• Education of Primary School Mathematics
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• v.26 no.3
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• pp.181-197
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• 2023

The importance of reasoning processes based on fractional concepts and number senses, rather than a formalized procedural method using common denominators, has been noted in a number of studies in relation to compare the magnitudes of unlike fractions. In this study, a unlike fraction magnitudes comparison test was conducted on fourth-grade elementary school students who did not learn equivalent fractions and common denominators to analyze the reasoning perspectives of the correct and wrong answers for each of the eight problem types. As a result of the analysis, even students before learning equivalent fractions and reduction to common denominators were able to compare the unlike fractions through reasoning based on fractional sense. The perspective chosen by the most students for the comparison of the magnitudes of unlike fractions is the 'part-whole perspective', which shows that reasoning when comparing the magnitudes of fractions depends heavily on the concept of fractions itself. In addition, it was found that students who lack a conceptual understanding of fractions led to difficulties in having quantitative sense of fraction, making it difficult to compare and infer the magnitudes of unlike fractions. Based on the results of the study, some didactical implications were derived for reasoning guidance based on the concept of fractions and the sense of numbers without reduction to common denominators when comparing the magnitudes of unlike fraction.

• 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.

• 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.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.17-37
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• 2015

In this paper, we compared and analyzed the Korean National Mathematics textbooks of the 2007 amendment curriculum and the Harcourt Math in America focused on fractions and decimals. To summarize the results of the analysis are as follows. First, both textbooks introduce fractions to the meaning of parts-whole concept, but the Harcourt Math is stronger than that of Korean Mathematics textbooks in the concept of unit fractions as a generator of fractions. Second, the fractions can be considered trivial materials - a fraction representing 1 whole, a fraction with it's denominator is 1 - were more clearly represented in our US textbooks than those of our Korean textbooks. Third, in the introduction of the term relating to the fractions, Korea is a strong point of view of the classification of fractions than the point of view of representation in comparison with the case of the United States. Fourth, the equivalent fraction and equivalent decimal concepts were described more detail in the United States of textbooks than those of the case of Korean textbooks. Finally, the approaches of fraction and decimal concepts were introduced more mathematically in the case of the United States than those of the case of Korean textbooks.

• 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 ($3\;{\div}\;\frac{1}{2}$).

• School Mathematics
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• v.11 no.4
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• pp.685-706
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• 2009

This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

• School Mathematics
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• v.5 no.3
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• pp.385-399
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• 2003

In our present elementary mathematics curriculum, natural numbers are taught by using the a method of one-to-one correspondence or counting operation which are not related to measurement, and fractional numbers are taught by using a method which is partially related to measurement. The most serious limitation of these teaching methods is that natural numbers and fractional numbers are separated. To overcome this limitation, Dewey and Davydov insisted that the natural number and the fractional number should be taught by measurement of quantity. In this article, we suggested a method of teaching the natural number and the fractional number by measurement of quantity based on the claims of Dewey and Davydov, and compare it with our current method. In conclusion, we drew some educational implications of teaching the natural number and the fractional number by measurement of quantity as follows. First, the concepts of the natural number and the fractional number evolve from measurement of quantity. Second, the process of transition from the natural number to the fractional number became to continuous. Third, the natural number, the fractional number, and their lower categories are closely related.

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.213-232
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• 2022

With the importance of number line in learning fractions, this study investigated how 4th grade students understand fractions and its operations in number line. The questionnaire consisted 22 items which were related to representing fractions, comparing the size of fractions, and operating addition and subtraction of fractions. Both structured number line and sub-structured number line were presented in the items. As results of the study, the overall success rates were not high and even some items showed higher incorrect answer rates than the success rates. Also, the students showed a difficulty in solving non-structured number line tasks. It was also noticeable that students showed several types of incorrect answers, which means that students had incomplete understanding of both fractions and number line. This paper is expected to shed light on elementary students' understanding of fractions and number line and to provide implications of how to deal with number line in teaching and learning fractions in the elementary school.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.154-160
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• 1997

On the base of the fractional Fourier transform(FRT) which is known as a generalized form of the conventional Fourier transform, the fractional correlation has been implemented. Shift-variance property of the fraction correlation has been evaluated and compared with the shift-invariance of the conventional correlation. The fractional correlation operation has been implemented by using a planar optics configuration which integrates all of the optical components on a single glass substrate. A good agreement between the experimental and calculated results has been obtained.