• Proceedings of the Korean Information Science Society Conference
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• 1999.10a
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• pp.180-182
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• 1999

지리 정보 시스템(Geographic Information System, GIS)에서 가장 주요한 부분을 차지하는 것 중의 하나가 공간 데이터 모델(spatial data model)에서 정의된 각 공간 데이터들간의 공간 관계 연산자(spatial relational operator)의 효과적인 구현이다. 공간 데이터는 점(point), 선(line), 면(area)으로 표현될 수 있다. 이들 사이의 모든 공간 관계는 Disjoint, Touch, Cross, In, Overlap의 다섯 가지 연산자로 표현 가능함이 알려져 가능함이 알려져 있으며, 이들에 대한 실체적인 위상 관계를 표현하는 다양한 수학적 모델링 방법이 존재한다. 하지만, 실제 이들 공간 연산자들을 수학적 모델에 따라 그대로 구현하려고 하면, 컴퓨터 상에서는 표현할 수 없다거나 많은 자원을 차지하는 데이터 구조를 필요로 한다거나, 또는 비효율적인 알고리즘으로 구현할 수 밖에 없는 현실적인 어려움에 봉착한다. 그 중에서도 구현하기 어려운 연산은 면과 선과의 관계, 면과 면과의 공간 관계를 찾아내는 공간 연산자이다. 본 논문에서는 선분의 양끝점을 이용하여 면과 선분(line segment)과의 관계를 찾아내는 알고리즘을 제안한다. 이 알고리즘을 사용하여 면과 선, 면과 면과의 관계를 찾아내는 공간 연산자를 효율적으로 구현할 수 있다.

• The Mathematical Education
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• v.59 no.3
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• pp.237-254
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• 2020

The current study investigated the relationships between mathematical knowledge for teaching and the mathematical quality in instruction in order to gain insight about teacher education for secondary teachers in South Korea. We collected and analyzed twelve high school teachers' scores of the multiple-choice assessment for mathematical knowledge for teaching developed by the Measures of Effective Teaching project. Their instruction was video recorded and analyzed with the mathematical quality in instruction developed by the Learning Mathematics for Teaching project. We also interviewed the teachers about how they planned and assessed their instruction by themselves in order to gain information about their intention and interpretation about instruction. There was a statistically significant and positive association between the levels of mathematical knowledge for teaching and the mathematical quality in instruction. Among three dimensions of the mathematical quality in instruction, mathematical richness seemed most relevant to mathematical knowledge for teaching because subject matter knowledge plays an important role in mathematical knowledge for teaching. Furthermore, working with students and mathematics as well as students participation were critical to decide the quality of instruction. Based on these findings, the current study discussed offering opportunities to learn mathematical knowledge for teaching and philosophy about how teachers need to consider students in high schools particularly in terms of constructivism.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.247-264
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• 2002

본 연구의 목적은 교사들이 갖고 있는 수학 및 수학을 어떻게 가르칠 것인가에 대한 신념과 수업 관행과의 관계를 문헌적 고찰을 통하여 교사 변화를 위한 모델을 제시하는데 있다. 이를 위하여 먼 저 신념에 대한 정의, 신념과 지식의 차이점, 그리고 신념이 교사들의 수업 관행과 어떻게 관련이 있는지를 논의하였다. 신념과 수업 관행과의 상호 관계를 통하여 본 연구에서는 수업 개선 프로그램의 개발을 위한 모델을 개인적 수준, 학급 수준, 및 학교 수준의 세 시각에서 논의하였다. 이들 모델들은 결국 교사의 학습도 학생들의 학습 방법과 유사한 형태를 띄고 있다는 점에서 현재의 주요한 수학 학습 이론들에 근거를 두고 있다. 결국, 교사들의 수업 관행에 큰 영향을 끼치는 것으로 알려진 교사들의 수학적 신념은 위에 논의된 세 요소의 측면에서 수업 개선 프로그램들이 운영될 때 수업 관행과 함께 변화한다는 것을 본 이론 연구에서는 암시해 주고 있다.

• School Mathematics
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• v.9 no.1
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• pp.65-97
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• 2007

Problem solving and mathematical applications have been increasingly emphasized in school mathematics over the past ten years. Recently it is recommended that mathematical applications and modeling situations be incorporated into the secondary school curriculum. Many researches on this approach have been conducted in Korea. But unfortunately two thirds of these researches have been studied by graduate students. Therefore, more professional researchers should be concerned with the study related to mathematical modelling activity. This study is planning to investigate and establish i) the concepts and meanings of mathematical model, mathematical modelling, and mathematical modelling process, ii) the properties of problem situations introduced and dealt with in mathematical modelling activity, and iii) relationship between mathematical modelling activity and problem solving activity, and so on. To accomplish this, this study is based on the analysis and comparison of 11 articles published in domestic journals and 22 domestic master papers.

• Journal of Gifted/Talented Education
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• v.15 no.2
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• pp.59-76
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• 2005

We examined the relations between the score of the divergent thinking in mathematical (Mathematical Creative Problem Solving Ability Test; MCPSAT: Lee etc. 2003) and non-mathematical situations (Torrance Test of Creative Thinking Figural A; TTCT: adapted for Korea by Kim, 1999). Subjects in this study were 213 eighth grade students(129 males and 84 females). In the analysis of data, frequencies, percentiles, t-test and correlation analysis were used. The results of the study are summarized as follows; First, mathematically gifted students showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than regular students. Second, female showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than males. Third, there was statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for middle students was r=.41 (p<.05) and regular students was r=.27 (p<.05). A test of statistical significance was conducted to test hypothesis. Fourth, the correlation between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students was r=.11. There was no statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students. These results reveal little correlation between the scores of the divergent thinking in mathematical and non-mathematical situations in both mathematically gifted students. Also but for the group of students of relatively mathematically gifted students it was found that the correlations between divergent thinking in mathematical and non-mathematical situations was near zero. This suggests that divergent thinking ability in mathematical situations may be a specific ability and not just a combination of divergent thinking ability in non-mathematical situations. But the limitations of this study as following: The sample size in this study was too few to generalize that there was a relation between the divergent thinking of mathematically gifted students in mathematical situation and non-mathematical situation.

• Education of Primary School Mathematics
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• v.19 no.2
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• pp.161-175
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• 2016

The purpose of this study is to measure the differences in affective characteristics and mathematical reasoning ability between gifted students and non-gifted students. This study compares and analyzes on the relations between the affective characteristics and mathematical reasoning ability. The study subjects are comprised of 97 gifted fifth grade students and 144 non-gifted fifth grade students. The criterion is based on the questionnaire of the affective characteristics and mathematical reasoning ability. To analyze the data, t-test and multiple regression analysis were adopted. The conclusions of the study are synthetically summarized as follows. First, the mathematically gifted students show a positive response to subelement of the affective characteristics, self-conception, attitude, interest, study habits. As a result of analysis of correlation between the affective characteristic and mathematical reasoning ability, the study found a positive correlation between self-conception, attitude, interest, study habits but a negative correlation with mathematical anxieties. Therefore the more an affective characteristics are positive, the higher the mathematical reasoning ability are built. These results show the mathematically gifted students should be educated to be positive and self-confident. Second, the mathematically gifted students was influenced with mathematical anxieties to mathematical reasoning ability. Therefore we seek for solution to reduce mathematical anxieties to improve to the mathematical reasoning ability. Third, the non-gifted students that are influenced of interest of the affective characteristics will improve mathematical reasoning ability, if we make the methods to be interested math curriculum.

• School Mathematics
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• v.12 no.3
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• pp.389-410
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• 2010

In this paper we examined the mutural relation of quadrilateral for the purpose to know the reason why we taught the mutural relation of quadrilateral in elementary school. We looked through the several materials, for example, national curriculum, textbooks, guide books for teachers in 1st, 2nd, 3rd curriculums. Finally we found that the mutural relation of quadrilateral was deeply involved in the concept of sets, or the concept of inclusion.

• School Mathematics
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• v.18 no.2
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• pp.397-423
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• 2016

Mathematics learning motivation is an important variable which is not only the primary goal of learning mathematics but also mediates the effects of the mathematics learning. Nevertheless, the present learning environment is full of impeding factors which reduce learners' motivation to learn mathematics and mathematical self-regulatory efficacy. The purpose of this study is to offer various suggestions for program to enhance and forster mathematics learning motivation based on empirical findings and theories on motivation, self-regulatory learning, regulatory focus, reducing academic stress and math anxiety. The concrete and practical ideas are suggested in terms of mathematical self-regulatory efficacy, learners' characteristics, learning task. The analysis of the effects revealed a positive effect on mathematical self-regulatory learning.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.4
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• pp.383-403
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• 2019

The purpose of this study was to examine how students' perception of their mathematics teachers' instructional practices is associated with students' attitude toward mathematics, taking into account their self-efficacy in mathematics. The sample contained 4669 Korean fourth graders who participated in Trends in International Mathematics Science Study 2015. We used exploratory factor analysis and confirmatory factor analysis to explore the factor structure of three latent variables and conducted structural equation modeling to examine the hypothesized model. The results revealed that when students positively perceived their teachers' instructional practices, they tended to have a positive attitude toward mathematics. We also found that students' self-efficacy beliefs in mathematics positively mediated the relationship between perceived teachers' instructional practices and personal attitude toward mathematics. We discuss the practical and methodological implications of these findings and offer directions for future studies.

• Education of Primary School Mathematics
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• v.23 no.1
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• pp.45-61
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• 2020

The concept of equality is given as a way of reading the equal sign without dealing it explicitly in elementary school mathematics. The meaning of the equal sign can be largely categorized as operational and relational views. However, most elementary school students understand the equal sign as an operational symbol for just writing the required answers. It is essential for them to understand a relational concept of the equal sign because algebraic thinking in middle school mathematics is based on students' understanding of a relational view of the equal sign. Recently, the relational meaning of the equal sign is emphasized in arithmetic. Hence it is necessary for elementary school students to have some activities so that they experience a relational meaning of the equal sign. In this study, we investigate the meaning of the equal sign and contexts of the equal sign in elementary school mathematics to discuss explicit ways to emphasize the concept of equality and relational views of the equal sign.