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

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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