• Journal of Gifted/Talented Education
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• v.24 no.1
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• pp.17-43
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• 2014

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.

• School Mathematics
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• v.7 no.2
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• pp.139-168
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• 2005

The purpose of this study is to investigate children's informal knowledge of the fractional multiplication and to develop a teaching material connecting the informal and the formal knowledge. Six lessons of the pre-teaching material are developed based on literature reviews and administered to the 7 students of the 4th grade in an elementary school. It is shown in these teaching experiments that children's informal knowledge of the fractional multiplication are the direct modeling of using diagram, mathematical thought by informal language, and the representation with operational expression. Further, teaching and learning methods of formalizing children's informal knowledge are obtained as follows. First, the informal knowledge of the repeated sum of the same numbers might be used in (fractional number)$\times$((natural number) and the repeated sum could be expressed simply as in the multiplication of the natural numbers. Second, the semantic meaning of multiplication operator should be understood in (natural number)$\times$((fractional number). Third, the repartitioned units by multiplier have to be recognized as a new units in (unit fractional number)$\times$((unit fractional number). Fourth, the partitioned units should be reconceptualized and the case of disjoint between the denominator in multiplier and the numerator in multiplicand have to be formalized first in (proper fractional number)$\times$(proper fractional number). The above teaching and learning methods are melted in the teaching meterial which is made with corrections and revisions of the pre-teaching meterial.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.105-122
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• 2014

In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.2
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• pp.191-196
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• 2016

Van der Pol's oscillators is non-conservative oscillator that having nonlinear damping phenomena. The energy of its system is dissipative at a high amplitude whereas its system creates the energy at low amplitude. This paper deals with the Van der Pol oscillator model with a fractional order when the external force apply into Van der Pol oscillator. This paper confirms the status of variation for the limit cycle according to the parameter variation of fractional order in the Van der Pol oscillator that can be represented by fractional differential equation.

• School Mathematics
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• v.12 no.3
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• pp.411-424
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• 2010

The fractional concept consists of various meaning, so that it is difficult to understand in primary school mathematics. In this article, we intend to analyze the cognition of 54 pre-service elementary teachers about the operations of partitioning and iterating that are based on Steffe's fraction schemes. The following fraction problem is used in this analysis: If the bar $\Box$ represent 3/8, then create a bar that is equivalent to 4/3. In our analysis, the 43% of pre-service elementary teachers can be well to treat the operations of partitioning and iteration. The 33% are use the equivalent fractions. But the 19% is not good. From the our analysis, it is important that pre-service elementary teachers must be have experimental(operational) thinking as the science education. And in this study we apply the operations of partitioning and iterating to the fraction activity of textbooks.

• 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.

• School Mathematics
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• v.16 no.4
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• pp.783-802
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• 2014

The purpose of this study was to explore in detail students' understanding of fraction as quotient. A total of 158 sixth graders in 6 elementary schools were surveyed by 8 tasks in relation to fraction as quotient. As a result, students used various partitioning strategies to solve the given sharing tasks such as partitioning the singleton unit, the composite unit, or the whole unit of the dividend. They also used incorrect partitioning strategies that were not appropriate to the given context. Students' partitioning strategies and performance of fraction as quotient varied depending on the given contexts and models. This study suggests that students should have rich experience to partition various units and reinterpret the context based on the singleton unit of the dividend.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.686-686
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• 2012

일반적으로 첨두 홍수량 경감을 위하여 유역종합치수계획 등에서 많이 계획되고 있는 방수로는 방수로 종단에서의 방류 방식에 따라 크게 자기 완결 방식과 타 하천 또는 해양 방류 방식으로 구분할 수 있다. 일반적으로 타 하천 또는 해양 방류 방식을 방수로라 부르며, 홍수 방어의 대상이 되는 지역을 우회하여 다시 본천으로 합류하는 자기 완결 방식으로 계획되는 방수로 즉 홍수 방어용 수로를 분수로라 부른다. 방수로를 계획하는 경우 가장 중요한 것은 본류에서의 첨두 홍수량 분담이기 때문에 방수로로 유입되는 분류량을 정확히 예측하는 것이 매우 중요하다. 하지만 분수로의 경우 다시 본천으로 재합류하기 때문에 재합류되는 지역에서 본류의 유량이 다시 크게 증가하고, 합류점 상류에서 예상치 못한 홍수위의 상승이 발생할 가능성이 있다. 따라서 만약 합류부에서 유황에 대한 적절한 검토 없이 합류 지역을 설계하는 경우 예상치 못한 수위 상승 및 국부 유속 증가에 의한 홍수 피해가 발생할 가능성이 있다. 따라서 본 연구에서는 분수로 형태의 방수로가 일정한 합류각을 가지고 본류로 합류하는 경우 본류에서의 유황 변화 및 수위 상승이 어떠한 형태로 나타나는지 실험을 통하여 검토하고자 하였다. 합류하는 분수로의 폭은 본수로의 폭이 에 대하여 0.50B, 0.75B, 1.00B가 되도록 하였으며, 합류각은 본류와 분수로 사이의 예각이 75도가 되도록 하였다. 이러한 수로 제원에 대하여 본류 유량 및 유입량을 다양하게 변화시켜 합류부에서의 수위 변화를 검토하였다.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.153-166
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• 2017

164 preservice elementary teachers' decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

• Proceedings of the KIEE Conference
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• 2015.07a
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• pp.1438-1439
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• 2015

수질정화를 위하여 여러 가지 방법이 연구되고 있다. 지금까지의 연구결과는 분수대고정 콘크리트 시공에 따른 유동적인 효과의 미흡과 1.2m이상의 높은곳에 위치함으로써 효율저하가 있었으나 본연구는 효율저하를 막고 수중펌프 흡입구와 분수노줄막힘을 방지하기 위하여 0.7m의 높이에 수질정화장치를 설치하고 임펠러 회전체를 개방함으로써 보다 높은 성능을 가진 수질 정화장치용 분수를 만들어 안전도를 증가 시켰다.