• Proceedings of the Korean Information Science Society Conference
• /
• 2000.10b
• /
• pp.508-510
• /
• 2000

본 논문은 서로 다른 스플라인 곡선들간의 위상적 상호관계로서 곡선과 곡면 설계상에서 중요한 작업인 주어진 영역 안에 한정된 보간곡선 제어방법을 제안한다. 위상적 상호관계는 곡선들간의 영향범위 관계 그리고 스플라인 곡선들과 곡면간의 기하학적 관계를 의미한다. 기존의 방법은 선형 분모를 가지는 분수식 3차 보간법을 사용하여 주어진 영역에서 제한된 보간 곡선을 제어하는 방법을 제안하였으나, 일반적인 경우에서 실행 상의 많은 계산량과 오차가 나타나는 문제점을 나타내었다. 본 논문은 이러한 문제점을 해결하기 위한 선형분모를 가지는 가중치된 분수식 3차 보간법을 제안한다. 이 방법은 변형 보간된 물체상의 변화량을 계산하여 불규칙한 패치들간의 결합부분과 제어 및 국부수정의 변형을 제어하는 방법을 제안한다.

• Journal of the Korean School Mathematics Society
• /
• v.10 no.2
• /
• pp.149-171
• /
• 2007

This study is aimed at development of pedagogical content knowledge on fraction in the elementary school mathematics. Elementary students regard fraction as the difficult topic in school mathematics. Furthermore, fraction is the fundamentally important concept in studying mathematics. So it is important to develop the pedagogical content knowledge on fraction. The reason of attention to the pedagogical content knowledge is that improving the quality of teaching is the central focus of a high quality mathematics education. Shulman suggested that various knowledges are required for teacher to improve their classes. Of course, pedagogical content knowledge is the most valuable in teaching mathematics. Pedagogical content knowledge is related to the promotion of students' understanding about the learning. Pedagogical content knowledges are categorized by five factors in this study. These are understanding about curriculum, understanding about students and students' knowledge, understanding about teachers and teachers' knowledge, understanding about the methods, contents, and management of class, and understanding about methods of assessments. I develop the pedagogical content knowledge on fraction according to the these categories. I concentrate on the two types of pedagogical content knowledges in developing. That is, I present knowledges which teachers have to know for teaching fraction effectively and materials which teachers can use during the teaching fraction. Pedagogical content knowledges guarantee teachers as the professionalists. Teachers should not teach only content knowledges but teach various knowledges including the meta-knowledges which have relation to fraction.

• Journal of Korea Water Resources Association
• /
• v.41 no.8
• /
• pp.773-784
• /
• 2008

The present study was carried out to examine flow properties in linear drainage channels such as road surface drainage facilities. The finite difference formulation for the varied flow analysis was solved for flow profiles in the channels. Starting the first step at the control section, the Newton-Raphson method was applied for producing numerical solutions of the equation. We considered two types of linear drainage channels, a channel with one outlet at downstream end and a channel with two outlets at both ends. Moreover, the flow analysis for various channel slopes was performed. However, we considered channels with the two outlets of slopes satisfying the condition that the both ends are the control section. The maximum of those slopes was decided from the relation between the channel slope and the location of control section. The flow of a channel with one outlet was calculated upward and downward from the control section existing in channel or upward from the control section at downstream end. The flow of a channel with two outlets at both ends were calculated for upstream and downstream channel segments divided by the water dividend, respectively and the flow analysis was completed when the water depth at the water dividend calculated from upstream end was equal to that calculated from downstream end. If the slope was larger than the critical slope, the channel with two outlets was likely to behave like the channel with one outlet. The maximum water depth was investigated and compared with that calculated additionally from the uniform flow analysis. The uniform flow analysis was likely to lead a excessive design of a drainage channel with mild slope.

• Journal of Elementary Mathematics Education in Korea
• /
• v.18 no.1
• /
• pp.1-17
• /
• 2014

Instructions for the commutative property of multiplication at elementary schools tend to be based on checking the equality between the quantities of 'a times b 'and b' times a, ' for example, $3{\times}4=12$ and $4{\times}3=12$. This article critically examined the approaches to teach the commutative property of multiplication from Kant's perspective of mathematical knowledge. According to Kant, mathematical knowledge is a priori. Yet, the numeric exploration by checking the equality between the amounts of 'a groups of b' and 'b groups of a' does not reflect the nature of apriority of mathematical knowledge. I suggest we teach the commutative property of multiplication in a way that it helps reveal the operational schema that is necessarily and generally involved in the transformation from the structure of 'a times b' to the structure of 'b times a.' Distributive reasoning is the mental operation that enables children to perform the structural transformation for the commutative property of multiplication by distributing a unit of one quantity across the other quantity. For example, 3 times 4 is transformed into 4 times 3 by distributing each unit of the quantity 3, which results in $3{\times}4=(1+1+1){\times}4=(1{\times}4)+(1{\times}4)+(1{\times}4)+(1{\times}4)=4+4+4=4{\times}3$. It is argued that the distributive reasoning is also critical in learning the subsequent mathematics concepts, such as (a whole number)${\times}10$ or 100 and fraction concept and fraction multiplication.

• Journal for History of Mathematics
• /
• v.23 no.3
• /
• pp.121-140
• /
• 2010

This study presents one universal mean formula of implicate quantity for speed, temperature, consistency, density, unit cost, and the national income per person in order to avoid the inconvenience of applying different formulas for each one of them. This work is done by using the principle of lever and was led to the formula of two implicate quantity, $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$, and to help the understanding of relationships in this formula. The value of ratio of fraction cannot be added but it shows that it can be calculated depending on the size of the ratio. It is intended to solve multiple additions with one formula which is the expansion of the mean formula of implicate quantity. $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$, where $f_1+f_2+{\cdots}+f_n=N$. For this reason, this mean formula will be able to help in physics as well as many other different fields in solving complication of structures.

• Education of Primary School Mathematics
• /
• v.19 no.4
• /
• pp.277-289
• /
• 2016

Fraction is one of the concepts which are difficult to elementary school students. So, many researches about fraction were performed in mathematics education research. In special, fraction has so many subordinative concepts-proper fraction, improper fraction, mixed number. We have to concentrate on the conceptual understanding in teaching of fraction. In this case, a mixed number and improper fraction are concepts which can convert respectively. And there are methods that a mixed number and improper fraction can be converted. So, it's needed to analyze the converting methods in textbooks for getting the implication of teaching in this areas. In this study, I analyzed the Korean and foreign's textbooks. I certified the methods-using addition expression, using part-whole model in the textbooks. For the conceptual understanding, I suggested to use the fusion of the various part-whole fraction models and addition expression more than the algorithm in converting between a mixed number and improper fraction. It's reason that the use of models in converting between a mixed number and improper fraction is important for the relational understanding.

• Journal of Educational Research in Mathematics
• /
• v.14 no.2
• /
• pp.207-219
• /
• 2004

There have been studies reporting the increase in student confidence in mathematics when using technology. However, past studies indicating a positive correlation between technology and confidence in mathematics do not explain why they see this positive outcome. With increased availability and easy access to the Internet in schools and the development of free online virtual manipulatives, this research was interested in how the use of virtual manipulatives in mathematics can affect students confidence in their mathematical abilities. Our hypothesis was that the classes using virtual manipulatives which allows students to connecting dynamic visual image with abstract symbols will help students gain a deeper conceptual understanding of math concept thus increasing their confidence and ability in mathematics. The participants in this study were 46 fifth-grade students in three ability groups: one high, one middle and one low. During a two-week unit on fractions, students in three groups interacted with several virtual manipulative applets in a computer lab. Data sources in the project included a pre and posttest of students mathematics content knowledge, Confidence in Learning Mathematics Scale, field notes and student interviews, and classroom videotapes. Our aim was to find evidence for increased level of confidence in mathematics as students strengthened their understanding of fraction concepts. Results from the achievement score indicated an overall main effect showing significant improvement for all ability groups following the treatment and an increase in the confidence level from the preassessment of the Confidence in Learning Mathematics Scale in the middle and high ability groups. An interesting finding was that the confidence level for the low ability group students who had the highest confidence level in the beginning did not change much in the final confidence scale assessment. In the middle and high ability groups, the confidence level did increase according to the improvement of the contest posttest. Through interviews, students expressed how the virtual manipulatives assisted their understanding by verifying their answers as they worked and facilitated their ability to figure out math concept in their mind and visually.

• The Journal of Korean Philosophical History
• /
• no.52
• /
• pp.107-130
• /
• 2017

The purpose of this study is to catch the characteristics of the Hanju Yi Jinsang (寒洲 李震相, 1818~1886)'s thought of the 'Li(理)' through Hanju's view on the Ido-seol(理到說), the Toegye Yi Hwang(退溪 李滉, 1501~1570)'s latter Mulgyuk(物格) theory, and to establish the foundation for identifying the aspects of development about Toegye School's concept of Li from Toegye's Ido-seol. The Ido-seol was criticized for regarding Li - the immovable principle - as 'living thing'. Toegye School's scholars tried to solve this problem by translating the 'word' correctly. Hanju also translated the word 'Do(到)', the verb of 'Ido', as meaning of 'perfectly understood' based on his translation of the word 'Gyuk(格)' as 'Ku(究)'. On the other hand, he also regarded the principle-application structure of Li and the its characteristic the 'Li as Hwalmul(活物)' as the main point of Toegye's Neo-confucianism thought his methodology 'Three viewpoints[三看法]'. Before Hanju, scholars dose not have more opinion from the translation of the word, and it is too difficult to identifying their scholarly identity through their viewpoints on Ido-seol. On the other hand, Hanju thought that the lack of the idea for comprehensive approach between Xin(心) and Li(理) will cause the misunderstanding the relationship between Xin and Li. In this reason, he evaluated Toegye's Ido-seol based on the concept of 'One principle and its manifoldness[理一分殊]'. Consequently, he concatenated the characteristic of Xin which includes all things with concept of Mulgyuk, and emphasized that Xin which penetrates the principle of all things has the characteristic of 'One principle(理一)'.

• Journal of Elementary Mathematics Education in Korea
• /
• v.12 no.1
• /
• pp.1-25
• /
• 2008

The purpose of this study was to identify pre-service teachers' Pedagogical Content Knowledge (PCK) about decimal calculation. A written questionnaire was developed dealing with decimal calculation. A total of 152 pre-service teachers from 3 universities were selected for this study; they had taken an elementary mathematics teaching method course and had no teaching experience. The results were as follows: First, with regard to the method of decimal calculation, most pre-service teachers were familiar with algorithms introduced in the textbook. But with regard to the meaning of decimal calculations, they had difficulties in understanding decimal multiplication or decimal division with decimal number. Second, pre-service teachers recognized reasons of errors as well as errors patterns that student might make. But this recognition was limited mainly to errors related to natural number calculation. Third, pre-service teachers frequently commented about decimals algorithms, picture models, the meanings of decimal calculations, and connections to natural number calculations. Many of them represented the meanings of decimal calculations through picture models as to help students' understanding, while they just mentioned algorithms or treated decimal calculation as natural number calculations with decimal point.

• The Journal of Korean Philosophical History
• /
• no.54
• /
• pp.77-113
• /
• 2017

In late Chosen(朝鮮), the concept of illustrious virtue(明德) became an important issue of debate. However, previous studies did not focus on how the concept emerged as an issue. This paper aimed to explore the problem, and for this purpose, paid attention to Horak(湖洛) debate. Oiam(巍巖) Yi Gan(李柬), in the course of discussion with Namdang(南塘), finally argued that mind(心) clearly distinguishes from temperament(氣質). The goals of the claim were to clearly divide mind and temperament, and to emphasize mind's control of temperament. Through this, he wanted to reject the possibility of being affected by temperament in aroused state(未發). And he presented the concept of illustrious virtue as a critical evidence supporting his argument. He argued that because mind is same with illustrious virtue, it has a special status that essentially distinguished from the temperament, even if both mind and temperament are all material force(氣). This argument led to new discussion trend in the debate. it was to form a definition of the mind, based on defining the relationship between spiritual perception(虛靈知覺), temperament and illustrious virtue. The trend was reflected in the debate on 'Whether illustrious virtue is the same for everyone or varies from person to person(明德分殊)'. Through the process of analysis in this paper, we could detect a tendency that definition of mind has become an independent subject.