• School Mathematics
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• v.11 no.1
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• pp.17-37
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• 2009

Concept and model of multiplication is not single. Concepts of multiplication can be classified into three cases: repeated addition, times idea, pairs set. Models of multiplication can be classified into four cases: measurement, rectangular pattern, combinatorial problem, number line. Among diverse cases of multiplication's concept and model, which case does elementary mathematics education lay stress on? This question is a controvertible didactical point. In this thesis, (1) mathematical and didactical analysis of multiplication's concept and model is performed, (2) a concrete program of teaching multiplication which is based on times idea is contrived, (3) With this new program, the teaching experiment is performed and its result is analyzed. Through this study, I obtained the following results and suggestions. First, the degree of testee's understanding of times idea is not high. Secondly, a sort of test problem which asks the testee to find times value is more easy than the one to find multiplicative resulting value. Thirdly, combinatorial problem can be handled as an application of multiplication. Fourthly, the degree of testee's understanding of repeated addition is high. In conclusion, I observe the fact that this new program which is based on times idea could be a alternative program of teaching multiplication which could complement the traditional method.

• Korean Journal of Food Science and Technology
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• v.43 no.3
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• pp.303-314
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• 2011

The purpose of this study was to determine the optimal mixing conditions for two different amounts of added mulberry powder and fresh cream to prepare functional chocolate with added mulberry powder. The experiment was designed according to the central composite response surface design, which showed 10 experimental points, and included two replicates for mulberry powder and fresh cream. The physiochemical, mechanical, and sensory properties of the test were measured, and these values were applied to the mathematical models. The results of the physiochemical and mechanical analyses of each sample, including pH, moisture content, total phenolic content, DPPH free radical scavenging activity, color L, color b, hardness, gumminess, and cohesiveness showed significant differences. The sensory characteristics of the samples tested were significantly different in flavor, texture, sourness, bitterness, and overall acceptability. The optimum formulation calculated by numerical and graphical methods was 25.76 g mulberry powder and 72.21 g fresh cream.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.81-109
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• 1999

This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

• Food Science and Preservation
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• v.24 no.2
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• pp.181-186
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• 2017

This study was conducted to investigate the weight loss, firmness, external color and vitamin C (VC) content of tomatoes (Lycopersicon esculentum) using non-destructive method to measure identical tomato samples during 15 days storage at low temperature and high humidity. Tomatoes were harvested at the light red stage, sorted, box packed and then stored in thermo-hygrostat ($10{\pm}1^{\circ}C$, $90{\pm}10%RH$). The quality changes in weight loss, firmness and external color were measured every 3 day interval. Weight loss was increased by $1.13{\pm}0.15%$, but it may not be considered to affect quality. Surface color of fruit was changed, especially in lightness and hue angle value. The color values were analyzed by analysis of variance (ANOVA), and the results were significant (p<0.001). Firmness of fruit declined during storage, but it did not decrease in direct proportion. On the storage of day 15, firmness was decreased to 40% of initial state. At last, all the experiment data are summarized and the relationship between firmness and weight loss is analyzed to construct a linear regression mathematical model that can predict the weight loss with the firmness value measured by non-destructive method. This research result could be useful in helping tomato exporters and suppliers to get real-time quality factor by using proposed method and regression model.

• Atmosphere
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• v.16 no.2
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• pp.97-110
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• 2006

This study investigates the response of a typhoon model to the change of the sea surface temperature (SST) throughout the model integration. The SST change is parameterized as a formulae of which the magnitude is given as a function of not only the intensity and the size but the moving speed of tropical cyclone. The formulae is constructed by referring to many previous observational and numerical studies on the SST cooling with the passage of tropical cyclones. Since the parameterized cooling formulae is based on the mathematical expression, the resemblance between the prescribed SST cooling and the observed one during the period of the numerical experiment is not complete nor satisfactory. The agreements between the prescribed and the observed SST even over the swath of the typhoon passage differ from case to case. Numerical experiments are undertaken with and without prescribing the SST cooling. The results with the SST cooling do not show clear evidence in improving the track prediction compared to those of the without-experiments. SST cooling in the model shows its swath along the incomplete simulated track so that the magnitude and the distribution of the sea surface cooling does not resemble completely with the observed one. However, we have observed a little improvement in the intensity prediction in terms of the central pressure of the tropical cyclone in some cases. In case where the model without the SST treatment is not able to yield a correct prediction of the filling of the tropical cyclone especially in the decaying stage, the pulling effect given by the SST cooling alleviates the over-deepening of the model so that the central pressure approaches toward the observed value. However, the opposite case when the SST treatment makes the prediction worse may also be possible. In general when the sea surface temperature is reduced, the amount of the sensible and the latent heat from the ocean surface become also reduced, which results in the weakening of the storms comparing to the constant SST case. It turns out to be the case also in our experiments. The weakening is realized in the central pressure, maximum wind, horizontal temperature gradient, etc.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.76-85
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• 1993

In order to predict the free surface signature of turbulent ship wakes two things are essential; a basic understanding of the mechanism of turbulent vortical flow/free surface interactions and a mathematical model to accurately predict the signature. The goal of the study described here is both to supplement experimental work to obtain basic understanding, as well as to condense this understanding in a model(or models) that captures the essential phenomena and thus allows predictions. To do so we followed two main paths guided by experimental observations. One is full simulations of the flow using the clavier-Stokes equations. The other is a vortex modeling, where the vortical structures of the flows are approximated by idealized structures, an the interaction assumed to be essentially inviscid. These approaches complement each other. Full simulations are only applicable to small scale phenomena, where the system is simple, and the Reynolds number is low. The vortex modeling, on the other hand, cannot represent essentially viscous aspects of the problem such as the effect of contamination gradient. Obviously, the modeling is what may eventually lead to a prediction method; the full simulations-too limited to mimic all but the simplest circumstances-are to aid and support the construction of realistic models. We address two-dimensional aspects of the vortex/free surface interaction first. Secondly we obtain some basic understanding of the interaction process through an experiment and then talk about several three-dimensional problems hoping to develop a successful prediction model.

• The Journal of Korean Academy of Prosthodontics
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• v.35 no.3
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• pp.517-534
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• 1997

It has been held that excessive mechanical forces to the osseous and soft tissues of the TMJ result in joint dysfunction. Understanding the stress pattern on TMJ is very important in TMJ research. But, it is very difficult to measure directly the biomechanical stress distribution in the TMJ when the mandible is loaded. Therefore, stress distribution in the TMJ during functional movement was studied through animal experiment or mathematical model. It was observed and compared the stress distribution occuring in the working and balancing condyle when lower right canine, lower right first molar and lower right second molar were clenched by the three dimensional finite element analysis. Also, stress distribution in the working and balancing condyles were observed and compared when $20^{\circ}$ forward and buccal bite forces were applied to the first molar. The results were as follows : 1. Stress distribution in the condyles during unilateral clenching of the first molar, second molar, canine showed no difference. In the working condyle, tensile force was concentrated on the lateral aspect of the condylar articular surface and condylar neck. And compressive force was concentrated on the anteromedial and lateral aspect of condyle. In the balancing condyle, tensile and compressive forces were concentrated on the lateral aspect of the condylar articular surface and stress transmission to the temporal bone was not observed. 2. When lateral forces were applied to the first molar, tensile forces were concentrated on the medial aspect of the condylar neck and condylar posterior surface in working and balancing condyle. Compressive force was concentrated on the anteromedial and lateral surface of the condyle and stress transmission to the temporal bone was not observed. 3. During unilateral clenching, stress in the working condyle decreased as the occlusal load moved posteriorly while the stress in the balancing condyle increased. when lateral force was applied to first molar, the incremental amount of stress was greater than vertical load. 4. During unilateral clenching, the average balancing/working condyle stress ratio was 2.52. There was a greater concentration of stress in the balancing condyle. The ratio increased as the occlusal load moved posteriorly and decreased considerably when lateral forces were applied to the first molar.

• Journal of radiological science and technology
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• v.21 no.1
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• pp.52-58
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• 1998

We can and must improve the diagnostic images using available knowledge and technology. At the same time we must strive to reduce the patient's integral and entrance radiation dose. Reducing the integral dose to the patient during the radiologic procedure is a primary concern of the patient, especially the pediatric patient, the radiologist and the technologist. A 100cm focal film distance generally is used for most over-table radiography. The early x-ray tubes and screen film combinations required long exposures, which often resulted in motion artifacts. But nowaday, we have the generators and x-ray tubes that can deliver the energy necessary in a very short time and the receptors that can record the information just as rapidly. And, we performed this studies to evaluate the patient exposure dose and the image quality by increasing focal film distance in diagnostic radiography. There are many factors which affected to exposure factor, but we studied to verify of FFD increase, only. Effect of increasing the focal film distance to a 140 cm distance was tested as follows; 1. The focal film distances were set at 100, 120, and 140cm. 2. A 18cm acryl(tissue equivalent) phantom was placed on the table top. 3. An Capintec 192 electrometer with PM 05 ion chamber was placed at the entrance surface of the phantom, and exposure were made at each focal film distances. 4. The procedure was repeated in the same manner as above except the ion chamber was placed beneath the phantom at the film plane. 5. Exit exposure were normalize to 8mR for each portions of the experiment. Based on the success of the empirical measurements, a detailed mathematical analysis of the dose reduction was performed using the percent depth dose data. The results of this study can be summerized as followings ; 1) Increasing FFD from 100 cm to 140 cm, we would create a situation that would have a significant effect on the overall quality of radiograph and achive the 17.42% reduction of entrance dose and the 18.95% reduction of integral dose that the patient receives. 2) Thickness of Al step wedge for equal film density increased with the long distance. 3) Increasing FFD, Magnification of image was lowered. 4) Resolution of image also increased with the FFD. As the results described above, we strongly recommend using the long FFD to provide better information for our patients and profession in abdomen radiographic studies.

• Journal of the Korean Society of Food Science and Nutrition
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• v.37 no.4
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• pp.497-504
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• 2008

This study was conducted for the optimization of ingredients in salad dressing using Bokbunja (Rubus coreanum Miquel) juice. The experiment was designed according to the D-optimal design of mixture design, which included 14 experimental points with 4 replicates for three independent variables (Bokbunja juice $15.70\sim47.10%$, oil $23.50\sim39.20%$, vinegar $3.90\sim19.60%$). The compositional and functional properties of the prepared products were measured, and these values were applied to the mathematical models. A canonical form and trace plot showed the influence of each variable on the quality attribute of final mixture product. By the use of F-test, viscosity, color values (L, a, and b), emulsion stability and sensory characteristics (color) were expressed by a linear model, while the color values (L) and sensory characteristics (smell, taste, and overall acceptance) were by a quadratic model. The optimum formulations by numerical and graphical method were analogous: Bokbunja juice, oil and vinegar of 36.02%, 26.48%, and 12.00% by numerical method, respectively; those of 36.00%, 26.44%, and 12.06% by graphical method, respectively.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.83-105
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• 2021

In this paper, we analyzed the misconceptions and errors incurred during factorization learning. We also examined whether online individualization classes had a positive effect on students' mathematical achievement. The experiment was conducted for 4 weeks (16 times in total) on middle school juniors in rural areas of Gyeonggi Province, where the influence of private extra education was small. In the class, the 'Google Classroom' was used as a LMS, the video lecture was uploaded to YouTube, and the teacher interacted with the students through "Zoom" and "Facetalk". In the online class situation, students' assignments and test answers were checked in real time through 'Google Classroom', and immediate feedback was provided to the experimental class group's students. However, for the control group students, feedback was provided only to those who desired. A total of 7 achievement evaluations were conducted in the order of pre-test, formative evaluation (5 times), and post-test to confirm the change in students' ability improvement and achievement. Through the formative evaluation analysis, it was possible to grasp the types of errors and misconceptions that occured during the factorization process. Students' errors were divided into four types: theorem or definition distortion error, functional errors such as calculation, operation, and manipulation, errors that do not verify the solution, and no response. As a result of ANCOVA, the two groups did not show any difference from the 1st to 4th formative assessment. However, the 5th formative assessment and post-test showed statistically significant differences, confirming that online individualization classes contributed to improvemed achievement.