• Education of Primary School Mathematics
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• v.15 no.2
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• pp.159-170
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• 2012

Many obstacles have been found in the learning of ratio and rate. The types of epistemological obstacles concern 'terms', 'calculations' and 'symbols'. It is important to identify the epistemological obstacles that students must overcome to understand the learning of ratio and rate. In this respect, the present study attempts to figure out what types of epistemological obstacles emerge in the area of learning ratio and rate and where these obstacles are generated from and to search for the teaching implications to correct them. The research questions were to analyze this concepts as follow; A. How do elementary students show the epistemological obstacles in ratio and rate? B. What is the reason for epistemological obstacles of elementary students in the learning of ratio and rate? C. What are the teaching implications to correct epistemological obstacles of elementary students in the learning of ratio and rate? In order to analyze the epistemological obstacles of elementary students in the learning of ratio and rate, the present study was conducted in five different elementary schools in Seoul. The test was administered to 138 fifth grade students who learned ratio and rate. The test was performed three times during six weeks. In case of necessity, additional interviews were carried out for thorough examination. The final results of the study are summarized as follows. The epistemological obstacles in the learning of ratio and rate can be categorized into three types. The first type concerns 'terms'. The reason is that realistic context is not sufficient, a definition is too formal. The second type of epistemological obstacle concerns 'calculations'. This second obstacle is caused by the lack of multiplication thought in mathematical problems. As a result of this study, the following conclusions have been made. The epistemological obstacles cannot be helped. They are part of the natural learning process. It is necessary to understand the reasons and search for the teaching implications. Every teacher must try to develop the teaching method.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Communications of Mathematical Education
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• v.32 no.2
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• pp.225-244
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• 2018

Problem solving and its mathematical applications have been increasingly emphasized in school mathematics over the past years. Recently it is recommended that mathematical applications and modelling situations be incorporated into the secondary school curriculum. Many researchers on the approach have been conducted in Korea. This study is planning to investigate and establish the meaning of mathematical modelling and model, mathematical modelling process. And also it does the properties of problem situations introduced and dealt with in mathematical modelling activity. To accomplish this, this study is based on the analysis and comparison of those 24 articles. They are ones which have been published from 2007 to 2017 and are included in the five types of publication. Prior to this study, the previous study was conduct in 2007 with the same purpose. Namely, by the subject of 11 articles and 22 master dissertations published domestically from 1991 to 2005, the analytic and explorative study on the mathematical modelling and its understanding had been conducted.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.41-59
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• 2016

There have been continuous improvements in human life expectancy. Life expectancy is as a key factor in an aging population and can wreak severe damage on the financial integrity of pension providers. Hence, the projection of the accurate future mortality is a critical point to prevent possible losses to pension providers. However, improvements in future mortality would be overestimated by a typical mortality projection method using the Lee-Carter model since it underestimates the mortality index ${\kappa}_t$. This paper suggests a mortality projection based on the projection of the skewness of the mortality versus the typical mortality projection of the Lee-Carter model based on the projection of the mortality index, ${\kappa}_t$. The paper shows how to indirectly estimate future t trend with the skewness of the mortality and compares the results under each estimation method of the mortality index, ${\kappa}_t$. The analysis of the results shows that mortality projection based on the skewness presents less improved mortality at an elderly ages than the original projection.

• The Korean Journal of Applied Statistics
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• v.27 no.2
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• pp.211-226
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• 2014

This paper discusses life expectancy differentials of beneficiaries of national pension old-age benefit and benefit-cost analysis in Korea. These results are useful indicators for the assessment of retirement income security of beneficiaries and old-age benefits. This paper analyzes benefit-cost ratio, internal rate of return and generation transfer amount, using life tables by lifetime incomes. The result of the actuarial analysis for male life expectancy is approximately 21.69 to 24.63 years. The result of the actuarial analysis for female life expectancy is approximately 27.63 to 29.81 years. The result of the actuarial analysis of low income level is that the benefit-cost ratio is lower approximately 2.68 to 4.83%, the internal rate of return lower approximately 0.00 to 0.74%, the generation transfer amount lower approximately 3.00 to 5.74%, than total income level. The result of the actuarial analysis of high income level is that the benefit-cost ratio is higher approximately 2.07 to 4.98%, the internal rate of return higher approximately 0.03 to 1.73%, the generation transfer amount higher approximately 2.53 to 9.68%, than the total income level. The results by income varies due to the effect of income redistribution and life expectancy on the national pension.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

• Archives of design research
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• v.11
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• pp.22-29
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• 1995

I have to find standpoint of sight moulding of Chi I Sung Hwa(seven stars picture) analysis of graphic systems of a symbol sight native to our nation. And I will comprehend emotion of folkways by simple and graphic lines and colors in mathematical Grid of which ancestor had expressed in gauge moulding consciousness. This papers aim is to make a contribution to lead by on part of communication design. About structural analysis of pictorial graphic side. I) Mathematical thought of the Orient and space constitution are first basically the Orient expressed number notion of mathematics of unlimitedness and notion of zero so called space and empty second can analigize a diagonal expansion method by development of symmetry notion to basic the dual principle of the negative and positive by degrees development expressed space division method by direction notion. 2) About the proportion analysis it based the golden section globularity and in modern layout it takes vision center of position, after appointing the brow of sacred image of Chil Sung Hwa as center point of proportion and applied to the point proportion and so analigized the posibility of established. Rule in union of each elements and rule of forms about picture image. 3) Mathematical structure analysis to search a unified principle at the balanced arrangement and rule of forms it analigized the standard the rule of forms. it analigized the standard the rule of forms to body module of basic movement of protagonist and follower above basic forms of grid that is the basis of design system.

• Archives of design research
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• v.15 no.1
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• pp.181-190
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• 2002

Every object's patterns is the balancing-relationship between the object's inner-energy and outer-stress. To see this as a balancing-relationship between an organism, inner-energy would be the occurrence of thermodynamic entropy which is for its existing maintenance. Outer-stress would be the friction that comes from the surrounding environment. Namely, we can see that object's figure exists in the balance between an extort to survive and fiction that disturb it. However, it is fourth that these figures are consisted of a curve and curved-surface which is not a straight line. So, it is impossible to find a figure made up of straight lines and surfaces in the existing object's world. It's true that we have regarded only a curve as the beautiful. Here, we have presented that in a curve, there exists an important function which protect our survival from the ancient humanity. And by closely observing the function in a physical dynamic-pattern sight, we've searched what is important in the design's origin that handle curve-patterns. Of course it would be more reasonable to analyze it in the standpoint of Mathematics, Chemistry, or Biology, and synthesize the points. However, due to the limitation of the researchability, we will concern about the physical structure in the design. Deficient details will be replenished through the study between educational systems. As a result, we have confirmed that, devoting the curve's physical structure-phenomenon (occurred in nature) to the design, is more beautiful in our eyes, too.

• Journal of Engineering Education Research
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• v.8 no.1
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• pp.84-98
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• 2005

This study is on improving the general engineering education for enhancing the quality of engineers at a local engineering school in which the students are not highly qualified for engineering education. Based on the analysis on the current engineering education by asking questions to professors, students and alumni of Hongik College of Science and Engineering, we have set the basic educational philosophy as educating practical engineers and have decided the goals of basic engineering education as changing to student oriented education, enhancing the field adaptation capability, improving the problem solving ability and introducing engineering design courses. For achieving the foregoing goals, we have changed several basic engineering courses. Mathematics, science courses, computer related courses, English, communication skill related courses are strengthened, but general college education courses are reduced. We also have encouraged students to participate the classes actively and study efficiently, think logically and creatively. For the operational details, we have tried to impose less courses to freshmen and sophomores, to impose the prerequisite courses, to activate summer and winter schools. Finally, we have tried to find the ways to support continuous improvement on the basic engineering education.

• Journal of Engineering Education Research
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• v.13 no.6
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• pp.57-71
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• 2010

This paper is a study on the perception of current competency and expected competency of engineering freshmen by extracting core competencies acquired from university education. It also aims to suggest proper way for engineering university education. This study extracts competencies in the following five areas as core competencies: 'knowledge on major area', 'cultural ability', 'foreign language ability', 'basic learning ability', 'intercommunication ability'. To achieve this purpose, this study surveyed 'C' university engineering department freshmen (584 students) with questionnaires about their perception of core competencies. The results are as follows. First, engineering freshmen perceived current competencies were weak in every area, especially their capacities in 'foreign language ability' area were perceived to be weakest. Their demand for education is the highest in 'foreign language ability' area, and the second higher in 'knowledge on major area'. Secondly, there exists meaningful difference between perception of current competency and expected competency depending on the gender, high school department (science/liberal arts), high school location, types of college admissions, and types of mathematics in NAST. According to these results, this study suggests enhancement of foreign language (English) education in engineering department, design and implementation of various educational program to overcome individual difference, promoting importance of competencies in the 'cultural abilty' and 'intercommunication abilty', necessity of continuous adjustment and complementation for engineering educational program through accumulation of feedback processes, activation of career education through engineering education and special programs.