In this paper we discussd the design principles of arithmetic lessons developed by Katori who was an arithmetic teacher at Seikei-elementary school and played a great role to improve the arithmetic education at the early decade of Shyowa era. The proposed mathematics lesson was a result of his attempts to accommodate Seikatu-Sanjutu itself well to the national curriculum. In this paper we conform that Katori used following two design principles on his lesson. (1) Katori’s design has the cycle between children’s real life and mathematics. (2) We find the joint between children’s real life and mathematics principle as Katori’s lesson method.

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Rikitaro Fujisawa (1861-1933) has been recognized for his remarkable achievements in various fields, i.e., mathematics, mathematics education in elementary and secondary education. He may also be recognized as a person in the creation of modern Japan with a career spanning from the Meiji era to the early Showa era. However, the research to date have focused on his achievements and ideas on mathematics educations in elementary and secondary schools, which has given an only limited perspectives on his full impact. Therefore, the purpose of this paper is to discover his coherent idea of education by investigating his views on higher education especially mathematics education at the Imperial University. In order to discover his coherent idea of education, especially that of mathematics, I will focus attention on “Fujisawa Seminary” where he lectured in the early days of Japan’s first university. I will also consider about the Fujisawa’s acceptance of the way of German education and research methodology, through reading again his “Summary Report on the Teaching of Mathematics in Japan”. This research, an attempt to elucidate his full impact, may also be an opportunity to reconsider his idea of his mathematics educations in elementary and secondary education.

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