Study on Mathematical Structure of Mathematical Educational Environment Referencing Semantics.

在本研究中，我们研究了构建教育环境的数学基础，并在此基础上制作了一个数学教育支持系统的原型。研究了图文法的基本理论，构建了面向社会学习的地形图教学信息可视化系统。数学教育环境由三个主要部分组成。首先是教科书等资源。人们还可以找到其他类型的资源，例如万维网中的开放资源。然而，后一种类型的资源通常没有必要的逻辑结构来提供构建教育系统的服务。为了使资源具有逻辑结构，我们用DTD定义了数学教材的标准。该标准被命名为Mathext.DTD。Mathext.DTD中有效的文档为构建数学教育支持系统提供了基础资源。第二是一个支持…的框架基于RDF和本体模式的数学教育测试系统。该框架的材料是通过转换MathText文档来生成的。在使用该框架学习数学时，自动分析和提供必要的信息和材料来支持学生或教师。该框架的素材命名为Mathext.RDF。第三，基于该框架的系统接口。我们计划使用鱼骨图来构建此界面。信息可视化教育是情报学的主要研究课题之一。对于数学教育来说，利用计算机图形学的可视化方法和工具也是理解几何对象，特别是三维对象的有效方法。本研究由三部分组成，一是数学教育的框架和支持系统，二是基于数学的计算机图形学教育的教材和实例，三是图文法及其在社会性地图教育中的应用研究

In this research, we have studied a mathematical foundation to construct an educational environment and made a prototype of a support system for mathematical education based on this foundation. We have also studied a fundamental theory of graph grammars and constructed information visualization systems for education of land maps in social study. The educational environment for mathematics consists of three main components. First is resources such as text books. One can also find another type of resources, for example open resources in World Wide Web. The resources of latter type, however, generally has no necessary logical structure to provide constructing an educational system. To grant resources a logical structure, we have defined a standard of the textbook for mathematics by DTD. This standard is named the Mathtext.DTD. Documents that is valid in Mathtext.DTD provide constructing fundamental resources of a support system for mathematical education. Second is a framework of a suppor … More t system for mathematical education based on RDF and ontology schema. Material of this framework is generated by transforming Mathtext documents. In studying mathematics using this framework, necessary information and material to support students or teachers are analyzed and supplied automatically. The material of this framework is named Mathtext.RDF. Third is an interface of this system based on this framework. We plan to construct this interface using a fishbone diagram. Education of information visualization is one of main item for study in information science. For education of mathematics, visualization method and tools using computer graphics are also effective for understanding geometrical objects especially such as three dimensional objects. We have provided a textbook and examples to learn this subject.This research is composed of three parts, first is a framework and a support system for mathematics education, second is a textbook and examples for computer graphics education based on mathematics, and third is a study of graph grammars and its applications for education of land maps in social study Less