• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.233-249
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• 2005

This study discusses on the historico-genetic instruction on fraction. The textbooks of the current curriculum include the variety of contexts of fraction to be intended to connect with the conception of ratio in the grade 6. However mary elementary students have understanding limited to whole-part relation only. This study propose a method on the basis of the process of measurement by an absolute unit. The idea is related to The genesis of fraction in Egypt.

• 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.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.

• 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.

• 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.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

• Proceedings of the Optical Society of Korea Conference
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• 2000.08a
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• pp.68-69
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• 2000

최근 정보 통신 및 우주 항공 분야 등에서 정밀한 시계에 대한 필요성이 증가함에 따라 현재의 원자시계 보다 더 우수한 원자시계에 대한 개발이 요구되고 있다. 이러한 요구에 부응하여 새로운 원자시계에 관한 연구가 활발히 진행되고 있다. 특히, 레이저 냉각기술이 발명됨에 따라 레이저 냉각된 원자를 이용하여 원자시계를 제작하려는 연구들이 있는데, 그 중에서 원자분수 방식을 이용하는 주파수표준기가 차세대 원자시계로 기대되고 있다. 원자분수 주파수표준기는 이미 프랑스 LPTF에서 제작하여 그 불확도가 3$\times$$10^{15}$인 것으로 알려져 있다. 한국표준과학연구원에서도 1996 년부터 원자분수 주파수 표준기 개발을 위한 예비실험으로 원자의 온도를 수 $\mu$K 까지 냉각하였으며, 자유낙하하는 원자의 형광을 관측하여 온도를 측정하였다. 이러한 일련의 예비실험을 통하여 레이저 냉각 기술 및 형광측정 능력 등을 확보하고 본격적인 원자분수 주파수표준기 제작에 착수하였다. (중략)

• The Mathematical Education
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• v.62 no.1
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• pp.1-21
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• 2023

The purpose of this study is to explore how the student, who interiorized three levels of units, constructed fractions as multipliers by analyzing her ways of conceiving improper fractions with three levels of units and coordinating two three-levels-of-units structures. Among the data collected from our teaching experiment with two 4th grade students meeting 13 times for three months, we focus on how Seyeon, one of the participating students, wrote numerical expressions in the form of "× fraction" for the given situations using her splitting operation for composite units. Given the importance of splitting operation for composite units for the construction of fractions as multipliers, implications for further research are discussed.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.537-555
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• 2017

This paper compared and contrasted Korean and Singaporean textbooks in order to explore the direction and possibility of teaching the big ideas related to the addition and subtraction of fractions with different denominators proposed by Lee & Pang (2016a). Firstly, we examined the teaching sequences related to the addition of fractions with different denominators in a series of elementary mathematics textbooks of Korea and Singapore. We then analyzed what types of representations are used and how the representations are presented for the big ideas related to the addition of fractions with different denominators. The results of the analysis showed that the contents related to fraction addition are addressed more gradually and systematically in Singaporean textbooks compared to Korean counterparts. The graphical representations appeared in the Singaporean textbooks provide specific implications for teaching the big ideas of the addition of fractions with different denominators. Based on such implications, we expect that the big ideas related to the addition of fractions with different denominators will be addressed explicitly and systematically in Korean textbooks.