• Title, Summary, Keyword: 분수의 개념

### A Study on Learner's Cognitive Structure in Division of Fraction (분수의 나눗셈에 대한 학습자의 인지구조)

• Lee, Youngju;Lee, Kwangho;Lee, Hyojin
• Journal of Elementary Mathematics Education in Korea
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• v.16 no.2
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• pp.295-320
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• 2012
• The purpose of this study is searching students' cognitive structures before and after learning division of fraction. Also the researchers investigated how their structures are connected when they solve division of fraction problems through individual interviews. The researcher suggested the instruction of division of fraction from the results.

### 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.

### Third grade students' fraction concept learning based on Lesh translation model (Lesh 표상 변환(translation) 모델을 적용한 3학년 학생들의 분수개념 학습)

• Han, Hye-Sook
• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009
• The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

### A Fourth Grade Student's Units Coordination for Fractions (단위 조정에 따른 초등학생의 분수 개념 이해 분석)

• Yoo, Jinyoung;Shin, Jaehong
• Education of Primary School Mathematics
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• v.23 no.2
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• pp.87-116
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• 2020
• The purpose of this study is to explore how units-coordination ability is related to understanding fraction concepts. For this purpose, a teaching experiment was conducted with one fourth grade student, Eunseo for four months(2019.3. ~ 2019.6.). We analyzed in details how Eunseo's units-coordinating operations related to her understanding of fraction changed during the teaching experiment. At an early stage, Eunseo with a partitive fraction scheme recognized fractions as another kind of natural numbers by manipulating fractions within a two-levels-of-units structure. As she simultaneously recognized proper fraction and a referent whole unit as a multiple of the unit fraction, she became to distinguish fractions from natural numbers in manipulating proper fractions. Eunseo with a reversible partitive fraction scheme constructed a natural number greater than 1, as having an interiorized three-levels-of-units structure and established an improper fraction with three levels of units in activity. Based on the results of this study, conclusions and pedagogical implications were presented.

### Middle School Mathematics Teachers' Understanding of Division by Fractions (중학교 수학 교사들의 분수나눗셈에 대한 이해)

• Kim, Young-Ok
• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.147-162
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• 2007
• This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.

### An Analysis on the Contents of Fraction in CA-CCSSM and its Textbook (미국 캘리포니아 주의 CA-CCSSM과 그에 따른 교과서에 제시된 분수 개념에 관한 내용 분석)

• Lee, Dae Hyun
• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.547-574
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• 2017
• The purpose of analysis of foreign curriculums and textbooks is to aimed to get the implications for the revision of curriculum, publishment of textbooks and teaching mathematics. In this study, Common Core State Standards and its textbooks was analyzed. The U. S. doesn't have the national mathematics curriculum. So, it can be happen some problems: students' lower mathematical achievement, assessment policy, decision of teaching contents, etc. In 2010, Common Core State Standards was developed by states. Furthermore, The California Department of Education reshaped standards: CA-CCSSM. This study analyzed the contents of fraction in CA-CCSSM and its textbooks. Fraction has many concepts and methods and models in teaching process. This study analyzed the equal parts, introducing fraction concept, the types of fraction, equivalent fractions, comparison of fractions. The conclusions are as follows; The equal parts are the important concept of fraction and introduced in geometry area before teaching of fraction. CA-CCSSM aims to understand a fraction as a number on the number line and represent fractions on a number line diagram. There are some similarity and difference in mixed number, fractions as a division and ratio, equivalent fractions and comparison of fractions between Korean curriculum and textbooks and CA-CCSSM.

### Analysis of Elementary Mathematics Textbooks Contents and 3rd Graders' Understanding on Unit and Whole of Fractions (분수의 단위와 전체에 관한 수학 교과서의 내용 고찰 및 초등학생의 이해 분석)

• Lim, Miin
• 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.

### The Historico-Genetic Instruction on Fractions (분수의 역사발생적 지도 방안)

• Seo, Dong-Yeop
• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.233-249
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• 2005
• This study discusses on the historico-genetic instruction on fraction. The textbooks of the current curriculum include the variety of contexts of fraction to be intended to connect with the conception of ratio in the grade 6. However mary elementary students have understanding limited to whole-part relation only. This study propose a method on the basis of the process of measurement by an absolute unit. The idea is related to The genesis of fraction in Egypt.

### The Conceptual Understanding of a Fraction in the Real World Problems (실생활문제에서 분수의 개념적 이해)

• 고상숙;고호경;강현희
• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.117-126
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• 2003
• In this article, we described students' conceptions of fraction, based on the mathematical learning theory of Skemp who contributed to the understanding of a mathematical conception in the real world problems. We analyzed students' responses to given three problems in order to examine a degree of the conceptual understanding in their responses. In conclusion, it suggests some instructional methods which facilitate students to understand the conceptions the fraction implies.

### A Study of the Sixth Graders' Knowledge of Concepts and Operations about Fraction (초등학생의 분수 이해 분석 - 6학년의 분수 개념 및 분수 나눗셈을 중심으로 -)

• Kim, Min-Kyeong
• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009
• The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).