• 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.

• 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.

• 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.

• 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 Aquaculture
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• v.6 no.3
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• pp.199-211
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• 1993

In order to elucidate the effect of dietary n-3 highly unsaturated fatty acids (n-3HUFA) on the changes of body weight and chemical compositions in the Korean rockfish during starvation, the fish were not fed for 9 weeks after fed different levels $(0\~1.5\%)$ of n-3 HUFA for 10 weeks. The higher level of n-3HUF A was contained in the diets, the slower body weight loss was resulted (P< 0.05). The decreasing rates of the body nutrients of the fish were significantly higher in the fish fed n-3HUF A deficient diets than those of the fish fed n-3 HUF A sufficient diets. Protein and lipid contents of the whole body were decreased with starvation whereas moisture content was increased. Decrease of lipid was mainly due to the decrease of nonpolar lipid. Amounts of polar lipid in the whole body were almost constant throughout the starvation, meaning not being affected by dietary n-3HUF A levels. Percentage of 22: 6n-3 was increased in the polar lipid fraction, but monoenic acids (16:1, 18:1), n-3 series (18:3, 18 4, 20:4) and n-6 series (20:2, 22:4, 22:5) were decreased with starvation. Fatty acid compositions of nonpolar lipid were not changed with starvation. These results suggest that all fatty acids of nonpolar lipid are equally utilized for energy during starvation.