• The Mathematical Education
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• v.15 no.1
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• pp.5-7
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• 1976

Euclid 기하학이 성립하는 공간은 우리들과 가장 밀접한 공간이다. Descartes의 해석기하학은 Euclid의 3차원공간에서 성립한다. 이 경우 점이라 해도 그것은 3개의 실수의 순서쌍(x, y, z)에 의해 표현되는 것으로 생각해도 좋다. 일반의 n차원 Euclid 공간 R$^n$에 대해서도 같은 생각으로 정의할 수 있다. 이 경우 n=1은 수치선, n=2는 평면, n=3은 소위 3차원의 공간으로서 직관적으로 상상할 수 있으나 n(equation omitted)4인 경우는 상상하기 어렵다. 여기서는 거리의 성질과 추상공간을 논하고 Euclid 공간의 거리에서 출발하여 그 성질중 삼각부등식을 계산을 통하여 증명하므로서 공간의 확장화가 이루워짐을 보였다.

• Communications of Mathematical Education
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• v.12
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• pp.397-409
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• 2001

‘수학을 한다는 것은 수학자가 하는 것처럼 하는 것이다.’ 이 말은 여러 번의 시도와 실패를 반복해 가면서 ‘왜 이렇게 될까?’ 라는 의문을 가지고 여러 가지 창의적인 수학적 사고를 먼저 해보고 문제를 대하는 것을 뜻한다. 생활 속의 수학 문제는 바로 이 점에서 시사하는 바가 크다. 이런 수학 문제를 풀 때 학생들은 수동적이 아닌 능동적인 논리적 사고를 한다. 본 연구에서는 대학 입시제도로 인해 지금까지의 수학을 암기위주로 수동적으로만 학습하였던 수학 부진학생들에게 생활과 연관된 수학문제들을 제시함으로써 수학 우수 학생과 비슷한 능동적 구성활동을 유발할 수 있었으며 수학 부진 학생들과 우수 학생들의 지금까지 배운 수학 학습의 전이에 어떤 요인이 영향을 주었는지를 조사하였다.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.347-366
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• 2004

Recently, there have been many assessment researches in Korea. The aim of this study is to reflect on framework for mathematics assessment in RME which is based on Jan de Lange's assessment theory and to induce desirable directions for our mathematics assessment in nation-level and class-level. In order to attain these purposes, the present paper reflects the philosophy of RME, Jan de Lange's framework for mathematics assessment, assessment framework of the unit 'Side Seeing', one of Mathematics in Context textbook series, as an exemplar to which Jan de Lange's framework is applied. Based on these reflections, it is discussed that it needs to specify achievement standards presented in mathematics curriculum more particularly in order to have framework including mathematical abilities of level 2 and level 3 in Jan de Lange's framework appropriate to our situations, to apply the framework to nation-level and class-level consistently, and to enhance abilities of teachers and student teachers for mathematics assessment.

• The Mathematical Education
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• v.47 no.3
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• pp.273-290
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• 2008

This article provides how to implement the use of Realistic Mathematics Education (RME) in a teaching a function at a school to improve the equity based on the gender in students' mathematization for their mathematical thinking using technology. This study was planed to get research results using the mixed methodology with qualitative and quantitative methodologies. 120 middle school students participated in the study to bring us data about their mathematical achievement. Through the data analysis used by ANCOVA for the qualitative method, the students with the experiment of the mathematization based on technology excelled the other groups of students who were not provided with technology or both of them. Through the data analysis used by the constant comparative method for the qualitative data, the technology environment had helped the female students manipulate learning trends easily, strong construction on horizontal mathematization, depending on discussion with peers, and more reflexive thinking using a calculator. This means that teachers can put careful assignment on each category of mathematization regarding the gender. The study results in a lot of resources for teachers to use into their teaching mathematics for improving students' equity in interactive technology environment.

• School Mathematics
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• v.9 no.2
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• pp.277-289
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• 2007

This research aims to look into the mathematically gifted 6th and 7th graders spatial visualization ability of solid figures. The subjects of the research was six male elementary school students in the 6th grade and one male middle school student in the 1th grade receiving special education for the mathematically gifted students supported by the government. The task used in this research was the problems that compares the side lengths and the angle sizes in 4 pictures of its two dimensional representation of a regular icosahedron. The data collected included the activity sheets of the students and in-depth interviews on the problem solving. Data analysis was made based on McGee's theory about spatial visualization ability with referring to Duval's and Del Grande's. According to the results of analysis of subjects' spatial visualization ability, the spatial visualization abilities mainly found in the students' problem-solving process were the ability to visualize a partial configuration of the whole object, the ability to manipulate an object in imagination, the ability to imagine the rotation of a depicted object and the ability to transform a depicted object into a different form. Though most subjects displayed excellent spatial visualization abilities carrying out the tasks in this research, but some of them had a little difficulty in mentally imagining three dimensional objects from its two dimensional representation of a solid figure.

• Communications of Mathematical Education
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• v.27 no.1
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• pp.1-17
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• 2013

This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

• 한국정보교육학회:학술대회논문집
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• 2004.08a
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• pp.475-484
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• 2004

공간 능력 및 공간 시각화 능력의 향상은 우리가 살고 있는 세계를 표현하고 설명하는데 도움을 주고 실생활과 직업에 관련된 문제해결 능력을 기를 수 있게 한다. 초등학교에서는 비형식적인 방법으로 일상생활에서 접하는 대상과 다른 구체적 자료를 사용한 조사, 실험, 탐구를 통하여 여러 위치에서 도형을 시각화하고, 그려보고, 비교하는 활동을 강조하고 있다. 제7차 수학과 교육과정에서 공간능력 및 공간 시각화 능력을 향상시키기 위한 학습으로 구체적 조작물과 학습지 사용을 병행하고 있다. 하지만 초등 기하는 공간적인 경험을 현실 상황이나 구체물 조작을 통하여 형성된 공간직관을 수학화하도록 하여야 하나, 실제 현장에서는 학교여건 등의 여러 실정으로 조작 자료들이 제대로 마련되어 있지 않거나 잘 사용하지 않고 있다. 3차원을 경험할 수 있는 공간 시각화 학습프로그램을 적극 활용하여 어떤 방향이든 상관없이 가상의 공간에서 물체를 옮기거나 회전시킬 수 있으며 시간적, 공간적 제약을 받지 않고 학습자들의 공간시각화 능력을 향상시킬 수 있는 학습 프로그램 개발이 필요하다. 이에 본 연구에서는 이런 요구에 의해 아동과의 상호 작용성과 접근성을 향상시킨 웹기반 가상현실 프로그램을 개발하고 그 효과 분석을 통해 웹 기반 가상현실 학습 프로그램에 대한 가능성을 진단해 보고자 한다.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.511-533
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• 2012

In order to determine whether there is a significant correlation between relational understanding and creative math. problem finding ability, this study performed relational understanding and problem finding ability tests on a sample of 186 8th grade middle school students. According to the study results, we found a very significant positive correlation between relational understanding and the creativity of the mathematising ability and the combining ability of mathematical concepts in the problem finding ability. Although there was no statistically significant correlation between relational understanding and the extension ability of mathematical facts, the results from analyzing the students response rate and actual scores in each test showed that students with high relational understanding scores also had high response rate and high scores in analogical reasoning and inductive reasoning. Through this study, therefore, relational understanding is found to have a positive impact on the creative mathematics problem finding ability.

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.1-19
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• 2005

There have been raised the question that students have been of no interst in mathematcs and incompetent for solving real world problem because students have been recognized mathematcs as abstract knowldege. We research whether students' modeles developed in modeling activity can mediate between concrete and abstract. The analysis of our case study revealed that students' modeles aren't decontextualized abstraction but is located in situated abstraction that is a network connecting between concrete and abstract. Thus, these modeles are a tool mediating between concrete and abstract. Also, students' modeling activities can provide students with the opportunity of being competent for solving real world problem.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.347-364
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• 2009

In this paper, the researchers investigated the influence of graphing calculator in learning the concept of linear function for the gifted students. Elementary students who were taking a course in enrichment mathematics at Science Education Institute for the Gifted in Mokpo National University were selected for this study. The researchers analyzed students' processes of mathematical inference and conjecture, and students' algebraic description. We found the facts that the visualization using a graphing calculator and CBL is helpful to the gifted students in understanding concepts of liner function, finding the relationship between variables, analyzing and presupposing of graph. But, using graphing calculator can be a factor that disturbs learning of students who have too much of curiosity on graphing calculator.