• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.403-420
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• 2016

Some of the critical changes in the revised 2015 Korean Mathematics curriculum were that direct proportion and inverse proportion were moved from elementary school to middle school and that supplementary content related to correlation was included. These decisions were based on comparative studies of international curriculum. Therefore in this study, we selected countries for comparison; United States, England, France, Finland, Australia, Japan, Singapore, China and Taiwan. We looked into the timing and scope for direct/inverse proportion and correlation in curricula of these countries. Along with this, we established four criteria; vertical sequence, horizontal sequence, external connection, and internal connection for an analysis framework. Then we compared and analysed the direct/inverse proportion and correlation in each curriculum. As a result, in most of these curricula, the direct/inverse proportions are introduced at middle school or are introduced at elementary school and then developed further at middle school. Most of curriculums on direct/inverse proportion and correlation match the four criteria. Correlation is introduced in high school mathematics in all counties except Finland and it is dealt in diverse context introducing related concepts, for example, correlation coefficient, regression straight line, and least square. We suggested that it is necessary to refer these international trends for the next revision of curriculum.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Journal of Families and Better Life
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• v.14 no.2
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• pp.127-138
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• 1996

The purpose of this study is to show farm women's stress under productive activity role multiple overload through family characteristic (pattern and number) and characteristic(type working time and involvement proportion) of productive activity. The outline of the study is as follow; 1. Stress by pattern and number of a family is highest in a four generation family and increases according as the number of the family increases. 2. The characteristic of productive activity : 1) Stress based on type of productive activity is highest in Type III of the most multiple overload roles. 2) in light of stress based working time area of household task activity is in inverse proportion to working time but area of farming and wage earning activity are approximately in direct proportion to it. The two-way ANOVA analysis show that stress in Type I of area of household task increases but in Type IV it decreases as working time increases 3) In stress based on involvement proportion to it. The wo-way ANOVA analysis show that stress in Type I of area of household task increases but in Type IV it decreases as working time increases. 3) In stress based on involvement proportion in three as working time increases 3). In stress based on involvement proportion in three activity areas the more the involvement proportion the less of the stress : an inverse ratio.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.103-121
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• 2008

The primary purpose of this study was to gather knowledge about $5^{th},\;6^{th},\;and\;7^{th}$ graders' proportional reasoning ability by investigating their reactions and use of strategies when encounting proportional or nonproportional problems, and then to raise issues concerning instructional methods related to proportion. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 12 questions, which included 8 proportional questions and 4 nonproportional questions. The following conclusions were drawn from the results obtained in this study. First, for a deeper understanding of the ratio, textbooks should treat numerical comparison problems and qualitative prediction and comparison problems together with missing-value problems. Second, when solving missing-value problems, students correctly answered direct-proportion questions but failed to correctly answer inverse-proportion questions. This result highlights the need for a more intensive curriculum to handle inverse-proportion. In particular, students need to experience inverse-relationships more often. Third, qualitative reasoning tends to be a more general norm than quantitative reasoning. Moreover, the former could be the cornerstone of proportional reasoning, and for this reason, qualitative reasoning should be emphasized before proportional reasoning. Forth, when dealing with nonproportional problems about 34% of students made proportional errors because they focused on numerical structure instead of comprehending the overall relationship. In order to overcome such errors, qualitative reasoning should be emphasized. Before solving proportional problems, students must be enriched by experiences that include dealing with direct and inverse proportion problems as well as nonproportional situational problems. This will result in the ability to accurately recognize a proportional situation.

• Journal of Korea Foundry Society
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• v.17 no.6
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• pp.608-614
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• 1997

The effect of mold preheating temperature on the microstructure such as grain size, eutectic silicon morphology was investigated for the Al-7wt%Si-0.3wt%Mg alloy. Microstructural variations have been characterized as a function of Sr addition and cooling rate during solidification. Microstructures were correlated with cooling rate, local solidification time and eutectic nucleation temperature, etc. In this study, Sr addition caused increase of local solidification time, undercooling and reduction of eutectic plateau temperature. In logarithmic scale, local solidification time was in inverse proportion to cooling rate. Eutectic nucleation temperature was in inverse proportion to cooling rate of logarithmic scale. Increasing the cooling rate refined dendrite arm spacing and eutectic silicon. Dendrite arm spacing was logarithmically in inverse proportion to cooling rate. Without modifier addition, eutectic silicon was modified at cooling rate of $7^{\circ}C/s$ or higher.

• Korea-Australia Rheology Journal
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• v.19 no.1
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• pp.35-42
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• 2007

The effects of particle size distribution on the magnetorheological response of inverse ferrofluids was investigated using controlled mixtures of two monodisperse non-magnetisable powders of sizes $4.6\;{\mu}m\;and\;80{\mu}m$ at constant volume fraction of 30%, subjected to large amplitude oscillatory shear flow. In the linear viscoelastic regime (pre-yield region), it was found that the storage and loss moduli were dependent on the particle size as well as the proportion of small particles, with the highest storage modulus occurring for the monodisperse small particles. In the nonlinear regime (post yield region), Fourier analysis was used to compare the behaviour of the $1^{st}\;and\;3^{rd}$ harmonics ($I_{1}\;and\;I_{3}\;respectively$) as well as the fundamental phase angle as functions of the applied strain amplitude. The ratio of $I_{3}/I_{1}$ was found to become more pronounced with decreasing particle size as well as with increasing proportion of small particles in the bidisperse mixtures. Furthermore, the phase angle was able to clearly show the transition from solid-like to viscous behaviour. The results suggested that the nonlinear response of a bidisperse IFF is dependent on particle size as well as the proportion of small particles in the system.

• Journal of the East Asian Society of Dietary Life
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• v.8 no.2
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• pp.155-161
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• 1998

Response surface methodology (RSM) was used for optimizing preparation conditions and monitoring the quality of buckwheat mook prepared using buckwheat starch. The textures(hardness, adhesiveness, cohesiveness and gumminess) of buckwheat mook were decreased in inverse proportion to the increase of water content. the L and b values of Hunter color parameters in buckwheat mook were increased in proportion to the increase of water content. However, The a value of Hunter color parameters of buckwheat mook were decreased in inverse proportion to the increase of water content. Organoleptic properties(color, form, taste and mouth-feel) of buckwheat mook showed a maximum score in 700ml(water content), 14min(gelatinization time)

• Proceedings of the Korea Concrete Institute Conference
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• 1997.04a
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• pp.329-334
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• 1997

Most of domestic pavement were non-permeable. However, in foreign country although it wasn't entirely satisfied, porous pavement was partially utilized with footpaths and soft-roadways. In this study, experiments were carried out to investigate the properties fundamental of porous concrete pavement. As a result of experiments, it was concluded that the coefficient of permeability was increased in proportion to continuous void ratio and decreased in proportion to S/a ratio and unit cement contents. On the other hand, the strength of porous concrete pavement was in inverse proportion to the void ratio.

• Journal of Sericultural and Entomological Science
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• v.15 no.2
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• pp.55-60
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• 1973

The statistical interpretations are on the correlations and the linear regressions between the various meteorological conditions the branch Pusan-Observatory of the National-Central-Meteorological-Observatory had measured from 1930 to 1962, and the production of silk worm cocon that the Section of Sericulture in the Ministry of Agriculture ＆ Fishery had recorded from 1930 to 1962 in Gyung Sang Nam Do Korea. These were most in proportion to the sun shine time, an inverse proportion to the atmosphere humidity and the lowest temperature, in proportion to the mean temperature, the highest temperature and the amount of the rain fall. The correlations and linear regressions between the various meteorological factors to control the production of the silkworm cocoon of both per a box of the silk worm egg and per 10a of mulberry field was as follows. (1) The production of the spring silk worm cocoon was dicided by the various meteorological factors. 1. This was in proportion to the total sun shine time between 5 and 6 month. r=0.40＊-(0.42$^{**}$) Y=0.0269$\chi$＋6.46-(0.2795$\chi$＋10.25) 2. This was an inverse proportion to the total amount between 5 and 6 month atmosphere humidity. r=-0.49$^{***}$-(-0.40＊) Y=-0.2989$\chi$＋62.77-(0.1474$\chi$＋31.86) 3. This wasin proportion to the total rain fall amount between 6 and 7 month. r=0.47$^{***}$-(0.44$^{***}$) Y=0.0037$\chi$＋16.42-(0.0035$\chi$＋8.35) (2) The production of the autumn silk worm cocoon was decided by the various meteorological factors. 1. This was in proportion to the total sun shine time between 5 and 6 month. r=0.37＊-(0.45$^{***}$) Y=0.0205$\chi$＋5.51-(0.0173$\chi$＋2.41) 2. This was an inverse proportion to the total amount between 5 and 6 month atmosphere humidity. r=-0.41$^{**}$-(-0.42$^{**}$) Y=-0.2085$\chi$＋45.33-(-0.0599$\chi$＋12.17) 3. This was in proportion to the total of rain fall amount of 6 and 7 month. r=0.48$^{***}$-(0.35＊) Y=0.0050$\chi$＋11.97-( ) 4. This was in proportion to the total sun shine time among 3, 4, 5, and 6 month. r=0.51$^{****}$-(0.49$^{***}$) Y=0.0178$\chi$-1.27-(0.0096$\chi$-3.60) 5. This was an inverse proportion to the total amount among 3, 4, 5, and 6 month atmosphere humidity r=-0.41/$^{**}$-(-0.44$^{***}$) Y=-0.0938$\chi$＋40.14-(-0.05693$\chi$＋20.49) 6. This was in proportion to the total of a year sun shine time. r=0.58$^{****}$-(0.43) Y=0.0037$\chi$＋5.35-(0.0015$\chi$＋1.02) (3) The production of the next year spring silk worm cocoon was decided by the this year various meteorological factors. 1. This was in proportion to the total of a year sun shine time. r=0.55$^{****}$-(0.52$^{****}$) Y=0.0034$\chi$＋12.02-(0.0025$\chi$＋3.84).>＋3.84).3.84).>＋3.84).

• Journal of the Korean Society of Combustion
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• v.13 no.3
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• pp.9-16
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• 2008

In this study, a cylindrical constant volume combustion chamber is used to investigate the flow and combustion characteristics of methane-air homogeneous mixture under various initial charge pressure, excess air ratios and ignition times. The flame and burning speed, mean gas speed are calculated by numerical analysis to analyze the combustion characteristics. It is found that the mean gas velocity during combustion has the maximum value around 300 ms and then decreased gradually on the condition of 10000 ms, and that the combustion duration is shorten and flame speed and burning velocity have the highest value under the conditions of an excess air ratio 1.1, an initial charge pressure of 0.2 MPa and an ignition time of 300 ms in the present study. And, the initial pressure and burning speed are in inverse proportion, so that it is in agreement with Strehlow who presented that the initial pressure and burning speed are in inverse proportion when the burning speed is under 50cm/s.