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

论学校数学分数模型理论的形成过程

基本信息

批准号：
17530645
负责人：
OKANO Tsutomu
金额：
$ 1.06万
依托单位：
Niigata University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

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

本研究的目的是通过对1886年至1904年日本政府实行教科书授权制度期间出版的教科书的分析，阐明作为学校数学内容的分数模型理论的形成过程。在本项目中，研究者从以下几个角度对算术教科书进行了分析：（1）分数课程的组成部分以及这些组成部分的顺序；（2）分数之间的关系。讲解整数和分数的性质；（3）分数的定义和意义的教学方法；（4）分数的性质和顺序的教学方法；（5）分数的四种算术运算（加、减、乘、除）的教学方法；（6）分数的代数性质的教学方法； 1886年至1904年可分为两个时期。第一个时期是1886年至1900年。这一时期的特点是作为初级数学的分数模型理论的形成（1886年至1894年）及其部分变化（1894年至1900年）。第二个时期是1900年至1904年。这一时期的特点是作为学校数学的分数模型论的形成。在本课题的报告中，研究者重点关注了第一时期的前半段（1886年到1894年），通过对这一时期出版的教科书的分析，阐明了作为初等数学的分数模型论的特征。