primary concepts of division and fraction, and how they formed a transformed primary concept based on the primary concept of decimal and carried out vertical mathematizing. According to the findings of this study, transformed primary concepts formed through the learning of accurate primary concepts, and schemas and transformed schemas built through the connection of the concepts played as crucial factors for the children's relational understanding of decimal and their vertical mathematizing.

### A Comparative analysis on the Fraction Contents of Korean, Japanese, Singaporean, American, and Finnish Mathematics Textbooks (한국, 일본, 싱가포르, 미국, 핀란드의 수학 교과서에 제시된 분수 지도 내용의 비교·분석)

• Lee, Dae Hyun
• Education of Primary School Mathematics
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• v.21 no.2
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• pp.111-130
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• 2018
• In this study, I compared and analyzed the contents of Korean, Japanese, Singapore, American, and Finnish textbooks about fraction which is one of the important and difficult concepts in elementary school mathematics. This is aimed to get the implications for meaningful fractional teaching and learning by analyzing the advantages and disadvantages of the methods and time of introducing the concept because fraction has the diversity of the sub-concepts and the introducing methods or process. As a result of the analysis, the fraction was introduced as part-whole(area) in all five countries' textbooks, but the use of number line, conversion between improper fraction and mixed number, whether to deal with part-whole(set) model. Furthermore, there are differences in the methods in obtaining of the equivalent fraction and the order of arrangement in comparison of fraction. Through this analysis, we discussed the reconsideration of the introducing contexts of fractions, the use of number line when introducing fractions, and the problem of segmentation and classification of contents.

### An Comparative Analysis of Fraction Concept in Mathematics Textbooks of Korea and Singapore (싱가포르와 우리나라 교과서의 비교 분석을 통한 분수 개념 지도 방안 탐색)

• Jeong, Eun-Sil
• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.25-43
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• 2009
• The fraction concept consists of various meanings and is one of the abstract and difficult in elementary school mathematics. This study intends to find out the implication for introducing the fraction concept by comparing mathematics textbooks of Korea and Singapore. Both countries' students peformed well in recent TIMMSs. Some implications are as follows; The term 'equal' is not defined and the results of various 'equal partitioning' activities can not easily examined in Korea's mathematics textbook. And contexts of introducing fractions as a quotient and a ratio are unnatural in Korea's mathematics textbook in comparison with Singapore's mathematics textbook. So these ideas should be reconsidered in order to seek the direction for improvement of it. And Korea's textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction.

### Geomorphic Conception and Function of the Divide (분수계의 지형적 개념과 기능)

• 이민부;한주엽
• 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.

### An Analysis of Elementary School Students' Strategy in Comparing the Size of Fractions (초등학생들의 분수의 크기 비교 전략 분석)

• Kim, Yukyung;Hwang, Hyunmi
• 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.

### A Study on the Misconceptions in the Self-directed Learning Using a Mathematics Digital Textbook: Focused on the Division of Fractions (수학과 디지털교과서 자기주도적 학습에서 나타난 오개념에 대한 연구: 분수의 나눈셈을 중심으로)

• Heo, Hae-Ja;Choi, Jeong-Im
• School Mathematics
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• v.11 no.4
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• pp.643-664
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• 2009
• This study was aimed to understand the problems that students experience during the self--directed study of a mathematics digital textbook and to find the implications for the design of digital textbook. For this study, we analyzed the process of self-directed learning on 'division of fractions with same denominator' using digital textbook by eight 6th graders. Students asked to use think aloud method while they study the unit. Their learning process was videotaped and analyzed by researchers after the experiment. After the self-directed learning, students filled out a test items and participated interview with a researcher. The result showed that students experienced several misconceptions and errors while using a digital textbook. The types of misconceptions and errors were cataegorized as "misconceptions and errors caused by a mathematics textbook" and "misconceptions and errors caused by a digital textbook". Especially, students showed several important misconceptions and errors because of the design factors. This implies we need to consider the causes of misconceptions for the design of a digital textbook.

### Case Study of Individualized Teaching for an ADHD Student's Learning of Fraction (ADHD 학생의 분수학습을 위한 개별지도 사례연구)

• Cheon, Jin-Seung;Chang, Hye-Won
• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.807-825
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• 2010
• Educational interest has been paid to ADHD students. Because of being easily distracted, lacking concentration, and committing hyperactive acts, they lag much behind other students in academic grades and their teachers have many difficulties in teaching them. This study aims to provide a case of enhancing an ADHD student's fraction-related achievement. To do this, we investigated his mathematical abilities in a preliminary study, devised an individualized teaching for the fractions unit, and applied them to him. And analyzing the results from observations and interviews of the student we can induce the following results: First, the ADHD student showed such types of errors in relation to fraction as lack of the concept of dividing into equal parts, lack of the concept of numerator and denominator, and errors in adding or subtracting fractions anc mixed fractions whose denominators were the same. And secondly, the fraction-related achievements of the ADHD student have improved thanks to the systematic teaching plan based on the accurate understanding of his academic gap relative to other students, his learning attitude, and his time difference. In addition, this study suggests several implications for ADHD students' learning of fractions.

### 왜 $\frac{3}{4}\;{\div}\;\frac{2}{5}=\;\frac{3}{4}\;{\times}\;\frac{5}{2}$인가?

• Park, Man-Gu
• Communications of Mathematical Education
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• v.13 no.1
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• pp.39-54
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• 2002
• 분수의 개념은 초등학교 수학에서 학생들이 이해하기에 가장 어려운 부분 중의 하나이다. 더욱이, 분수의 나눗셈은 이를 가르치는 교사들이나 배우는 학생들 모두에게 다루기가 쉽지 않은 과제로 남아 있다. 본고에서는 한국과 미국의 교과서에서 (분수)${\div}$(분수)를 어떻게 도입하며 전개하고 있는지 살펴보고, 이에 대한 학생들의 이해를 돕기 위한 제안을 하고자 한다.

### A Study on the Teaching of 'a Concept of Fraction as Division($b{\div}a=\frac{b}{a}$)' in Elementary Math Education - Based on a Analysis of the Korean Successive Elementary Math Textbooks (초등수학에서 '나눗셈으로서의 분수($b{\div}a=\frac{b}{a}$)' 개념 지도에 관한 연구 - 한국의 역대 초등수학 교과서에 대한 분석을 중심으로)

• Kang, Heung Kyu
• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.425-439
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• 2014
• The concept of a fraction as division is a core idea which serves as a axiom in the process of a extension of the natural number system to rational number system. Also, it has necessary position in elementary mathematics. Nevertheless, the timing and method of the introduction of this concept in Korean elementary math textbooks is not well established. In this thesis, I suggested a solution of a various topics which is related to this problem, that is, transforming improper fraction to mixed number, the usage of quotient as a term, explaining the algorithm of division of fraction, transforming fraction to decimal.