古诗 (gǔshī): classical Chinese poem

Two related senses: (1) loosely, any poem in classical Chinese — what students mean by 'I memorised a 古诗 today'. (2) Technically, 古体诗 — pre-Tang or unregulated verse, contrasted with 近体诗/格律诗 (regulated Tang verse like 律诗 and 绝句). School usage is sense (1).

grammar

Counted with 首 (shǒu): 一首古诗 = one classical poem. The MW 首 also counts songs and other short lyrical works.