The aim of this paper is to clarify the characteristics of the geometrical instruction of “Mizuiro-Hyoshi” which are the 5th national elementary arithmetic textbooks. This textbooks consist of “Kazu-no-Hon” for the 1st and 2nd grade students and “Syotoka-Sansu” for the 3rd to 6th grade students. As the occasion demands, I also made comparison between “Mizuiro-Hyoshi” and the 4th national elementary arithmetic textbooks “Jinjo Syogaku Sanjutsu” that are called “Midori-Hyoshi”. The geometrical instruction of “Mizuiro-Hyoshi” is based on the theory of geometrical education of Ryuichi Maeda. The Maeda’s theory was influenced by the Japanese scientific theory of Kunihiko Hashida and puts emphases on the point that the total intuitive grasp of shapes is fundamental for the recognition of space. In the Maeda’s theory, the geometrical instruction consisted of three stages, as follows; (1) The observed science of shapes. (2) The experimental science of shapes. (3) The theoretical science of shapes. The stage (1) corresponds to “Kazu-no-Hon” and stage(2) is to “Syotoka-Sansu”. The geometrical instruction of “Kazu-no-Hon” is characterized by the observation with continuous movement. On the other hand, that of “Syotoka-Sansu” is characterized by the experiment with the actual activity. The Maeda’s theory deeply reflects “Kazu-no-Hon” at the geometrical instruction, because Ryuichi Maeda edited directly the textbook “Kazu-no-Hon”, but the textbook “Syotoka-Sansu” is edited by another person, Toshiro Maruyama, so the influence of the Maeda’s theory is partial.

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