On a Forming Process of a Model Theory on Fraction as School Mathematics; Focusing on a Textbooks Published from 1886 to 1904

本文旨在通过分析日本政府实施教科书授权制的1886年至1904年出版的教科书，阐明分数模型论作为学校数学内容的形成过程。在这个项目中，研究者从以下几个方面对算术教科书进行了分析。(1)分数课程的组成部分及其顺序；(2)整数性质解释与分数性质解释的关系；(3)分数的定义和含义的教学方式；(4)分数的性质和顺序的教学方式；(5)分数的四种算术运算（加、减、乘、除）的教学方式；(6)分数代数性质的教学方法；从1886年到1904年可以分为两个时期。第一个时期是从1886年到1900年。这一时期的特点是将分数作为初级数学模型理论的形成（从1886年到1894年）及其部分变化（从1894年到1900年）。第二个时期是从1900年到1904年。这一时期的特点是学校数学中分数模型理论的形成。在该项目的报告中，研究者将重点放在了第一个时期的前半段（1886年至1894年），并通过分析这一时期出版的教科书，阐明了分数模型论作为初级数学的特点

The aim of this study is to clarify the a forming process of a model theory on fraction as a content of school mathematics by analyzing textbooks published from 1886 to 1904, when the Japanese government carried out the textbook authorization system.In this project, the investigator analyzed the arithmetical textbooks from following points of views.(1) Components of curriculum on fractions and the order of these components;(2) Relationship between the explanations on the properties of integral numbers and fractions;(3) The way in which the definitions and meanings of fractions are taught;(4) The way in which the properties and order of fractions are taught;(5) The way in which the four arithmetical operations (addition, subtraction, multiplication and division)of fractions are taught;(6) The way in which the algebraic properties of fraction are taught;The years from 1886 to 1904 can be divided into two periods. The first period is from 1886 to 1900. This Period is characterized by a formation of a model theory on fractions as primary mathematics (from 1886 to 1894) and its partial changes (from 1894 to 1900). The second period is from 1900 to 1904. This period is characterized by a formation of a model theory of fractions as school mathematics.In the report of this project, the investigator gave a focus on the first half of the first period (from 1886 to 1894), and the clarified the characteristics of a model theory of fraction as primary mathematics by analyzing textbooks published in this period