This song's lyrics was written by 清水かつら (Shimizu Katsura) and the melody by 弘田龍太郎 (Hirota Ryuutarou) in 1921.
Apparantely, the sounds ちいちいぱっぱ was inspired by the sound of his young daughter learning to talk (ちいちい) and by the sound of the fluttering of sparrow's wings (ぱっぱ). For a discussion on this, click here.
雀 suzume - sparrow
の no - 's (possessive)
学校 gakkou - school