• Communications of Mathematical Education
• /
• v.18 no.2 s.19
• /
• pp.383-410
• /
• 2004

DGS(dynamic Geometry System)와 WBI(Web Based Instruction)를 고찰해보고, 동적 기하 프로그램의 대표적인 프로그램인 GSP, Cabri, Cinderella를 이용하여 WBI를 제작해 보고 웹 환경 하에서 세 프로그램의 효율성을 비교 ${\cdot}$ 분석하였으며, 이들 세 프로그램의 장점을 정리하여 웹 환경에서 동적 기하 프로그램의 개선 방향을 제시하였다.

• Journal of Educational Research in Mathematics
• /
• v.23 no.4
• /
• pp.585-604
• /
• 2013

This study is based on the problem that most middle school students cannot recognize the generality of geometrical theorems even after having proved them. By considering this problem from the point of view of empirical verification, the particularity of geometrical representations, and the role of geometrical variables, we suggest that some experiences in dynamic geometry environment (DGE) can help students to recognize the generality of geometrical theorems. That is, this study aims to observe students' cognitive changes related to their recognition of the generality and to provide some educational implications by making students experience some geometrical explorations in DGE. To do so, we selected three middle school students who couldn't recognize the generality of geometrical theorems although they completed their own proofs for the theorems. We provided them exploratory activities in DGE, and observed and analyzed their cognitive changes. Based on this analysis, we discussed the effects of DGE on studensts' recognition of the generality of geometrical theorems.

• Communications of Mathematical Education
• /
• v.16
• /
• pp.67-80
• /
• 2003

함수적 사고는 수학적 문제 해결에 있어 기본적인 사고이다. 함수적 사고에서는 변수 사이의 종속성 파악이 그 핵심이 된다. 이는 DGS 동적 기하의 동적(변화), 종속적(구성)이라는 특성에 잘 부합한다. 이에 우리는 동적 기하 환경에서 타당한 종속성 부여를 통해 primitive한 생성자를 알아보고, 이들의 조작과 역 조작, 합성 조작하는 과정을 통해 함수적 사고에 접근하는 방법을 연구해 보려 한다. 나아가 자취 기능을 이용함으로써 시각화를 통해 종속적 관계를 표현해 보고자 한다. 이것은 MicroWorld 환경에서 학습자가 스스로 대상을 구성하는 경험을 통해 함수적 사고를 자연스럽게 형성하도록 하는 것이 바람직하다는 관점에 바탕을 두고 있다.

• Journal of Educational Research in Mathematics
• /
• v.27 no.1
• /
• pp.89-112
• /
• 2017

In this study we have analyzed processes of generalization in which students have geometrically solved cubic equation $x^3+ax=b$, regarding geometrical solution of cubic equation $x^3+4x=32$ as examples. The result of this research indicate that students could especially re-interpret the geometric solution of the given cubic equation via dynamically understanding the variables in dynamic geometry environment. Furthermore, participants could simultaneously re-interpret the given geometric solution and then present a different geometric solutions of $x^3+ax=b$, so that the level of generalization could be improved. In conclusion, the study could provide useful pedagogical implications in school mathematics that the dynamic geometry environment performs significant function as a means of students-centered exploration when understanding variables and enhancing the level of generalization in problem solving.

• The Mathematical Education
• /
• v.60 no.4
• /
• pp.543-554
• /
• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• Communications of Mathematical Education
• /
• v.16
• /
• pp.81-91
• /
• 2003

이 논문에서는 학습자가 동적 수학 개념과 관련하여 오개념을 가지고 있는 현상에 주목하여 대학생들이 가지고 있는 동적 개념과 관계된 오개념을 분석하고 지도방법을 제시하고 있다. 오개념 분석은 대학생을 대상으로 한 설문조사결과를 바탕으로 하였으며, 그 결과 많은 학생들이 동적인 개념을 정적인 개념으로 이해하고 있는 것으로 나타났다. 이러한 오개념을 진단하고 처방하는 방법으로 동적 기하(Dynamic Geometry System)을 택하고, 이를 이용한 동적 수학 탐구학습이 가지는 특징을 살펴본다.

• School Mathematics
• /
• v.13 no.1
• /
• pp.19-36
• /
• 2011

This study provides middle school students with an opportunity to construct elementary functions with dynamic geometry based on the proportion between lengths of triangle to activate students' intuition in handling elementary algebraic functions and their geometric properties. In addition, this study emphasizes the process of justification about the choice of students' construction method to improve students' deductive reasoning ability. As a result of the pilot lesson study, this paper shows the characteristics of the students' construction process of elementary functions and the roles the teacher plays in the process.

• Journal of the Korean School Mathematics Society
• /
• v.20 no.3
• /
• pp.303-323
• /
• 2017

This is a multiple-case study of how preservice secondary mathematics teachers teach a particular mathematics using a technological tool. In a performance interview, the preservice teachers demonstrated how they would teach a specific mathematical topic using Geometer's Sketchpad. The results of this study showed that the preservice teachers designed diverse types of lesson plans and implemented different pedagogical and technological techniques in their teaching demonstrations. The findings suggest that preservice teachers' pedagogical content knowledge is an important factor in the integration of technology into their mathematics teaching. Thus, mathematics teacher educators should help preservice teachers gain a robust pedagogical content knowledge in order to effectively teach mathematics with technological tools.

• Journal of the Korea Society of Computer and Information
• /
• v.28 no.12
• /
• pp.89-96
• /
• 2023

In this paper, we propose a GPU-based method for real-time processing of dynamic re-meshing required for tearing cloth. Thin shell materials are used in various fields such as physics-based simulation/animation, games, and virtual reality. Tearing the fabric requires dynamically updating the geometry and connectivity, making the process complex and computationally intensive. This process needs to be fast, especially when dealing with interactive content. Most methods perform re-meshing through low-resolution simulations to maintain real-time, or rely on an already segmented pattern, which is not considered dynamic re-meshing, and the quality of the torn pattern is low. In this paper, we propose a new GPU-optimized dynamic re-meshing algorithm that enables real-time processing of high-resolution fabric tears. The method proposed in this paper can be used for virtual surgical simulation and physics-based modeling in games and virtual environments that require real-time, as it allows dynamic re-meshing rather than pre-split meshes.

• Proceedings of the Korean Information Science Society Conference
• /
• 2001.04b
• /
• pp.622-624
• /
• 2001

영상기반 렌더링(image-based rendering) 기법은 전통적인 컴퓨터 그래픽 기법과는 다르게 장면 생성 시 복잡한 3차원 정보들을 2차원 영상들의 조합으로 표현하여 렌더링 하는 방법이다. 그 중에서 원통맵을 이용한 렌더링은 파노라마 영상을 이요해 관찰자에게 보다 빠르게 실시간으로 장면을 렌더링하여 보여준다. 이러한 영상기반 렌더링에서도 ㅅㄹ제감을 보다 더 높이기 위해서는 빛과 빛에 의해 생기는 그림자, 하이라이트의 역할이 매우 중요하다. 하지만 파노라마 영상의 경우 미리 촬영된 영상들을 사용하므로 실시간으로 동적인 광원의 변화와 그로인한 그림자와 하이라이트 부분을 표현하기 위해서는 변화된 영상들을 재촬영하여 새로운 파노라마 영상을 제작해야 한다. 본 논문에서는 OpenGL을 이용하여 실내 공간을 표현한 원통 영상 기반 환경 맵에서 광원의 위치변화에 의해 가상 하이라이트 (virtual highlight)의 움직임을 파노라마 이미지의 재 촬영 없이 몇 가지 기하학 정보만으로 계산하여 표현해 주는 방법을 제안한다.