• East Asian mathematical journal
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• v.36 no.1
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.369-384
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• 2007

This study examined and compared the level of mathematical anxiety according to the types of students' characteristics based on the former research study showing that there exists a close relationship between characteristics and mathematical anxiety. The subjects of this study are 159 students enrolled in Chungnam Gongju and Kyunggi-do Ahnyang. They were categorized into groups following various standards such as preference index(E-1, S-N, T-F, J-P), ability & disposition, 16 types of characteristics. Then these were tested for types and the level of mathematical anxiety by the factors of mathematical anxiety. The results show that Type E students show the greatest anxiety in learning motivation, and Type N students in the pedagogy of teaching and loaming for the subfactor of mathematical anxiety. Further, Type NT students respond strongly to the pedagogy of teaching and loaming in psychological ability and disposition, which shows that mathematical anxiety and sub-factors of mathematical anxiety are closely somehow related.

• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• Journal of the Korean School Mathematics Society
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• v.8 no.2
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• pp.249-271
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• 2005

The study was aimed to show effects of the newly step branch's feedback models on the mathematics underachievers' mathematics achievement and attitude toward the mathematics, extent of self-check. The subject are 26 mathematics underachievers in the End grade of H middle school located in Taejeon. They were divided into an experimental group and a control group, and the attribution disposition. Experiment group was provided step branch's feedback and control group was provided general formative' feedback. The duration of the treatment was over a period of six weeks. The result of study, the step branch's feedback was effects for increasing he mathematics achievement and attitude toward the mathematics than the general formative' feedback(p<.05). In addition, the step branch's feedback group had better extent of self-check than the general formative' feedback.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.407-428
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• 2013

The purpose of this research is to develop an effective teaching-learning model and suggest efficient methods for improving the learning abilities in mathematics of the students of engineering college. For this purpose, we examined their learning styles and learning attitudes toward Mathematics, which are important factors in teaching-learning process, and analyzed the relation between them. As a result, we found that participants had a disposition of being dependent and highly participating, so we made an effort to develop a teaching-learning model which can make the students active and highly involved in. After applying the developed teaching-learning model to Engineering Mathematics class for one semester, we conducted survey of the participants' responses. In conclusion, we found that this model is very helpful for Engineering students to utilize a self-directed learning by diagnosing and adjusting their learning process in Meta-cognitive way. Also, it is confirmed that this model has a considerable influence in which students can actively participate in class and have positive attitude to Mathematics learning.

• School Mathematics
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• v.13 no.4
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• pp.543-562
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• 2011

In this research, the PBL program was developed in terms of 'classroom practice ability', 'self-develop ability', and 'teaching profession character' which classroom friendly teachers get ready and was applied to the classroom friendly elementary mathematics teachers for studying the effectiveness of the program. From the result elementary preservice teachers' disposition in terms of thought about mathematics, mathematics learning, and mathematics teaching was changed to the positive direction through the PBL. They could developed their classroom practice ability, self-develop ability, and teaching profession character through application of new knowledge and plan for problem solving and reflection after solving the problems.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.209-227
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• 2006

From this research, we want to get results that have interested the difference from character of students with the motivation of the learning, confidence and habit through the activity oriented class. When teacher teach students of the learning disability with participant class and activity class, they have encouraged and have positive disposition about mathematics. Therefore teachers should try to give chance doing in mathematics class to students with learning disability.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.369-385
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• 2017

This study is to figure out the activity and disposition of gifted students with face plot in exploratory data analysis at middle school mathematics class. This study has begun on the basis of the doing mathematics at multivariate analysis beyond one variable and two variables. Gifted students were developed the good learning habits theirselves. According to this result, Many gifted students have an interesting experience at data analysis with Face Plot. And they felt the useful methods of creative thinking about graphics with doing mathematics at mathematical tasks. I think that teachers need to learn the visualization methods and to make and to develop the STEAM education tasks connected real life. It should be effective enough to change their attitudes toward teaching and learning at exploratory data analysis.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• Advances in concrete construction
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• v.14 no.2
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• pp.103-113
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• 2022

On the basis of fabrication, the utilization of nano material in numerous industrial and technological system, obtained the utmost significance in current decade. Therefore, the current investigation presents a theoretical disposition regarding the flow of electric conducting Williamson nanoliquid over a stretchable surface in the presence of the motile microorganism. The impact of thermal radiation and magnetic parameter are incorporated in the energy equation. The concentration field is modified by adding the influence of chemical reaction. Moreover, the splendid features of nanofluid are displayed by utilizing the thermophoresis and Brownian motion aspects. Compatible similarity transformation is imposed on the equations governing the problem to derive the dimensionless ordinary differential equations. The Homotopy analysis method has been implemented to find the analytic solution of the obtained differential equations. The implications of specific parameters on profiles of velocity, temperature, concentration and motile microorganism density are investigated graphically. Moreover, coefficient of skin friction, Nusselt number, Sherwood number and density of motile number are clarified in tabular forms. It is revealed that thermal radiation, thermophoresis and Brownian motion parameters are very effective for improvement of heat transfer. The reported investigation can be used in improving the heat transfer appliances and systems of solar energy.