• Education of Primary School Mathematics
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• v.14 no.1
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• pp.27-41
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• 2011

This study is the consideration to 'The Data' and 'On Divisions' of Euclid which is the historical start of analysis and synthesis. 'The Data' and 'On Divisions' compared to Euclid's Elements is not interested. In this study, analysis and synthesis were examined for significance. In this study, means for 'analysis' and 'synthesis' were examined through an analysis of 'The Data' and 'On Divisions'. First, the various terms including analysis and synthesis were examined and the concepts of the terms were analyzed. Then, analysis was divided into 'external analysis' and 'internal analysis'. And synthesis was divided into 'theoretical synthesis' and 'empirical synthesis'. On the basis of this classification problem presented in elementary textbooks and the practical applications were explored.

• Education of Primary School Mathematics
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• v.23 no.4
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• pp.157-173
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• 2020

Although there are various form of statistical graphs in the real world, the statistical graphs in elementary mathematics textbooks are very formalized by the pedagogical constraints. In this study, I examine the frames of statistical graphs and their educational importance, and analyze the frames in Korean, Australian, and MiC textbooks. As a result, the frames of statistical graphs in elementary mathematics textbooks (1) draws students' attention to the components of the graphs, (2) plays a supplementary role in students' drawing graphs by hands, and (3) helps to apply school mathematics to statistical problem solving in real life. The frames of statistical graphs in Korean textbooks is the form of tables focusing on (1) and (2), but these of MiC textbooks has various forms focusing on (3). On the other hand, Austalian textbooks introduced the table-form frames of statistical graphs at the lower graders, but gradually changed to the axis-form frames as the grade level increased. Based on this, a recommendation was drawn on how to deal with the frames of statistical graphs in elementary mathematics textbooks.

• Journal of Korea Spatial Information System Society
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• v.12 no.1
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• pp.37-48
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• 2010

In this paper, we analyze the shortcomings of the previous declustering methods, which are based on grid-like partitioning and a mapping function from a cell to a disk number, for high-dimensional space and propose a solution. The problems arise from the fact that the number of splitting is small(for the most part, binary-partitioning is sufficient), and the side length of a range query whose selectivity is small is quite large. To solve this problem, we propose a mathematical model to estimate the performance of a grid-like partitioning method. With the proposed estimation model, we can choose a good grid-like partitioning method among the possible schemes and this results in overall improvement in declustering performance. Several experimental results show that we can improve the performance of a previous declustering method up to 2.7 times.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.379-398
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• 2011

In learning environment at mathematics education, prove and refute are essential abilities to demonstrate whether and why a statement is true or false. Learning proofs and counter examples within the domain of limit of sequence is important because preservice teacher encounter limit of sequence in many mathematics courses. Recently, a number of studies have showed evidence that pre service and students have problem with mathematical proofs but many research studies have focused on abilities to produce proofs and counter examples in domain of limit of sequence. The aim of this study is to contribute to research on preservice teachers' productions of proofs and counter examples, as participants showed difficulty in writing these proposition. More importantly, the analysis provides insight and understanding into the design of curriculum and instruction that may improve preservice teachers' learning in mathematics courses.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5841-5846
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• 2013

In this work, we consider the effect of doppler bandwidth on the performance of channel sounding. We develop the mathematical formulation of the problem and compare the MMSE channel estimator to the simple correlator. Examples of the performance of the MMSE and correlator estimators are presented for the single-input single-output (SISO) case with various values of Doppler bandwidth to assess the impact of time variation. The results show that as the $f_dT$ product increases the performance of both the MMSE and correlator estimates gets worse, and that the performance of the MMSE estimator improves relative to the correlator.We also consider case that the exact statistics of the channel are unknown It is shown that when the mismatch is not too large, the MMSE estimator with mismatch still does better than the simple correlator, but if the mismatch is large, then the correlator can do better.

• Journal of Biosystems Engineering
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• v.28 no.1
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• pp.1-10
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• 2003

A computer simulation was carried out to determinate the optimum capacity of bulk type trailer which is used as a tractor attachment. Soil physical properties. such as soil moisture content. bulk density, soil hardness and soil texture were measured in the 10 major rice production area for computer simulation. Mathematical model which include soil physical properties and vehicle factor was used for computer simulation. Most of the soil texture of the investigated area was silty loam. Soil moisture content ranged between 30 and 40% mostly. Soil bulk density was in the range of 1.500 to 1.700 kg/㎥. Soil hardness ranged between 1 to 18 kg/$\textrm{cm}^2$. Soil hardness incorporate the effects of many soil physical properties such as moisture content texture and bulk density, and so the range of soil hardness was greater than any other physical properties. The capacity of bulk type trailer was above 3000 kg$_{f}$ fer the most of the investigated area. and mostly in the range of 4000 to 6000 kg$_{f}$ depending upon the slip. But for the soft soil area such as Andong and Namyang. tractor itself had mobility problem and showed minus trailer capacity for some places. For this area. the capacity of bulk type trailer ranged between 1000 and 2000 kg$_{f}$ mostly so bulk type trailer should be designed as a small capacity compared to the other area.ared to the other area. area.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.381-393
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• 2007

The study focuses on what to consider and do for the improvement of math education of Korean Universities by comparing freshmen and seniors of department of math education in their beliefs in mathematics and math. education. The major comparing topics in the beliefs are composed of perception of mathematics as a science, learning methods of mathematics, teaching methods of mathematics, and roles and qualifications of math. teachers. The results of the study show that junior students tend to be more positive in their beliefs, especially in math education area than that of mathematics, compared to the freshmen. It implies that how important the role of topics covered in math education during college years is for changing the future teachers' beliefs in math and math education more positively. The supposed influencing contents of the curriculum of math. education are composed of learning reflection method based on problem-based learning, understanding mathematics as originated from the real world, mathematical pedagogy, text analysis, practice in classroom, and understanding various concepts in math. education area.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.49 no.2
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• pp.144-152
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• 2013

In an effort to find the optimum porous of Taewoo through the mathematical model 2 - dimensional tank water experiment among the approached to a problem related to ocean engineering, this study analyzed the porosity by dividing it into 9 cases. As the wave penetrates through the longitudinal porous of the Taewoo model, it was found that there is a wave energy loss because of the phenomenon of the separation of the porous due to the eddy. Looking into the general tendency based on the wave-height meter (probe) data, it was found that the shorter wavelength and higher frequency area, the more reflection coefficients increased, but in contrast, the longer wavelength and lower frequency area, the transmission coefficients showed the increasing trend and energy dissipation was in a similar way with reflection coefficients. In addition, it was found that the bigger the porosity was, the narrower distribution range of reflection coefficients was, and the more its average value decreased. On the other hand the transmission coefficients in direct opposition to reflection was found to show the wider range and the more gradual increase in the average value as porosity was the bigger around the average value. In contrast, energy dissipation rate was found to increase linearly as porosity increased the more around the porosity of 0.2518 but it decreased gradually around the peak point. Through the above results, it is judged that the porous of optimum in the longitudinal direction of the Taewoo model perforated plate was about 2.6cm because it was found that the porosity which produced the lowest reflection and transmission coefficient and the highest energy dissipation. As a result of comparing this to the case where there was no porosity at all, it showed the function of wave absorbing about 31.60%.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.843-863
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• 2010

The basic purpose of 2007 revision curriculum is content of activity oriented, management of differentiated instruction, communication, introduction of story mathematics, mathematical exploration and problem solving ability and so on. In this paper, we investigate some characteristics of number teaching in the primary school of New Zealand. Especially, focused on materials and methods and so on. So we've got the following results. First, there are no fundamental differences in materials and methods in teaching number between Korea and New Zealand but in New Zealand there are no national textbook like us so there is a possibility not to teach number systematically like our Korea. On the contrary, they divide number region from one to six level and are offering achievement objects, suggestive learning experiences, sample assessment activities for each level and also they do not guide activities itself in detail like us and so have learners themselves think about the given problems. Second, there is a strategy stage in getting knowledge about number in New Zealand and so children can take advantage of this steps according to the type of problems. Third, it must be developed some materials and idea to reach the learning purpose rousing interest of children.

• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.