• The Mathematical Education
• /
• v.61 no.1
• /
• pp.157-178
• /
• 2022

Mathematics teachers' content knowledge is an important asset for effective teaching. To enhance this asset, teacher's knowledge is required to be diagnosed and developed. In this study, we employed problem-posing and problem-solving tasks to diagnose preservice teachers' understanding of fraction multiplication. We recruited 41 elementary preservice teachers who were taking elementary mathematics methods courses in Korea and the United States and gave the tasks in their final exam. The collected data was analyzed in terms of interpreting, understanding, model, and representing of fraction multiplication. The results of the study show that preservice teachers tended to interpret (fraction)×(fraction) more correctly than (whole number)×(fraction). Especially, all US preservice teachers reversed the meanings of the fraction multiplier as well as the whole number multiplicand. In addition, preservice teachers frequently used 'part of part' for posing problems and solving posed problems for (fraction)×(fraction) problems. While preservice teachers preferred to a area model to solve (fraction)×(fraction) problems, many Korean preservice teachers selected a length model for (whole number)×(fraction). Lastly, preservice teachers showed their ability to make a conceptual connection between their models and the process of fraction multiplication. This study provided specific implications for preservice teacher education in relation to the meaning of fraction multiplication, visual representations, and the purposes of using representations.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.3
• /
• pp.431-455
• /
• 2013

In this thesis, I classified various meanings of fraction into two categories, i.e concept(rate, operator, division) and model(whole-part, measurement, allotment), and surveyed appearances which is shown in Korea elementary mathematics textbook. Based on this results, I derived several implications on learning-teaching of fraction in elementary education. Firstly, we have to pursuit a unified formation of fraction concept through a complementary advantage of various concepts and models Secondly, by clarifying the time which concepts and models of fraction are imported, we have to overcome a ambiguity or tacit usage of that. Thirdly, the present Korea's textbook need to be improved in usage of measurement model. It must be defined more explicitly and must be used in explanation of multiplication and division algorithm of fraction.

• Journal of the Korean Society of Radiology
• /
• v.9 no.6
• /
• pp.417-420
• /
• 2015

We obtained Surviving Fraction (SF) after irradiation carbon beam to compare the applicability of the Linear-Quadratic model, Incomplete Repair model, Marchese model. Mathematica software(ver 9.0) used to calcurate parameters and compared result. LQ model could not explain the entire response of fractionated carbon beam irradiation. It becomes necessary to construct models that extend the LQ model of conventional radiotherapy for the carbon beam therapy. By combining both Potentially Lethal Damage Repair (PLDR) and Sublethal Damage Repair (SLDR) a new LQ model can develop that aptly modeled the cellular response to fractionated irradiation.

• Journal of Welding and Joining
• /
• v.17 no.4
• /
• pp.60-68
• /
• 1999

The previously developed two dimensional model was modified in order to predict more accurately the degree of microsegregation and eutectic fraction on in weld metal whose solidification rate is very fast. The model employed the same assumptions with previous model but considered of a tip undercooling. The previously predicted microsegregation and eutectic fraction has the discrepancies between simulated and examined results in the weld metal solidification. The experiments for the weld metal solidification of 2024 A1 and Fe-Ni alloy were carried out in order to examine the reasonability and feasibility of this modified model. The concentration profile of the solute and eutectic fraction predicted by the simulation agreed well with those found from experimental works. According to the results, it was believed that the dendrite tip undercooling considered in the modified model be reasonable for predicting the degree of microsegregation more accurately in weld metla solidification. In the GTA welds, degree of dendrite-tip undercooling increases with increasing solidification rage(welding speed). This serves to increase the concentration of dendrite core and thus result in reducing the degree of segregation. And solid state diffusion(back diffusion) during solidification is very low in the weld metal solidification so that little additional homogenization of solute occurs during solidification. With consideration of tip undercooling this modified model can predict exactly degree of microsegregation and eutectic fraction from slow solidification(casting) to fast solidification(welding).

• Proceedings of the KSRS Conference
• /
• 2007.10a
• /
• pp.468-470
• /
• 2007

This paper is to present an approach for generating coarse resolution (MODIS data) fraction images of forested region in Korea peninsula using forest type area fraction derived from high resolution data (ASTER data) in regional forest area. A 15-m spatial resolution multi-spectral ASTER image was acquired under clear sky conditions on September 22, 2003 over the forested area near Seoul, Korea and was used to select each end-member that represent a pure reflectance of component of forest such as different forest, bare soil and water. The area fraction of selected each end-member and a 500-m spatial resolution MODIS reflectance product covering study area was applied to a linear mixture inversion model for calculating the fraction image of forest component across the South Korea. We found that the area fraction values of each end-member observed from high resolution image data could be used to separate forest cover in low resolution image data.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.12 no.1
• /
• pp.55-60
• /
• 2004

Residual gas acts as a diluent which results in reducing the in-cylinder temperature as well as the flame speed, significantly affecting fuel economy, NOx emissions and combustion stability. Therefore it is important to determine the residual gas fraction as a function of the engine operating parameters accurately. However, the determination of the residual gas fraction is very sophisticated due to the unsteady state of induction and exhaust process. There has been little work toward the development of a generally applicable model for quantitative predictions of residual gas fraction. In this paper, a simple model for calculating the residual gas fraction in SI engines was suggested. The amount of fresh air was evaluated through AFR and fuel consumption. After this, from the intake temperature and pressure, the amount of total cylinder-charging gas was estimated. The residual gas fraction was derived by comparing the total charging and fresh air. This results coincide with measured EGR value very well.

• 한국연소학회:학술대회논문집
• /
• 2003.12a
• /
• pp.57-61
• /
• 2003

In the combustion modeling of non-premixed flames, the mixture fraction conserved scalar approach is widely utilized because reactants are mixed at the molecular level before burning and atomic elements are conserved in chemical reactions. In the mixture fraction approach, combustion process is simplified to a mixing problem and the interaction between chemistry and turbulence could be modelled by many sophisticated combustion models including the flamelet model and CMC. However, most of the mixture fraction approach is restricted to one mixture system. In this study, the flamelet model based on the two-feed system is extended to the multiple fuel-feeding systems by the two mixture fraction conserved scalar approach.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.48 no.3
• /
• pp.85-94
• /
• 2006

Practially useful method of steel fiber for construction work is presented in this study. The most important purpose of this study is to develop a model which can predict mechanical behavior of the structure according to aspect ratio and volume fraction of steel fiber. Experiments on compressive strength, elastic modulus, and splitting strength were performed with self-made cylindrical specimens of variable aspect ratios and volume fractions. The experiment showed that compressive strength was not in direct proportion to volume fraction which doesn't seem to have great influence over compressive strength. However, splitting strength showed almost direct proportion to aspect ratio and volume fraction. Improvement of optimal efficiency was confirmed when the aspect ratio was 70. Experiments on flexural strength, fracture energy, and characteristic length were carried out with self-manufactured beams with notch. As a result, increases of flexural strength, fracture energy, and characteristic length according to increase of volume fraction tend to be prominent when aspect ratio is 70. The steel fiber improves concrete to be more ductile and tough. Moreover, regression analysis was the performed and predictable model was developed after determining variables. With comparison and analysis of suggested estimated values and measured data, reliance of the model was verified.

• Steel and Composite Structures
• /
• v.7 no.5
• /
• pp.355-376
• /
• 2007

The purpose of this study is to predict and investigate the time-dependent creep behavior of composite materials. For this, firstly the evaluation method for the modulus of elasticity of whole fiber and matrix is presented from the limited information on fiber volume fraction using the singular value decomposition method. Then, the effects of fiber volume fraction on modulus of elasticity of GFRP are verified. Also, as a creep model, the nonlinear curve fitting method based on the Marquardt algorithm is proposed. Using the existing Findley's power creep model and the proposed creep model, the effect of fiber volume fraction on the nonlinear creep behavior of composite materials is verified. Then, for the time-dependent analysis of a composite material subjected to uniaxial tension and simple shear loadings, a user-provided subroutine UMAT is developed to run within ABAQUS. Finally, the creep behavior of center loaded beam structure is investigated using the Hermitian beam elements with shear deformation effect and with time-dependent elastic and shear moduli.

• Nuclear Engineering and Technology
• /
• v.47 no.6
• /
• pp.669-677
• /
• 2015

A mechanistic model for void fraction prediction with improved interfacial friction factor in nearly horizontal tubes has been proposed in connection with the development of a condensation model package for the passive auxiliary feedwater system of the Korean Advanced Power Reactor Plus. The model is based on two-phase momentum balance equations to cover various types of fluids, flow conditions, and inclination angles of the flow channel in a separated flow. The void fraction is calculated without any discontinuity at flow regime transitions by considering continuous changes of the interfacial geometric characteristics and interfacial friction factors across three typical separated flows, namely stratified-smooth, stratified-wavy, and annular flows. An evaluation of the proposed model against available experimental data covering various types of fluids and flow regimes showed a satisfactory agreement.