• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.53-68
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• 2012

This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.317-328
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• 2011

We analyzed errors committed by Korean prospective elementary teachers in finding and interpreting quotient and remainder within measurement division of fractions. 65 prospective elementary teachers were participated in this study. They solved a word problem about measurement division of fractions. We analyzed solutions of all participants, and interviewed 5 participants of them. The results reveal many of these prospective teachers could not tell what fractional part of division result means. Thses results suggest that teacher preparation program should emphasize interpreting calculation results within given situations.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.197-201
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• 2013

Let D be an integral domain with quotient field K, * a star-operation on D, $GV^*(D)$ the set of nonzero finitely generated ideals J of D such that $J_*=D$, and $*_{\omega}$ a star-operation on D defined by $I_{*_{\omega}}=\{x{\in}K{\mid}Jx{\subseteq}I\;for\;some\;J{\in}GV^*(D)\}$ for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for $*_{\omega}$-Noetherian domains.

• Journal of information and communication convergence engineering
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• v.16 no.2
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• pp.114-124
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• 2018

This paper illustrates a vision-based vehicle positioning method at an intersection to support the C-ITS. It removes the minor shadow that causes the merging problem by simply eliminating the fractional parts of a quotient image. In order to separate the occlusion, it firstly performs the distance transform to analyze the contents of the single foreground object to find seeds, each of which represents one vehicle. Then, it applies the watershed to find the natural border of two cars. In addition, a general vehicle model and the corresponding space estimation method are proposed. For performance evaluation, the corresponding ground truth data are read and compared with the vision-based detected data. In addition, two criteria, IOU and DEER, are defined to measure the accuracy of the extracted data. The evaluation result shows that the average value of IOU is 0.65 with the hit ratio of 97%. It also shows that the average value of DEER is 0.0467, which means the positioning error is 32.7 centimeters.

• School Mathematics
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• v.4 no.4
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• pp.633-642
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• 2002

This paper focuses on the concepts of a value of ratio and a rate in elementary school mathematics. Although the concept of a value of ratio can be distinguished meaningfully from that of a rate by phenomenological analyses, this distinction is impossible at the elementary school level. Two concepts tend to be treated as identical, therefore they need to be classified by the other methods. By analyzing the series of mathematics textbooks from the first curriculum to the present 7th curriculum, this paper investigated how two concepts have been transposed into the products of school mathematics. In addition, we discussed how the difference of two concepts in the changing process of definitions have been presented clearly to the students. As a result, this paper concluded that the difference of two concepts has not been developed clearly for elementary students in general, except the textbook by the 7th curriculum. The definitions of two concepts were described obscurely so that the students may confuse the concept of a value of ratio with that of a rate. The role of a value of ratio needs to be reconsidered when it is applied to set proportional expressions. Therefore, this paper suggests not adhering to the terminology ‘value of ratio’ to present the ratio as a quotient or the rate as a fractional representation in school mathematics.

• Korean Journal of Biological Psychiatry
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• v.22 no.2
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• pp.78-86
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• 2015

Objectives Although ginseng has been reported to protect neuronal cells and improve various cognitive functions, relationship between ginseng supplementation and response inhibition, one of the important cognitive domains has not been explored. In addition, effects of ginseng on in vivo human brain have not been investigated using the diffusion tensor imaging (DTI). The purpose of the current study is to investigate changes in intrusion errors and white matter microstructure after Korean Red Ginseng supplementation using standardized neuropsychological tests and DTI. Methods Fifty-one healthy participants were randomly allocated to the Korean Red Ginseng (n = 26) or placebo (n = 25) groups for 8 weeks. The California Verbal Learning Test was used to assess the number of intrusion errors. Intelligence quotient (IQ) was measured with the Korean Wechsler Adult Intelligence Scale. Depressive and anxiety symptoms were evaluated using Hamilton Depression Rating Scale, Hamilton Anxiety Rating Scale, and Hopkins Symptom Checklist-25. The fractional anisotropy (FA) was measured from the brain DTI data. Results After the 8-week intervention, Korean Red Ginseng supplementation significantly reduced intrusion errors after adjusting age, sex, IQ, and baseline score of the intrusion errors (p for interaction = 0.005). Change in FA values in the left anterior corona radiata was greater in the Korean Red Ginseng group compared to the placebo group (t = 4.29, p = 0.04). Conclusions Korean Red Ginseng supplementation may be efficacious for improving response inhibition and white matter microstructure integrity in the prefrontal cortex.