• Title, Summary, Keyword: 분수의 모델

### 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.

### Models and the Algorithm for Fraction Multiplication in Elementary Mathematics Textbooks (초등수학 교과서의 분수 곱셈 알고리즘 구성 활동 분석: 모델과 알고리즘의 연결성을 중심으로)

• Yim, Jae-Hoon
• School Mathematics
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• v.14 no.1
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• pp.135-150
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• 2012
• This paper analyzes the activities for (fraction) ${\times}$(fraction) in Korean elementary textbooks focusing on the connection between visual models and the algorithm. New Korean textbook attempts a new approach to use length model (as well as rectangular area model) for developing the standard algorithm for the multiplication of fractions, $\frac{a}{b}{\times}\frac{d}{c}=\frac{a{\times}d}{b{\times}c}$. However, activities with visual models in the textbook are not well connected to the algorithm. To bridge the gap between activities with models and the algorithm, distributive strategy should be emphasized. A wealth of experience of solving problems of fraction multiplication using the distributive strategy with visual models can serve as a strong basis for developing the algorithm for the multiplication of fractions.

### 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.

### 분수 학습에서 정신모델 구성을 위한 유추의 역할

• Go, Sang-Suk;Kim, Gyu-Sang
• Communications of Mathematical Education
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• v.15
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• pp.105-111
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• 2003
• 본 연구자는 아동이 분수 개념을 이해하는 정신모델 속에서 인지과정이 어떻게 나타나며, 적용되는지, 그리고 이를 바탕으로 분수 학습에 표현되는 정신모델 구성을 위한 유추의 역할을 살펴보고자 하는 것이 본 연구의 목적이다.

### 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.

### Justifying the Fraction Division Algorithm in Mathematics of the Elementary School (초등학교 수학에서 분수 나눗셈의 알고리즘 정당화하기)

• Park, Jungkyu;Lee, Kwangho;Sung, Chang-geun
• Education of Primary School Mathematics
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• v.22 no.2
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• pp.113-127
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• 2019
• The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

### A Comparative Study on Didactical Aspects of Fraction Concept and Algorithm Appeared in the Textbook of McLellan, MiC, and Korea (분수 개념과 알고리듬 지도 양상 비교: McLellan, MiC, 한국의 교재를 중심으로)

• Kang, Heung-Kyu
• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.375-399
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• 2005
• In this article, I identified many points of commonness and differences at)feared in the fraction units of three conspicuous textbooks -McLellan, MiC and Korea. After that, 1 evaluated these results with reference to more general didactics on which each text-book is based. A background theory of Mc-Lellan's textbook was Dewey's experientialism, and that of MiC was Freudenthal's realistic mathematics education. Through this study, I have reached the fact that these three textbooks could not exhibit the phenomenological wholeness of fraction. Driven by measuring number model which is very abstractive, McLellan's text-book is disregarding the lower level context. MiC textbook, driven by real context, is ignoring higher level model which is close to rational number concept. From an excess of formulation and practice of algorithm, Korea's textbook is overlooking the real context. It is necessary that a textbook which would display the phenomenological wholeness of fraction is developed.

### An Analysis of the Multiplication and Division of Fractions in Elementary Mathematics Instructional Materials (분수의 곱셈과 나눗셈에 관한 초등학교 수학과 교과용 도서 분석)

• Pang, Jeong-Suk;Lee, Ji-Young
• School Mathematics
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• v.11 no.4
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• pp.723-743
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• 2009
• This paper analyzed the main contents of multiplication and division of fractions in elementary mathematics textbooks and workbooks aligned to the national mathematics curriculum. This paper first explored the adequacy of when to teach the contents, the connection of instructional flow across grades, and the method of constructing a unit to teach multiplication or division of fractions. This paper then analyzed in detail the contents with regard to the types and frequency of word problems, the types of visual models and frequency, and the process of formalizing the calculation methods and principles. It is expected that the issues and suggestions stemming from this analysis of current textbooks and workbooks are informative in developing new instructional materials aligned to the recently revised mathematics curriculum.

### The Re-inspection on The Explanatory Model ofXi Ming of Chu Hsi'sThought of "Li Yi Fen Shu" (朱熹 「理一分殊」 的 <西銘> 詮釋模式再考察)

• Lin, Le-chang
• Journal of Korean Philosophical Society
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• v.141
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• pp.167-185
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• 2017
• Chu Hsi inherited the proposition of Cheng Yi, and it spent him over ten years to finish writing the works of Xi Ming Jie, thus, making the thought of "Li Yi Fen Shu" bethe explanatory model of Xi Ming, therefore, playing the role to determine the tone of Xi Ming. At first, the thought of "Li Yi Fen Shu is a concept to embody the ethical significance of Xi Ming. But in terms of all the discussion about "Li Yi Fen Shu" of Chu Hsi in his life, this proposition is not only for the ethical significance of Xi Ming, but also includes much more general philosophical significance, revealing the general and special relationship of things. The former is the narrow "Li Yi Fen Shu", but the latter is the generalized one. This article won't discuss the generalized one, and it will take the narrow one as the research object. In the past research in academic circles, some scholars thinks that the proposition of "Li Yi Fen Shu" accords with the aim of Xi Ming, some others don't think so. Contrary to both of the two views, this article thinks that there is some conformity and inconformity between the explanatory model of "Li Yi Fen Shu" of Chu Hsi and the aim of Xi Ming. In other words, Contributions and limitations coexist when Chu Hsi explains Xi Ming in the model of "Li Yi Fen Shu", and there is not only the development to the intention of Xi Ming, but alsothe far meaning away from the aim of Xi Ming.

### 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 ($3\;{\div}\;\frac{1}{2}$).