• The Mathematical Education
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• v.51 no.1
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• pp.21-45
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• 2012

The purpose of the study was to investigate how students understand each operations with whole numbers and fractions, and the relationship between their knowledge of operations with whole numbers and conceptual understanding of operations on fractions. Researchers categorized students' understanding of operations with whole numbers and fractions based on their semantic structure of these operations, and analyzed the relationship between students' understanding of operations with whole numbers and fractions. As the results, some students who understood multiplications with whole numbers as only situations of "equal groups" did not properly conceptualize multiplications of fractions as they interpreted wrongly multiplying two fractions as adding two fractions. On the other hand, some students who understood multiplications with whole numbers as situations of "multiplicative comparison" appropriately conceptualize multiplications of fractions. They naturally constructed knowledge of fractions as they build on their prior knowledge of whole numbers compared to other students. In the case of division, we found that some students who understood divisions with whole numbers as only situations of "sharing" had difficulty in constructing division knowledge of fractions from previous division knowledge of whole numbers.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.1-16
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• 2011

This study is to review division of whole numbers which is dealt in the revised elementary mathematics textbook and manual for teacher. The textbook and manual for teachers are most important documents to teach mathematics. And they are important to the would-be teachers who study the elementary mathematics with such documents. Therefore the textbook and manual for teachers should have no errors. But I found they have some errors and problems regarding division of whole numbers. In this paper, I discuss the problems and suggest the alternative plans.

• The Journal of Korean Physical Therapy
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• v.25 no.5
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• pp.260-265
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• 2013

Purpose: This study was conducted in order to evaluate the quantitative effectiveness of region of interest (ROI) setting in MR-DTI analysis with and without fMRI activation results. Methods: Ten right-handed normal volunteers participated in this study. DTI and fMRI datasets for each subject were obtained using a 1.5T MRI system. For neural fiber tracking, ROIs were drawn using two methods: The drawing points were located in the fMRI activation areas or areas randomly selected by users. In this study, the neural fiber tract targeted the corticospinal tract (CST) Quantitative analyses were performed and compared. The pixel numbers passing through the fiber tract in the individual brain volume were counted. The ratios between the ROI pixel numbers and the extracted fiber pixel numbers, and the ratios between the fiber pixel numbers and the whole-brain pixel numbers were also calculated. Results: According to our results, extracted CST fiber tract in which the ROI was drawn with fMRI activation areas showed higher distribution than drawing the ROI by users' hands. In addition, the quantitatively measured values represented higher pixel distribution: The counted average pixel numbers were 4553.8 and 1943.3. The average ratios of the ROI areas were 33.87 and 22.52. The average percentages of the individual whole-brain volume numbers were 2.06 and 0.87. Conclusion: Results of this study appear to indicate that use of this method can allow for more objectives and significant for study of the recovery of neural fiber mechanisms and brain rehabilitation.

• Education of Primary School Mathematics
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• v.8 no.1
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• pp.1-11
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• 2004

Whole number concept is an important part of mathematics learning. Elementary school students should understand and master whole number concept. Models can help students learn whole number concepts. Realistic Mathematics Education in Netherlands had investigated and developed three different structural models: line model, group model, combination model. These models are related whole number concepts and structures closely and compatible. The purpose of this study is to investigate models related with whole numbers in 7th elementary textbooks. As a result of analyses, we found out some pattern and several problems. On the foundation of the analyses, we discussed the better ways of using models in teaching whole number and the research issues concerning these.

• The Mathematical Education
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• v.50 no.1
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• pp.41-59
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• 2011

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.399-405
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• 2009

In this paper, we study the Genoochi-zeta functions which are entire functions in whole complex s-plane these zeta functions have the values of the Genocchi numbers and the Genoochi polynomials at negative integers respectively. That is ${\zeta}_G(1-k)={\frac{G_k}{k}}$ and ${\zeta}_G(1-k,x)={\frac{G_k(x)}{k}}$.

• School Mathematics
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• v.19 no.1
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• pp.209-228
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• 2017

Understanding decimal numbers is important in mathematics as well as real-life contexts. However, lots of students focus on procedures or algorithms of decimal numbers without understanding its meanings. This study analyzed teaching method related to decimal numbers in a series of mathematics textbooks of Korea, Japan, Singapore and the US. The results showed that three countries except Japan introduced the decimal numbers as another name of fraction, which highlights the relation between the concept of decimal numbers and fractions. And limited meanings of decimal numbers were shown such as 'equal parts of a whole' and 'measurement'. Especially in the korean textbooks, relationships between the decimals were dealt instrumentally and small number of models such as number lines or $10{\times}10$ grids were used repeatedly. Based these results, this study provides implications on what and how to deal with decimal numbers in teaching and learning decimal numbers with textbooks.

• Journal of The Korean Society of Grassland and Forage Science
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• v.10 no.3
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• pp.164-171
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• 1990

This study was carried out to enhance the nutritional value of whole crop corn silage and the utilization of animal waste as a ruminant feedstuffs. Whole crop corn were ensiled with cage layer excreta and concentrate. Treatments included whole crop corn silage (control), 10% cage layer excreta and concentrate-corn silage (CES lo), 20% cage layer excreta and 10% concentrate-corn silage (CES 20) and 30% cage layer excreta and 10% concentrate-corn silage (CES 30). The characteristics of silage fermentation was evaluated. Digestibility and palatability of the silage were observed through the feeding trial with four male Corridale sheep. The results obtained are summarized as follows: 1. Cage layer excreta-corn silage showed higher contents of crude protein and crude ash than control silage, while crude fibre content was significantlv lower than that of control silage (P(.01). 2. Total nitrogen and ammonia nitrogen content of the cage layer excreta-corn silage was significantly (P< .01) higher than that of control, but CES 10 silage was good in quality. 3. Lactic acid content of CES 10 silage was the highest, but that of CES 20 and CES 30 silage was lower than that of control. CES 20 and CES 30 silage was lower lactic acid content and higher pH than control. Therefore Flieg's score was wrose than that of control silage. 4. The numbers of total bacteria and lactic fermentation bacteria were estimated lo7-10' and 10"1OH, respectively, and there were no significant differences among treatments. Coliform numbers were not detected with CES 10 silage while were detected lo3 per gram in CES 30 silage. 5. Digestibility of crude protein, crude fibre and ADF was improved significantly in the animals fed the cage layer excreta-corn silage compared with animals fed the control silage. DCP and TDN were the highest in the CES 10 silage. 6. The intake of daily nitrogen and dry matter per metabolic body weight was the highest in animals fed the CES 10 silage.lage.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.351-373
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• 2017

The meanings of division don't change and rather are connected from whole numbers to rational numbers. In this respect, connecting division of natural numbers, division of fractions, and division of decimal numbers could help for students to study division in meaningful ways. Against this background, the units of division of fractions and division of decimal numbers in fifth grade were redesigned in a way for students to connect meanings of division and procedures of division. The results showed that most students were able to understand the division meanings and build correct expressions. In addition, the students were able to make appropriate division situations when given only division expressions. On the other hand, some students had difficulties in understanding division situations with fractions or decimal numbers and tended to use specific procedures without applying diverse principles. This study is expected to suggest implications for how to connect division throughout mathematics in elementary school.

• Korean Journal of Plant Taxonomy
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• v.48 no.4
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• pp.260-277
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• 2018

The evolution of chromosome numbers and the karyotype structure is a prominent feature of plant genomes contributing to or at least accompanying plant diversification and eventually leading to speciation. Polyploidy, the multiplication of whole chromosome sets, is widespread and ploidy-level variation is frequent at all taxonomic levels, including species and populations, in angiosperms. Analyses of chromosome numbers and ploidy levels of 252 taxa of Korean non-commelinid monocots indicated that diploids (ca. 44%) and tetraploids (ca. 14%) prevail, with fewer triploids (ca. 6%), pentaploids (ca. 2%), and hexaploids (ca. 4%) being found. The range of genome sizes of the analyzed taxa (0.3-44.5 pg/1C) falls well within that reported in the Plant DNA C-values database (0.061-152.33 pg/1C). Analyses of karyotype features in angiosperm often involve, in addition to chromosome numbers and genome sizes, mapping of selected repetitive DNAs in chromosomes. All of these data when interpreted in a phylogenetic context allow for the addressing of evolutionary questions concerning the large-scale evolution of the genomes as well as the evolution of individual repeat types, especially ribosomal DNAs (5S and 35S rDNAs), and other tandem and dispersed repeats that can be identified in any plant genome at a relatively low cost using next-generation sequencing technologies. The present work investigates chromosome numbers (n or 2n), base chromosome numbers (x), ploidy levels, rDNA loci numbers, and genome size data to gain insight into the incidence, evolution and significance of polyploidy in Korean monocots.