• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.25-43
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• 2009

The fraction concept consists of various meanings and is one of the abstract and difficult in elementary school mathematics. This study intends to find out the implication for introducing the fraction concept by comparing mathematics textbooks of Korea and Singapore. Both countries' students peformed well in recent TIMMSs. Some implications are as follows; The term 'equal' is not defined and the results of various 'equal partitioning' activities can not easily examined in Korea's mathematics textbook. And contexts of introducing fractions as a quotient and a ratio are unnatural in Korea's mathematics textbook in comparison with Singapore's mathematics textbook. So these ideas should be reconsidered in order to seek the direction for improvement of it. And Korea's textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction.

• The Korean Journal of Financial Management
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• v.18 no.1
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• pp.23-41
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• 2001

본 연구에서는 여러 계량 모형을 이용하여 계산한 헤지 비율의 성과를 비교하였다. 특히 헤지 비율을 추정하기 위하여 분수 공적분 오차 수정 모형을 이용하였다. KOSPI200 현물과 선물 지수를 이용하여 검증한 결과 현물, 선물 지수는 1차 적분된 시계열이며 베이시스는 분수 적분된 시계열이었다. 따라서 현물과 선물 지수는 분수 공적분된 시계열이었다. 최소 분산 헤지 비율을 최적 헤지 비율로 하여 성과를 측정한 결과 다음과 같은 결과를 얻었다. 헤지 성과는 GARCH 항이 있는 모형이 없는 모형에 비해 크게 나타나며 각 모형에서 고려하고 있는 정보 집합의 크기가 큰 순서인 FIEC, EC, VAR, OLS 순으로 헤지 성과는 크게 나타나고 있다. 그러나 OLS 방법에 의한 헤지에 의해서도 수익률 변동의 많은 부분이 사라져, 다른 모형들은 OLS 모형과 비교하여 추가적인 분산 감소 효과는 크지 않았다.

• Education of Primary School Mathematics
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• v.16 no.2
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• pp.93-106
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• 2013

A large part of students' difficulties with fractional division algorithms in the current algorithm textbooks, seem to be due to self-induction methods. Through concrete analysis of surveys and interviews, we confirmed the educational value of fractional algorithms used to elicit alternative ways of context of determination of a unit rate. In addition, we suggested alternative methods based on the results of the teaching methods and curriculum configuration.

• 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.1
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• pp.83-102
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• 2014

The purpose of this study was to explore students' understanding on units embedded in multiple interpretations of fractions: (a) part-whole relationships, (b) measures, (c) quotients, (d) ratios, and (e) operators. A total of 150 sixth graders in elementary schools were surveyed by a questionnaire comprised of 20 tasks in relation to multiple interpretations of fractions. As results, students' performance on units varied depending on the interpretations of fractions. Students had a tendency to regard the given whole as the unit, which led to incorrect answers. This study suggests that students should have rich experience to identify and operate various units in the context of multiple fractions.

• 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.

• School Mathematics
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• v.6 no.3
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• pp.235-249
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• 2004

The purpose of this study was to analyze the error patterns and sentence types in word problems with respect to 1$\frac{3}{4}$$\div$$\frac{1}{2}$ which were made by the pre-service elementary teachers, and to suggest the clues to the education in pre-service. Korean elementary teachers in pre-service misunderstood 'divide with $\frac{1}{2}$' to 'divide to 2' by the Korean linguistic structure. And they showed a new error type of 1$\frac{3}{4}$$\times$2 by the result of calculation. Although they are familiar to 'inclusive algorithm' they are not good at dealing with the fractional divisor. And they are very poor at the 'decision the unit proportion' and the 'inverse of multiplication'. So, it is necessary to teach the meaning of the fractional division as 'decision the unit proportion' and 'inverse of multiplication' and to give several examples with respect to the actual situation and context.

• School Mathematics
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• v.7 no.2
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• pp.103-121
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• 2005

This article compares and analyzes mathematics textbooks of North Korea, South Korea, China and Japan and draws meaningful ways for introducing the division algorithm of fractions. The analysis is based on the five contexts: 'measurement division', 'determination of a unit rate', 'reduction of the quantities in the same measure', 'division as the inverse of multiplication or Cartesian product', 'analogy with multiplication algorithm of fractions'. The main focus of the analysis is what context is used to introduce the algorithm and how much it can appeal to students. This analysis supports that there is a few differences of introducing methods the division algorithm of fractions among those countries and more meaningful way can be considered than ours. It finally suggests that we teach the algorithm in a way which can have students easily see the reason of multiplying the reciprocal of a divisor when they divide with fractions. For this, we need to teach the meaning of a reciprocal of fraction and consider to use the context of determination of a unit rate.

• Communications of Mathematical Education
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• v.29 no.2
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• pp.215-239
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• 2015

A goal of this study is figuring out how fraction learning centered on various representation activities influences the fraction comprehension and mathematical attitudes. The study focused on 33 4th-grade students of B elementary school in Seoul. In the study, 15 fraction learning classes comprising enactive, iconic, and symbolic representations took place over 6 weeks. After the classes, the ratio of the students who achieved relational understanding increased and the students averagely recorded 90 pt or more on the fraction comprehension test I, II and III. Two-dependent samples t-test was conducted to analyze a significant difference in mathematical attitudes between pre-test and post-test. On the test result, there was the meaningful difference with 0.01 level of significance. To conclude, the fraction learning centered on various representation activities improves students' relational understanding and fraction understanding. In addition, the fraction learning centered on various representation activities gives positive influences on mathematical attitudes since it increases learning orientation, self-control, interests, value cognition, and self-confidence of the students and decreases fears of the students.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.