• 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.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.101-112
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• 2002

Gu-Jang-San-Sul is a book of Chinese ancient mathematics and has had an impact on Korean mathematics. The book is organized into nine chapters and each chapter is composed of problems, answers, and their computation algorithms. The contents reflect the practicality of Chinese mathematics. Especially the first chapter covers the computation of fractions for land surveying. This paper suggests how the computation methodology is used in teaching fractions for primary school students. Five strategies for fractions related to the reduction, addition, subtraction, multiplication, and division are followed by: 1) developing the ability to apply rules to problems by practicing the computation process according to the given algorithm; 2) developing the communication skill by comparing the differences of various computation algorithms; 3) setting computation problems; 4) understanding the characteristics of terminology in mathematics; and 5) being exposed to new ideas in mathematics.

• Steel and Composite Structures
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• v.27 no.3
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• pp.297-310
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• 2018

A simple and efficient numerical optimization approach for the lightweight optimal design of composite laminated beams is presented in this paper. The proposed procedure is a combination between the finite element method (FEM) and a global optimization algorithm developed recently, namely Jaya. In the present procedure, the advantages of FEM and Jaya are exploited, where FEM is used to analyze the behavior of beam, and Jaya is modified and applied to solve formed optimization problems. In the optimization problems, the objective aims to minimize the overall weight of beam; and fiber volume fractions, thicknesses and fiber orientation angles of layers are selected as design variables. The constraints include the restriction on the first fundamental frequency and the boundaries of design variables. Several numerical examples with different design scenarios are executed. The influence of the design variable types and the boundary conditions of beam on the optimal results is investigated. Moreover, the performance of Jaya is compared with that of the well-known methods, viz. differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO). The obtained results reveal that the proposed approach is efficient and provides better solutions than those acquired by the compared methods.

• Computers and Concrete
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• v.9 no.5
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• pp.389-402
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• 2012

In this study, the modulus of elasticity of low, normal and high strength steel fiber reinforced concrete has been predicted by developing a fuzzy logic model. The fuzzy models were formed as simple rules using only linguistic variables. A fuzzy logic algorithm was devised for estimating the elastic modulus of SFRC from compressive strength. Fibers used in all of the mixes were made of steel, and they were in different volume fractions and aspect ratios. Fiber volume fractions of the concrete mixtures have changed between 0.25%-6%. The results of the proposed approach in this study were compared with the results of equations in standards and codes for elastic modulus of SFRC. Error estimation was also carried out for each approach. In the study, the lowest error deviation was obtained in proposed fuzzy logic approach. The fuzzy logic approach was rather useful to quickly and easily predict the elastic modulus of SFRC.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.385-403
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• 2018

Fraction division can be categorized as partitive division, measurement division, and the inverse of a Cartesian product. In the contexts of quotitive division and the inverse of a Cartesian product, the multiply-by-the-reciprocal algorithm is drawn well out. In this study, I analyze the potential and significance of the method of using $1{\div}$(divisor) as an alternative way of developing the multiply-by-the-reciprocal algorithm in the context of quotitive division. The method of using $1{\div}$(divisor) in quotitive division has the following advantages. First, by this method we can draw the multiply-by-the-reciprocal algorithm keeping connection with the context of quotitive division. Second, as in other contexts, this method focuses on the multiplicative relationship between the divisor and 1. Third, as in other contexts, this method investigates the multiplicative relationship between the divisor and 1 by two kinds of reasoning that use either ${\frac{1}{the\;denominator\;of\;the\;divisor}}$ or the numerator of the divisor as a stepping stone. These advantages indicates the potential of this method in understanding the multiply-by-the-reciprocal algorithm as the common structure of fraction division. This method is based on the dual meaning of a fraction as a quantity and the composition of times which the current elementary mathematics textbook does not focus on. It is necessary to pay attention to how to form this basis when developing teaching materials for fraction division.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.1-18
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• 2011

The purpose of this study was to investigate the effects of estimation strategy on placing decimal point in multiplication and division of decimals. To examine the effects of improving calculation ability and reducing decimal point errors with this estimation strategy, the experimental research on operation with decimal was conducted. The operation group conducted the decimal point estimation strategy for operating decimal fractions, whereas the control group used the traditional method with the same test paper. The results obtained in this research are as follows; First, the estimation strategy with understanding a basic meaning of decimals was much more effective in calculation improvement than the algorithm study with repeated calculations. Second, the mathematical problem solving ability - including the whole procedure for solving the mathematical question - had no effects since the decimal point estimation strategy is normally performed after finishing problem solving strategy. Third, the estimation strategy showed positive effects on the calculation ability. Th Memorizing algorithm doesn't last long to the students, but the estimation strategy based on the concept and the position of decimal fraction affects continually to the students. Finally, the estimation strategy assisted the students in understanding the connection of the position of decimal points in the product with that in the multiplicand or the multiplier. Moreover, this strategy suggested to the students that there was relation between the placing decimal point of the quotient and that of the dividend.

• Journal of the Korean earth science society
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• v.42 no.6
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• pp.623-631
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• 2021

The increased transport of marine hazardous and noxious substances (HNS) has resulted in frequent HNS spill accidents domestically and internationally. There are about 6,000 species of HNS internationally, and most of them have toxic properties. When an accidental HNS spill occurs, it can destroys the marine ecosystem and can damage life and property due to explosion and fire. Constructing a spectral library of HNS according to wavelength and developing a detection algorithm would help prepare for accidents. In this study, a ground HNS spill experiment was conducted in France. The toluene spectrum was determined through hyperspectral sensor measurements. HNS present in the hyperspectral images were detected by applying the spectral mixture algorithm. Preprocessing principal component analysis (PCA) removed noise and performed dimensional compression. The endmember spectra of toluene and seawater were extracted through the N-FINDR technique. By calculating the abundance fraction of toluene and seawater based on the spectrum, the detection accuracy of HNS in all pixels was presented as a probability. The probability was compared with radiance images at a wavelength of 418.15 nm to select abundance fractions with maximum detection accuracy. The accuracy exceeded 99% at a ratio of approximately 42%. Response to marine spills of HNS are presently impeded by the restricted access to the site because of high risk of exposure to toxic compounds. The present experimental and detection results could help estimate the area of contamination with HNS based on hyperspectral remote sensing.