• Title, Summary, Keyword: concept of fraction

### A Didactical Analysis of the Decimal fraction Concept (소수 개념의 교수학적 분석)

• Woo, Jeong-Ho;Byun, Hee-Hyun
• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.287-313
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• 2005
• The decimal fraction concept plays an important role in understanding the real number which is one of the major concepts in school mathematics. In the school mathematics of Korea, the decimal fraction is treated merely as a sort of name of the common fraction, while many other important aspects of the decimal fraction concept are ignored. In consequence students fail to understand the decimal fraction concept properly, and merely consider it as a kind of number for formal computation. Preceding studies also identified students' narrow understanding of the decimal fraction concept. But none of them succeeded in clarifying the essences of the decimal fraction concept, which are crucial for discussing the didactical problems of it. In this study we attempted a didactical analysis of the decimal fraction concept and disclosed the roots of didactical problems and presented measures for its improvement. First, we attempted a phenomenological analysis of the decimal fraction concept and extracted 9 elements of the decimal fraction concept. Second, we has analyzed of the essence of the decimal fraction concept more clearly by relating it to the situations where it functions and its representations. For this we tried to construct the conceptual field of the decimal fraction. Third, we categorized he developmental levels of the decimal fraction concept from the aspect of external manifestation of the internal order. On the basis of these results, we attempted hierarchical structuring of the elements of the decimal fraction concept. And using the results of such a didactical analysis on the decimal number concept we analyzed the mathematics curriculum and textbooks of our country, investigated levels of students' understanding of the decimal fraction concept, and disclosed related problems. Finally we suggested directions and measures for the improvement of teaching decimal fraction concept.

### A Study on Elementary School Students' Understanding of Fractions (초등학생의 분수이해에 관한 연구)

• 권성룡
• School Mathematics
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• v.5 no.2
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• pp.259-273
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• 2003
• A fraction is one of the most important concepts that students have to learn in elementary school. But it is a challenge for students to understand fraction concept because of its conceptual complexity. The focus of fraction learning is understanding the concept. Then the problem is how we can facilitate the conceptual understanding and estimate it. In this study, Moore's concept understanding scheme(concept definition, concept image, concept usage) was adopted as an theoretical framework to investigate students' fraction understanding. The questions of this study were a) what concept image do students have\ulcorner b) How well do students solve fraction problems\ulcorner c) How do students use fraction concept to generate fraction word problem\ulcorner By analyzing the data gathered from three elementary school, several conclusion was drawn. 1) The students' concept image of fraction is restricted to part-whole sub-construct. So is students' fraction understanding. 2) Students can solve part-whole fraction problems well but others less. This also imply that students' fraction understanding is partial. 3) Half of the subject(N=98) cannot pose problems that involve fraction and fraction operation. And some succeeded applied the concept mistakenly. To understand fraction, various fraction subconstructs have to be integrated as whole one. To facilitate this integration, fraction program should focus on unit, partitioning and quantity. This may be achieved by following activities: * Building on informal knowledge of fraction * Focusing on meaning other than symbol * Various partitioning activities * Facing various representation * Emphasizing quantitative aspects of fraction * Understanding the meanings of fraction operation Through these activities, teacher must help students construct various faction concept image and apply it to meaningful situation. Especially, to help students to construct various concept image and to use fraction meaningfully to pose problems, much time should be spent to problem posing using fraction.

### An Educational Analysis on Fraction Concept (분수 개념의 의미 분석과 교육적 시사점 탐구)

• Jeong Eun-Sil
• 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.

### An Analysis on the Students' Understanding in Concept and Operations of Decimal Fraction (초등학생들의 소수 개념과 그 연산에 대한 이해도 분석)

• Moon, Beomshik;Lee, DaeHyun
• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.237-255
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• 2014
• The purpose of this study is to investigate elementary school students' understanding the concept and operations of decimal fraction. The survey research was performed for this study. This survey was done by selecting 156 students. Questionnaire were made in five areas with reference to the 2007 revised mathematics curriculum. Five areas were the concept of decimal fraction, the addition, the subtraction, the multiplication and the division of decimal fraction. The results of such analysis are as follow: The analyzed result of understanding about concepts and operation of decimal fraction showed a high rate of correct answer, more than 85%. Students thought that multiplication and division of decimal fraction is more difficult than addition, subtraction, concept of decimal fraction. As the learning about concepts and operation of decimal fraction progress, the learning gap is bigger. Effort to reduce the learning deficits are needed in the lower grades. Mathematics is the study of the hierarchical. Learning deficits in low-level interfere with the learning in next-level. Therefore systematic supplementary guidance for a natural number and decimal fraction in low-level is needed. And understanding concepts and principles of calculations should be taught first.

### 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.

### An Analysis on Concepts and Methods of Teaching Fractions (분수 개념 지도 내용과 방법 분석)

• Kang, Wan
• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.467-480
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• 2014
• Concepts related to the fraction should be taught with formative thinking activities as well as concrete operational activities. Teaching improper fraction should follow the concept of fraction as a relation of two natural numbers. This concept is also important not to be skipped before teaching the fraction such as "4 is a third of 12". Mixed number should be taught as a sum of a natural number and a proper fraction. Fraction as a quotient of a division is a hard concept to be taught since it requires very high abstractive thinking process. Learning the transformation of division into multiplication of fractions should precede that of fraction as a quotient of a division.

### An Analysis on Aspects of Concepts and Models of Fraction Appeared in Korea Elementary Mathematics Textbook (한국의 초등수학 교과서에 나타나는 분수의 개념과 모델의 양상 분석)

• Kang, Heung Kyu
• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.431-455
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• 2013
• In this thesis, I classified various meanings of fraction into two categories, i.e concept(rate, operator, division) and model(whole-part, measurement, allotment), and surveyed appearances which is shown in Korea elementary mathematics textbook. Based on this results, I derived several implications on learning-teaching of fraction in elementary education. Firstly, we have to pursuit a unified formation of fraction concept through a complementary advantage of various concepts and models Secondly, by clarifying the time which concepts and models of fraction are imported, we have to overcome a ambiguity or tacit usage of that. Thirdly, the present Korea's textbook need to be improved in usage of measurement model. It must be defined more explicitly and must be used in explanation of multiplication and division algorithm of fraction.

### 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.

### A Case Study on the Effects of Primary Concept of Division upon the Concept Composition Process as to Division of Fraction for 3-rd grade Child Prodigies of Elementary Schools (나눗셈의 1차적 개념이 초등학교 3학년 영재아의 분수의 나눗셈에 대한 개념구성과정에 미치는 영향에 대한 사례연구)

• Kim, Hwa Soo
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• v.24 no.3
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• pp.339-358
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• 2014
• On the subjects of elementary 3-rd grade three child prodigies who learned primary concept of division, this study explored how they could compose schema and transformed schema through recognition of precise concepts and linking with the contents of division of fraction. That is to say, this study examined in depth what schema and transformed schema as primary concept of division they composed to get relational understanding of division of fraction, and how they used the schema and transformed schema composed by themselves to approach problem solving as well as how they transformed the schema in their concept composition and problem solving competence. As a result, it was found that learning of primary concept of division played a key role of composing schema and transformed schema needed for coping with division of fraction, and that at this time, composition of the transformed schema and transformed schema derived from the recognition of primary concept of division could play the inevitable role of problem solving for division of fraction.

### On Teaching Fraction of Elementary Mathematics Textbooks in Korea, New Zealand and Singapore (한국과 뉴질랜드, 싱가포르에서의 분수지도에 관한 고찰)

• Choi, Chang Woo
• East Asian mathematical journal
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• v.33 no.2
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• pp.235-255
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• 2017
• This study focuses on the teaching of fraction related to curriculum, introducing time of fraction, the meaning of fractions in textbook, material of teaching of fraction concept, teaching model of introducing time of fraction concept, special cases of teaching fraction and common points of representation of fraction among Korea, New Zealand and Singapore. For this study, Korea's mathematics textbooks(3-1, 3-2, 4-1, 5-1, 6-1) and New National Curriculum Mathematics(3, 4, 5. 6. 7)of New Zealand and New Syllabus Primary Mathematics(2B, 3B, 4A, 4B, 5A, 6A)of Singapore were selected for comparison and analysis. As a results we will suggest a reference to the development of mathematical curriculum, teaching fraction and improving the quality of the textbook through a method of comparative analysis of Korea, New Zealand and Singapore.