The Ordinance Concerning Middle Schools, enacted first in 1886, was revised sweepingly in 1899 to cope with the growth of the scale of secondary education in Japan. Here, a middle school, chugakko in Japanese, is a five-year boys' school for general education in the former educational system in Japan. Then, the Enforcement Regulations of the Ordinance Concerning Middle Schools, in which the outline of the curriculum was prescribed, was enacted in 1901. As to the mathematics curriculum, it was a drastic cut of the contents: solid geometry and trigonometry were deleted from the curriculum, and algebra was restricted to the elementary level. As the former mathematics curriculum included too much contents for the school hours allotted to mathematics and pupils had difficulty in learning mathematics, the Ministry of Education decided to reduce the contents to improve mathematics education in middle schools. The new mathematics curriculum was affected considerably by the view of mathematics education of Rikitaro Fujisawa, Professor of Mathematics at the Imperial University of Tokyo. There were arguments for and against the new curriculum. Dairoku Kikuchi, the President of the Imperial University of Tokyo and the former Professor of Mathematics at the University, criticized the new curriculum, especially the reduction of the contents in the mathematics curriculum. This criticism was due to the difference in policy for the improvement of mathematics education between the officials in the Ministry of Education and Kikuchi. This difference in policy was due mainly to the difference in views of mathematics and mathematics education between Fujisawa and Kikuchi, and the formation of their views was affected by their mathematical experiences. However, the curriculum was revised in the next year, and solid geometry and trigonometry were included in the mathematics curriculum again.

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This paper aims to clarify the characteristics of the explanations of the meaning and the rule of multiplication of fractions in the arithmetic textbooks published from 1894 to 1904. The author published a paper on the characteristics of the same contents in the textbooks published from 1886 to 1894. As a continuation of the paper, this paper deals with the development of the characteristics (1) The meaning of multiplication of whole numbers and that of multiplication of fractions were explained by consistent logic. The explanation was an important characteristics of the textbooks published from 1886 to 1894. However, in the textbooks published from 1894 to 1904, the explanation of the meaning of multiplication of fractions was simplified using the concept of “b/a of X”, in which X represents whole numbers or fractions. As a result, the important characteristics was lost or partially inherited. (2) The rule b/a * d/c = (b*d)/(a*c) is the general rule of multiplication of fractions. In the textbooks published from 1886 to 1894, there existed a textbook which explained this fact. In the textbooks published from 1894 to 1904, this important characteristic was found in many textbooks. In addition, among them, there existed a textbook which explained the rule b/a * d/c = (b*d)/(a*c) in the first place.

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