The importance of the arithmetic education that accorded with initiative of children and life was insisted by a renovation of arithmetic in a new education movement in Taisho era. However, a meaning of “life” in a renovation of arithmetic is not clarified. I examined a change of arithmetic education theory in 1910's under the World War I of the elementary school attached to the Tokyo higher normal school and aimed at clarifying the notion of “life”. Goto Taneyasu and Higo Morikuma discussed mainly on this point. Goto insisted on taking in “life” as an educational method from interest of children, and respecting the sense of them. In addition, he thought that he encouraged children adapt themselves to a real social “life” with a purpose of education. On the other hand, Higo objected to taking in “life” as both an educational method and purpose, and thought about an educational purpose with “the intellectual power” training, When a scientific promotion was demanded under the World War I, it was Higo that took leadership. Higo changed his opinion according to a claim of mathematics education remodeling the movement and took in “life” in arithmetic. A method of induction to encourage children observe test “life”, and arrive at mathematical laws by themselves was focused.