• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.59-78
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• 2008

The purpose of this study was to research and analyze students' informal knowledge before they learned formal knowledge about fraction concepts and to see how to apply this informal knowledge to teach fraction concepts. According to this purpose, research questions were follows. 1) What is the students' informal knowledge about dividing into equal parts, the equivalent fraction, and comparing size of fractions among important and primary concepts of fraction? 2) What are the contents to can lead bad concepts among students' informal knowledge? 3) How will students' informal knowledge be used when teachers give lessons in fraction concepts? To perform this study, I asked interview questions that constructed a form of drawing expression, a form of story telling, and a form of activity with figure. The interview questions included questions related to dividing into equal parts, the equivalent fraction, and comparing size of fractions. The conclusions are as follows: First, when students before they learned formal knowledge about fraction concepts solve the problem, they use the informal knowledge. And a form of informal knowledge is vary various. Second, among students' informal knowledge related to important and primary concepts of fraction, there are contents to lead bad concepts. Third, it is necessary to use students' various informal knowledge to instruct fraction concepts so that students can understand clearly about fraction concepts.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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 ($3\;{\div}\;\frac{1}{2}$).

• 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.

• 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.

• School Mathematics
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• v.17 no.4
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• pp.571-591
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• 2015

Even though fractions make up one of the most important concepts in the domain of numbers in elementary math, it is difficult to teach or learn them due to their different quantity concepts and notation methods from natural numbers and their various concepts. The didactic transposition of fractions is thus important, and there is a need to examine the didactic concepts of fractions used in the South Korean textbooks for its research. This study compared elementary math textbooks among South Korea, Taiwan, and China and investigated differences in the instructional time and order of fraction concepts in the textbooks according to their didactic concepts and also differences in the instructional methods according to quantitative concepts.