• 한국CDE학회논문집
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• 제2권1호
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• pp.11-18
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• 1997

Scientific volume visualization addresses the representation, manipulation, and rendering of volumetric data sets, providing mechanisms for looking closely into structures and understanding their complexity and dynamics. In the past several years, a tremendous amount of research and development has been directed toward algorithms and data modeling methods for a scientific data visualization. But there has been very little work on developing a mathematical volume model that feeds this visualization. Especially, in flow visualization, the volume model has long been required as a guidance to display the very large amounts of data resulting from numerical simulations. In this paper, we focus on the mathematical representation of volumetric data sets and the method of extracting meaningful information from the derived volume model. For this purpose, a B-spline volume is extended to a high dimensional trivariate model which is called as a flow visualization model in this paper. Two three-dimensional examples are presented to demonstrate the capabilities of this model.

• East Asian mathematical journal
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• 제26권4호
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권1호
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• pp.45-58
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• 2002

This study was conducted to investigate the gender-related effects of two instructional programs on spatial visualization skills of ninth grade students. Two instructional programs were developed for this study: a web-based virtual reality program and a paper-based program. 194 ninth graders from two middle schools in Seoul participated in this study. Six classes were divided into experimental groups and control groups. The Middle Grades Mathematics Projects (MGMP) Spatial Visualization Test was used to measure spatial visualization skills. The data analysis indicated that both the web-based and paper-based programs were effective to improve spatial visualization skills to treatment groups. Although boys'test mean scores were higher than girls' in the pretest, when deleting the effect of covariance of pretest, there were no statistical significance in the post-test. Girls in the treatment groups favored the paper-based spatial visualization program. These results imply that spatial training may benefit girls' performance more than that of boys and mode of instructional programs can create gender-related differences regarding spatial visualization skills.

• 대한수학교육학회지:학교수학
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• 제1권1호
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• pp.135-156
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• 1999

The purpose of this study is to discuss about the role of the visualization as an effective method of teaching abstracted mathematics, to analyze visual materials in middle and high school mathematics and to suggest various visualized materials for teaching mathematics effectively. Though formal, symbolic and analytical teaching method is a major characteristic of mathematics, the students should be taught to understand through intuition and insight, and formalize the mathematical concepts progressively. Especially the sight is one of the most important basics of cognition for intuition and insight. Therefore, suggesting mathematical contents through the visual method makes the students understand and formalize the mathematical concepts more easily. In this study, we tried to investigate the meaning and role of visualization in mathematics teaching. And, we discussed about the four roles of visualization in the process of mathematics teaching and learning confirmation and memorization of the mathematical truth, proving theorem and solving problems which is one of the most important purposes of teaching mathematics, According to the roles of visualization, we analyzed visual materials currently taught in middle and high school, and suggested various visual materials useful in teaching mathematics. The investigated fields are algebra where visual materials are little used, and geometry where they are use the most. The paper-made-textbook can't show moving animation vigorously. Hence we suggested visual materials made by GSP and applets in IES .

• 대한수학교육학회지:학교수학
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• 제14권1호
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• pp.1-28
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• 2012

본 연구는 30명의 고등학교 2학년 학생들을 통해서 수학적 시각화의 구성 요소를 알아보고, 시각화 구성 요소들이 수학 문제 해결 과정에서 어떻게 활용되는지를 알아보는 것이다. 특히, 30명의 학생들 중 시각성 평가가 높은 5명의 학생들에 대해서 질적 사례 연구를 실시하였다. 분석 결과를 보면, 시각화의 구성 요소는 크게 정신적 이미지, 외적 표상, 이미지의 변형 및 조작, 공간 시각화 능력으로 범주화 (Guti$\acute{e}$rrez, 1996) 되었고, 각 요소마다 더 세분화되어져 나타났다. 또한, 수학 문제 해결 과정에서 시각화 요소들은 외적 표상을 생성하기 전에 기본적으로 정신적 이미지를 생성하고 있었고, 정형화된 정신적 이미지의 경우 문제 해결에 대한 학생들의 풍부한 사고를 억제하고 문제에 대한 부적절한 풀이 결과를 이끌어낼 수 있는 부정적인 영향을 주었다. 차원 변화에 의해서 이루어지는 이미지 변형 및 조작을 어려워하는 학생들이 있었으나, 문제 해결 과정에서 답을 추론하기 위한 이미지 탐색 활동과 도출된 답의 정당화를 위해서 이미지 조작 활동을 활용하고 있었다.

• Korean Journal of Mathematics
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• 제14권1호
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• pp.35-46
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• 2006

The concept of convolution is a fundamental mathematical concept in a wide variety of disciplines and applications including probability, image processing, physics, and many more. The visualization of convolution for the continuous case is generally predetermined. On the other hand, the convolution structure embedded in the discrete case is often subtle and its visualization is non- trivial. This paper purports to develop the CAS techniques in visualizing the logical structure in the concept of a discrete convolution.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권3호
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• pp.263-273
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• 2006

The purpose of this paper is to research the factors and the effects of immediacy in mathematics teaching and learning and mathematical problem solving. The factors of immediacy are visualization, functional fixedness and representatives. In special, students can apprehend immediately the clues and solution using the visual representation because of its properties of finiteness and concreteness. But the errors sometimes originate from visual representation which come from limitation of the visual representation. It suggests that students have to know conceptual meaning of the visual representation when they use the visual representation. And this phenomenon is the same in functional fixedness and representatives which are the factors of immediacy The methods which overcome the errors of immediacy is that problem solvers notice the limitation of the factors of immediacy and develop the meta-cognitive ability. And it means we have to emphasize the logic and the intuition in mathematical teaching and learning. Clearly, we can't solve all mathematical problems using only either the logic or the intuition.

• East Asian mathematical journal
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• 제37권4호
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• 한국컴퓨터정보학회논문지
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• 제21권7호
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• pp.85-92
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• 2016

The law of large numbers, central limit theorem, and connection among binomial distribution, normal distribution, and statistical estimation require dynamics of continuous visualization for students' better understanding of the concepts. During this visualization process, the differences and similarities between statistical probability and mathematical probability that students should observe need to be provided with the intermediate steps in the converging process. We propose a visualization method that can integrate intermediate processes and results through Excel. In this process, students' experiences with dynamic visualization help them to perceive that the results are continuously changed and extracted from multiple situations. Considering modeling as a key process, we developed a classroom exercise using Excel to estimate the population mean and standard deviation by using a sample mean computed from a collection of data out of the population through sampling.

• 대한수학교육학회지:수학교육학연구
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• 제12권1호
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• pp.71-79
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• 2002

Visualization have strong driving force that enables us to recognize abstract mathematics by direct and specific method in school mathematics. Specially, visual thinking helps in effective problem solution via intuition in mathematics education. So, this paper examines the meaning of visualization, the role of visualization in intuitive problem solving process and the methods for enhancement of intuition using visualization in mathematics education. Visualization is an useful tool for illuminating of intuition in mathematics problem solving. It means that visualization makes us understand easily mathematical concepts, principles and rules in students' cognitive structure. And it makes us experience revelation of anticipatory intuition which finds clues and strategy in problem solving. But, we must know that visualization can have side effect in mathematics learning. So, we have to search for the methods of teaching and learning which can increase students' comprehension about mathematics through visualization and minimize side aspect through visualization.