This paper attempted investigating some aspects of mathematics education and mathematics teacher training in KOGYOKUSHA, which was a private school to teach English, navigation, surveying and mathematics, in the Meiji era. At first, there were analytic geometry and differential calculus in the curriculum of early KOGYOKUSHA. And especially spherical trigonometry education was taken seriously for mastering navigation and surveying. Therefore many graduates of this school were good at mathematics and many of them acquired a mathematics teacher license. Then they played an important part at provincial secondary schools while the teacher training of the Government doesn't proceed. In addition, some of them published the mathematics textbook by translating from some English mathematics books and editing them. Moreover, they edited the answer book for the beginner or the self-educated person. Secondly, this paper attempted inquiring into the curriculum, textbooks, the faculty and the graduates of SENSHU-SUGAKUKA which was founded at this school in 1886 as one of a pioneer of the mathematics department. Although the advanced mathematics such as differential equation was taught in the early period, but this department repeated the revision of curriculum several times for the difficulty of this subject itself, and was unwillingly closed after about 10 years since the foundation because of the student's extreme decrease. But many of the graduates, who were about thirty even in all, contributed to the mathematics education in being a mathematics teacher or editing mathematics answer books.

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In 1935, the fourth national elementary mathematics textbook ‘Jinjo-Shogaku-Sanjutsu’ was published. In this textbook, geometrical content was introduced into elementary school mathematics using new a theory of instruction. It was influenced by Tokuro Kunimoto's ‘Chokkan-Kika’ (intuitive geometrical instruction) which is the theory of instruction of Geometry based on students intuition. In this article, to show how ‘Chokkan-Kika’ influenced the introduction of Geometry into elementary mathematics, the characteristics of ‘Chokkan-Kika’ are identified and their use is pointed out as a significant change in this textbook. ‘Chokkan-Kika’ was contrasted with ‘Ronsho-Kika’ (logical geometrical instruction). By comparing the two forms of instruction, we can see two characteristics of ‘Chokkan-Kika’. First it is intended that students try to find the properties of figures through inductive research. Second it is intended that students perceive the properties of figures as correct by their intuition. In the third revision of the national elementary mathematics textbook, we cant see the intention that students try to find the properties of figures through inductive research. But in Jinjo-Shogaku-Sanjutsu we can see this intention. So this characteristic was a significant change in ‘Jinjo-Shogaku-Sanjutsu’. Therefore Geometry instruction of Jinjo-Shogaku-Sanjutsu was influenced by ‘Chokkan-Kika’ in this aspect.

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Japan adopted a modern system of education in 1872. After the establishment of the fundamental law for the educational system, “Gakusei”, which means School System, regulations concerning schools and curricula were enacted. The “Curriculum for Secondary Schools, Taught by Foreign Teachers”, and the “Curriculum for Elementary Schools”, both enacted in 1872, were among these. As to mathematics, it was intended to teach Western mathematics at all school levels, abandoning traditional Japanese mathematics. In the “Curriculum for Secondary Schools, Taught by Foreign Teachers”, examples of textbooks written in English, French and German were shown for almost every subject. As to arithmetic, however, there were some differences between the contents of the curriculum and those of the textbooks shown as examples. The curricula of arithmetic in both regulations were almost the same, and the contents and the arrangement of the contents in order of these curricula of arithmetic were influenced by the book “Shuxue qimeng”(“Sugaku Keimo” in Japanese) by Alexander Wylie, which was an introduction of Western arithmetic written in Chinese and published in China in 1853. An outline of the curriculum of Western arithmetic in Japan had been established by referring books on arithmetic written in Western languages as well as “Sugaku Keimo”, with some consideration on the cultural climate of Japan, before the official introduction of modern educational system in Japan in 1872.

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After World War Ⅱ, Japanese education was under the strict control of the Civil Information & Education Section (CI&E) of General Headquarters / Supreme Commander for the Allied Powers (GHQ/SCAPS). What was the suggestion or recommendation given by CI&E for the Japanese Ministry of Education when they were faced with the reorganization of the curriculum for elementary schools? By using the restricted documents of GHQ/SCAPS, this thesis clarified the curriculum reorganization. The features of CI&E’s suggestion or recommendation were as follows: （1）CI&E criticized Japanese elementary curriculum for having been organized by subject matter type and suggested that it should be changed over to an empirical widespread curriculum. （2）CI&E recommended that centralism should be eliminated and that decentralization should be implemented in Japanese education. The CI&E’s intentions had a great influence on the creation of Japanese elementary curriculum, and were especially clear in the argument about the time allotment for subjects.

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