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，并在此基础上构建了一个数学教育支持系统的原型。我们还研究了图语法的基本理论，并构建了用于社会研究中土地地图教育的信息可视化系统。数学教育环境由三个主要部分组成。首先是课本等资源。人们还可以找到另一种类型的资源，例如万维网上的开放资源。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。为了赋予资源逻辑结构，我们通过DTD定义了数学教科书的标准。这个标准被命名为Mathtext.DTD。在Mathtext中有效的文档。DTD为数学教育支持系统的构建提供了基础资源。二是基于RDF和本体模式的数学教育支持系统框架。该框架的材料是通过转换Mathtext文档生成的。在使用该框架学习数学时，可以自动分析和提供必要的信息和材料来支持学生或教师。这个框架的材料名为Mathtext.RDF。第三部分是基于该框架的系统接口。我们计划使用鱼骨图来构造这个接口。信息可视化教育是信息科学研究的主要课题之一。在数学教育中，使用计算机图形学的可视化方法和工具对于理解几何对象，特别是三维对象也是有效的。我们提供了学习这门学科的课本和例子。本研究由三部分组成，一是数学教育的框架与支持系统，二是基于数学的计算机图形学教育的教材与实例，三是图语法及其在社会学科土地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