Abstract
The aim of this paper is to clarify the change of mathematical curriculums on fractions by analyzing arithmetical textbooks published from 1886 to 1904, when the Japanese government carried out the textbook authorization system. Having published his paper on the characteristics of the curriculum from 1886 to 1894, the author gives his focus on change of the curriculums from 1894 to 1904. As in the previous paper, the author analyzes the arithmetical textbooks from the following points of views. (1) Components of the 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 properties and order of fractions are taught; (4) The way in which the addition and subtraction of fractions are taught. The years from 1886 to 1904 can be largely divided into two periods. The first period is from 1886 to 1900. The curriculum during the first period is characterized by its "systematic construction" (from 1886 to 1894) and its partial changes (1894 to 1900). In this period, the curriculum which was composed of four components, namely the definition of fractions, their properties, order, and the four arithmetical operations of fractions, was established, and went through partial changes. The second period is from 1900 to 1904. In this period, the curriculum was totally reconstructed and the systematically constructed curriculum was abandoned. This change was given rise to because the arithmetical operations of fractions were thought to be the most important, and, thus, given undue weight in the curriculum. The analysis of the mathematical textbooks shows the followings. (1) In the latter half of the first period, the component on the properties of integral numbers, which existed independently of the components on fractions in the first half of the first period, was deleted. The component on the properties of integral numbers was divided into smaller components and they were allocated in several academic years. These fragmentized smaller components were related with the components on fractions. In the second period, these smaller components were abandoned and the explanations of the properties of integral numbers were included in the components on fractions. (2) As the systematic construction of the curriculum on fractions collapsed,the component on fractions was divided into the smaller components and they were allocated in different academic years. What is essential in fractions was not taught in comprehensive way and the fragmentized explanations were given separately. The order of the components became complicated. (3) The component on "transformation of fractions" -the properties and order of fractions- was deleted. The explanation of properties were given when they were necessary in order to teach the arithmetical operations of fractions. (4) In the latter half of the first period, the component on the arithmetical operation of fractions was divided into two smaller components: the component on the addition and subtraction of fractions of which denominators are same and the component on the addition and subtraction of fractions of which denominators are different. They were allocated in the curriculum in the way that hid their close relationship. In the second period, some parts of the former smaller component were moved to the component on the definition of fractions. And a detailed explanation on the arithmetical operation was given in the component on the operation of fractions with different denominators. In this component, the algorism of the operation is formed by the method of "accumulation."
