• Proceedings of the Korea Information Processing Society Conference
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• 2011.11a
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• pp.1017-1020
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• 2011

터치스크린은 키보드나 마우스와 같은 입력장치를 사용하지 않고, 스크린에 손가락, 펜 등을 접촉하여 입력하는 방식이다. 터치스크린은 정확성, 입력속도, 문자입력 등에서는 개선이 필요하나, 누구나 쉽게 입력할 수 있는 장점으로 인해 기존에는 현금인출기, 키오스크(Kiosk) 등 공공분야에서 주로 많이 사용되어 왔다. 터치스크린은 손가락을 접촉하는 것만으로 컴퓨터, 모바일 기기 등을 직관적으로 쉽게 사용할 수 있다는 것이 가장 큰 장점이다. 현재는 단순 터치스크린 환경을 넘어 동시 다중 입력이 가능한 멀티터치 환경의 터치스크린이 상용화 되면서 동시 다중 입력을 통한 어플리케이션들이 주목받고 있다. 본 논문에서는 동시에 입력한 여러 개의 아이템을 인식하는 방법을 다중 입력 패스워드를 통해 시뮬레이션 해보았다. 선택된 아이템으로 리스트를 구성하고 이를 동시 입력 단위로 사용함으로써 사용자 입장에서의 다중 입력의 정확성과 시스템 입장에서의 인식률을 높이고자 하였다.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.345-366
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• 2006

In this study, we investigated the methods of using the Cabri3D program for education of problem solving in school mathematics. Cabri3D is the program that can represent 3-dimensional figures and explore these in dynamic method. By using this program, we can see mathematical relations in space or mathematical properties in 3-dimensional figures vidually. We conducted classroom activity exploring Cabri3D with 15 pre-service leachers in 2006. In this process, we collected practical examples that can assist four stages of problem solving. Through the analysis of these examples, we concluded that Cabri3D is useful instrument to enhance problem solving ability and suggested it's educational usage as follows. In the stage of understanding the problem, it can be used to serve visual understanding and intuitive belief on the meaning of the problem, mathematical relations or properties in 3-dimensional figures. In the stage of devising a plan, it can be used to extend students's 2-dimensional thinking to 3-dimensional thinking by analogy. In the stage of carrying out the plan, it can be used to help the process to lead deductive thinking. In the stage of looking back at the work, it can be used to assist the process applying present work's result or method to another problem, checking the work, new problem posing.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• The Journal of Korean Association of Computer Education
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• v.8 no.1
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• pp.73-80
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• 2005

To achieve a natural and plausible interaction with deformable objects and to setup the desirable initial conditions of simulation, user should be able to define and control the geometric constraints intuitively. In addition, user should be able to utilize the simulation as a problem solving platform by experimenting various simulation situations without major modification of the simulator. The proposed physically based geometric constraint simulation system solves the problem using a non-linear finite element method approach to represent deformable objects and constraint forces are generated by defining geometric constraints on the nodes of the object to maintain the restriction. It allows user to define and modify geometric constraints and an algorithm converts these geometric constraints into constraint forces which seamlessly integrate controllability to the simulation system. Simulator can handle linear, angular, inequality based geometric constraints on the objects. Our experimental results show that constraints are maintained in the tight error bound and preserve desired shape of deformable object during the entire simulation.

• School Mathematics
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• v.14 no.3
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• pp.331-355
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• 2012

All the method used in teaching the ellipse was to have students draw the points which have the same sum of distances from the two points so that they can confirm the shapes of the ellipse before showing them the definition of ellipse. In this process, students would not get an opportunity to think or make the definition of ellipse for themselves. This deductive way can hinder students from having clear understanding of why such definition was made. This paper introduces a method of defining the ellipse based on the similarity between a circle and an ellipse, leading into the equation. This method is possible by introducing Analytic Geometry taught in current school mathematics and Transformation Geometry. By doing so, this paper will discuss a fundamental understanding about the ellipse and the feature of the ellipse expandable by intuition. Furthermore this paper will also show various advantages which can be given by defining the ellipse in Transformation Geometry.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.81-90
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• 2008

It has been noticed the greater importance of mathematical education, particularly of multi-variable calculus in the undergraduate level with remarkable progress of all sorts of sciences requiring mathematical analysis. However, there was lack of variety of introducing the definition of differentiation of multi-variable functions - in fact, all of them basically rely on the chain rules. Here we will introduce a way of defining the geometrical differentiation of the multi-variable functions based upon our teaching experience. One of its merits is that it provides the geometric explanation of the differentiation of the multi-variable functions, so that it conveys the meaning of the differentiation better compared with the known methods.

• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.373-394
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• 2016

The "Figure Equation" chapter of current high school curriculum prevents students from relating the concept with what they studied in middle school Euclidean geometry. Woo(1998) concerns that the curriculum introduces the concept merely in algebraic ways without providing students with opportunities to relate it with their prior understanding of geometry, which is based on Euclidean one. In the present study, a sequence of GeoGebra-embedded-geometry lessons was designed so that students could be introduced to and solve problems of the Analytic Geometry by triggering their prior understanding of the Euclidean Geometry which they had learnt in middle school. The study contributes to the field of mathematics education by suggesting a sequence of geometry lessons where students could introduce to the coordinate geometry meaningfully and conceptually in high school.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Proceedings of the Korea Information Processing Society Conference
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• 2004.11a
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• pp.701-704
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• 2004

일반적으로 프로그램의 수행과정은 직관적으로 파악하기 어려워, 이에 대한 이해를 돕기 위하여 시각화 분야에 대한 다양한 연구가 필요하다. 시각화는 프로그램의 디버깅이나 개선에도 효과적으로 이용될 수 있을 뿐 아니라 컴퓨터 교육 분야에서도 폭넓게 활용될 수 있다. 본 논문에서 제안하는 시스템은 C 언어로 작성된 프로그램에 간단한 시각화 명령을 추가하고 이를 자동 변환하여 SVG 애니메이션 코드를 생성한다. 생성된 애니메이션 코드는 웹 브라우저 상에서 실행될 수 있으며 알고리즘 시각화를 위한 별도의 프로그램 작성 없이 기존 알고리즘에 간단한 명령어를 추가하여 시각화할 수 있다는 장점이 있다.

• Smart Media Journal
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• v.13 no.5
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• pp.45-51
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• 2024

Recently, realistic contents such as virtual reality(VR) and augmented reality (AR) are widely used for education to provide beneficial learning environments with thee-dimensional(3D) information and interactive technology. Specially, AR technology will be helpful to intuitively understand by adding virtual objects registered in the real learning environment with effective ways. In this paper, we developed an AR learning system using 3D spatial information in the 2D based textbook for studying math related to geometry. In order to increase spatial learning effect, we applied to solid shapes such as prisms and pyramids in mathematics education process. Also, it allows participants to use various shapes and expression methods (e.g., wireframe mode) with interaction. We conducted the experiment with our AR system, evaluated achievement and interest. Our experimental study showed positive results, our results are expected to provide effective learning methods in various classes through realistic visualization and interaction methods.