• Research in Mathematical Education
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• v.22 no.4
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• pp.283-304
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• 2019

This paper investigates what informal knowledge and strategies fifth-grade students brought to a classroom and how much they had potential to solve fraction division story problems. The findings show that most of the participants were engaged to understand the meaning of fraction division prior to their formal instruction at school. In order to solve the story problems, the informal knowledge related to fractions as well as division was actively utilized in student's strategies and justification. Students also used various informal strategies from mental calculation, direct modeling, to relational thinking. Formal instructions about fraction division at schools can be facilitated for sense-making of this complex fraction division conception by unpacking informal knowledge and thinking they might bring to the classrooms.

• East Asian mathematical journal
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• v.32 no.4
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• pp.565-587
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• 2016

The purpose of this study was to analyze the understanding of the meaning of fraction division and fraction division algorithm of elementary mathematical gifted students through the process of problem posing and solving activities. For this goal, students were asked to pose more than two real-world problems with respect to the fraction division of ${\frac{3}{4}}{\div}{\frac{2}{3}}$, and to explain the validity of the operation ${\frac{3}{4}}{\div}{\frac{2}{3}}={\frac{3}{4}}{\times}{\frac{3}{2}}$ in the process of solving the posed problems. As the results, although the gifted students posed more word problems in the 'inverse of multiplication' and 'inverse of a cartesian product' situations compared to the general students and pre-service elementary teachers in the previous researches, most of them also preferred to understanding the meaning of fractional division in the 'measurement division' situation. Handling the fractional division by converting it into the division of natural numbers through reduction to a common denominator in the 'measurement division', they showed the poor understanding of the meaning of multiplication by the reciprocal of divisor in the fraction division algorithm. So we suggest following: First, instruction on fraction division based on various problem situations is necessary. Second, eliciting fractional division algorithm in partitive division situation is strongly recommended for helping students understand the meaning of the reciprocal of divisor. Third, it is necessary to incorporate real-world problem posing tasks into elementary mathematics classroom for fostering mathematical creativity as well as problem solving ability.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.319-339
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• 2014

Recently, the discussion about division and partition of fraction increases in Korea's national curriculum documents. There are varieties of assertions arranging from the opinion that both interpretations are unintelligible to the opinion that both interpretations are intelligible. In this paper, we investigated a possibility that division and partition interpretation of fraction become valid. As a result, it is appeared that division and partition interpretation of fraction can be defined reasonably through expansion of interpretation of natural number. Besides, division and partition interpretation of fraction can be work in activity, such as constructing equation from sentence problem, or such as proving algorithm of fraction division.

• 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.

• School Mathematics
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• v.11 no.1
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• pp.71-91
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• 2009

The purpose of this study was to analyze operation sense in detail with regard to division of fraction. For this purpose, two sixth grade students who were good at calculation were clinically interviewed three times. The analysis was focused on (a) how the students would understand the multiple meanings and models of division of fraction, (b) how they would recognize the meaning of algorithm related to division of fraction, and (c) how they would employ the meanings and properties of operation in order to translate them into different modes of representation as well as to develop their own strategies. This paper includes several episodes which reveal students' qualitative difference in terms of various dimensions of operation sense. The need to develop operation sense is suggested specifically for upper grades of elementary school.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.715-731
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• 2005

There are five contexts of division algorithm of fractions such as measurement division, determination of a unit rate, reduction of the quantities in the same measure, division as the inverse of multiplication and analogy with multiplication algorithm of fractions. The division algorithm, however, should be taught by 'dividing by using reciprocals' via 'measurement division' because dividing a fraction by a fraction results in 'multiplying the dividend by the reciprocal of the divisor'. If a fraction is divided by a large fraction, then we can teach the division algorithm of fractions by analogy with 'dividing by using reciprocals'. To achieve the teaching-learning methods above in elementary school, it is essential for children to use the maniplatives. As Piaget has suggested, Cuisenaire color rods is the most efficient maniplative for teaching fractions. The instruction, therefore, of division algorithm of fractions should be focused on 'dividing by using reciprocals' via 'measurement division' using Cuisenaire color rods through analogy if necessary.

• Journal of Gifted/Talented Education
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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.

• Food Science and Biotechnology
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• v.18 no.1
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• pp.124-129
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• 2009

Antioxidant activities of the extract of red seaweed, Polysiphonia morrowii, were evaluated using several in vitro assay systems. Activity-guided fractionation revealed that the 90% MeOH fraction of the P. morrowii extract exhibited the highest antioxidant activity, and that this fraction had a high total phenolic content ($135.7{\pm}5.0\;mg$ gallic acid/g extract). Therefore, the antioxidant activities of the 90% MeOH fraction against 2,2-diphenyl-1-picrylhydrazyl (DPPH), hydroxyl radical, reducing power, ferrous chelating, and hydrogen peroxide were investigated. The results revealed that the antioxidant activities of the 90% MeOH fraction were similar and/or superior to that of commercial antioxidants such as butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT). In addition, the ability of the 90% MeOH fraction to inhibit oxidative damage to DNA was assessed by measuring the conversion of the supercoiled pBR322 plasmid DNA to the open circular form. The 90% MeOH fraction was found to significantly protect this hydroxyl radical-induced DNA damage in a dose-dependent manner. Taken together, these findings suggest that the 90% MeOH fraction of P. morrowii extract and/or its constituents has the potential for use as a new bioresource of antioxidants.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.521-539
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• 2016

The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.