• School Mathematics
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• v.19 no.1
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• pp.59-75
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• 2017

This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.323-345
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• 2019

This study examines the introduction of fractions in the third grade mathematics textbooks focusing on stages of units coordination and suggests alternative activities to help students develop their understanding of fractions. As results, the sessions of introduction units in textbooks was well organized to allow students to construct more extensive fraction schemes (i.e., Part-whole fraction scheme → Partitive unit fraction scheme → Partitive fraction scheme). However, most of the activities in textbooks were related to stages 1 and 2 of units coordination. In particular, the operations and partitioning schemes (i.e., equi-partitioning and splitting schemes), which are key to the development of students' fraction knowledge, were not explicitly revealed. Fraction schemes also did not extend to the Iterative fraction scheme, which is central to the construction of improper fractions. Based on these results, this study is expected to provide implications for the introduction of fractions in textbooks focusing on stages of units coordination to teachers and textbook developers.

• Education of Primary School Mathematics
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• v.23 no.2
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• pp.87-116
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• 2020

The purpose of this study is to explore how units-coordination ability is related to understanding fraction concepts. For this purpose, a teaching experiment was conducted with one fourth grade student, Eunseo for four months(2019.3. ~ 2019.6.). We analyzed in details how Eunseo's units-coordinating operations related to her understanding of fraction changed during the teaching experiment. At an early stage, Eunseo with a partitive fraction scheme recognized fractions as another kind of natural numbers by manipulating fractions within a two-levels-of-units structure. As she simultaneously recognized proper fraction and a referent whole unit as a multiple of the unit fraction, she became to distinguish fractions from natural numbers in manipulating proper fractions. Eunseo with a reversible partitive fraction scheme constructed a natural number greater than 1, as having an interiorized three-levels-of-units structure and established an improper fraction with three levels of units in activity. Based on the results of this study, conclusions and pedagogical implications were presented.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.219-222
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• 2015

The kinetic analysis of energetic materials using Differential Scanning Calorimetry (DSC) is proposed. Friedman Isoconversional method is applied to DSC experiment data and AKTS software is used for analysis. The frequency factor and activation energy are extracted as a function of product mass fraction. The extracted kinetic scheme does not assume multiple chemical steps to describe the response of energetic materials; instead, multiple set of Arrhenius factors are used in describing a single global step. The proposed kinetic scheme has considerable advantage over the standard method based on One-Dimenaionl Time to Explosion (ODTX). Reaction rate and product mass fraction simulation are conducted to validate extracted kinetic scheme. Also a slow cook-off simulation is implemented for validating the applicability of the extracted kinetics scheme to a practical thermal experiment.

• Korean Management Science Review
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• v.24 no.1
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• pp.113-126
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• 2007

This paper deals with a mathematical approach for finding the time-fractions for the time-fraction based scheduling method in multimedia wireless networks. By introducing a constraint that regulates the performance fairness amongst users, we present a systematic method for harmonizing both the system and user performance. Numerical results show that the time-fraction based scheduling method reinforced with our scheme is very effective especially in multimedia environments.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.09a
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• pp.56-63
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• 2003

Fractional composition and mobility of sediments some heavy metals in Okdong stream are investigated. The fractional scheme for sediment heavy metal was made for five chemically defined heavy metal forms as adsorbed fraction, carbonate fraction, reducible fraction, organic fraction, and residual fraction (Tessier et at., 1979). The most abundant fraction of the sediment heavy metal is reducible and secondly abundant organic fraction. Adsorbed fraction is minor part of the total heavy metals. Mobilization of sediment heavy metals in stream Okdong is occur 19.8∼56.7% of total cadmium concentrate. The most abundant fraction of the sediment metal is organic fraction in Cu, Pb metals investigated. Labile fraction of sediment metals are 0.5%∼48.5% of total Zn, 2.6%∼48.1% of total Pb, 0.2∼36.9% of total Cu respectively, Most of labile fraction consists of reducible fraction for Cd, Zn, adsorbed fraction for Pb, reducible fraction for Cu, adsorbed fraction for Ni. The Mobilization of Zn and Cu is most likely to occur when oxygen depletes and that of Pb and Ni occurs when physical impact, oxygen depletion and pH reduction.

• Journal of Advanced Marine Engineering and Technology
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• v.32 no.8
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• pp.1215-1220
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• 2008

To obtain the shape of the free surface more accurately, computations are carried out by a finite volume method using unstructured meshes and an interface capturing method. Free-surface flow, which is very important in the fields of ship and marine engineering, is numerically simulated for flows of both water and air. Control volumes are used with an arbitrary number of faces and allows a local mesh refinement. The integration is of second order, with a midpoint rule integration and linear interpolation. The method is fully implicit and uses quadratic interpolation. The solution method of pressure-correction type solves sequentially equations of momentum, continuity, conservation, and two-equations turbulence model. Comparison are quantitatively made between the computation and experiment in order to confirm the solution method.

• Journal of Korea Foundry Society
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• v.18 no.6
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• pp.555-562
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• 1998

Modified fluid critical solid fraction method was utilized as a prediction parameter to describe the shrinkage formation including the position, shape and amount of shrinkage cavities. A numerical scheme was implemented adapting this method for the evaluation of solidification defects in various casting processes. In the present numerical code, the form of shrinkage cavity can be simultaneously determined when an isolated loop is predicted to occur by the fluid critical solid fraction method. An auxiliary parameter, shrinkage potential, was also used in order to calculate the amount of residual liquid during solidification. Solidification analysis was carried out for the validation of the present scheme. It was shown that the calculated results were in good agreement with those of practical casting runs in all of the casting processes envolved in the present research. It may be concluded that the present program successfully predicts the detailed shrinkage formation behavior without the consideration of interdendritic fluid flow analysis.

• School Mathematics
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• v.14 no.2
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• pp.191-212
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• 2012

In the field of arithmetic in mathematics education, there has been lack of fine-grained investigations addressing the relationship between students' construction of division knowledge with fractional quantities and their whole number division knowledge. This study, through the analysis of part of collected data from a year-long teaching experiment, presents a possible constructive itinerary as to how a student could modify her unit-segmenting scheme to deal with various fraction measurement division situations: 1) unit-segmenting scheme with a remainder, 2) fractional unit-segmenting scheme. Thus, this study provides a clue for curing a fragmentary approach to teaching whole number division and fraction division and preventing students' fragmentary understanding of the same arithmetical operation in different number systems.

• Transactions of Materials Processing
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• v.8 no.4
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• pp.374-383
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• 1999

To determine the flow stress of semi-solid materials, a new combined method has been studied by experimental and analytic technique in the current approach. Using backward extrusion experiment and its numerical analysis, the characterization scheme of semi-solid materials according to the change of initial solid volume fraction has been proposed. Because that solid volume fraction is sensitive to temperature change, it is required to precisely control the temperature setting. Model materials can guarantee the establishment of material characterization technique from the noise due to temperature change. Thus, clay mixed with bonded abrasives was used for experiment and the change of initial solid fraction was copied out through the variation of mixing ratio. Upper bound method was adapted to increase in efficiency of the calculation in numerical analysis and new kinematically admissible velocity field was employed to improve the accuracy of numerical solution. It is thought that the material characterization scheme proposed in this study can be applied to not only semi-solid materials, but also other materials that is difficult to obtain the simple stress state.