The nation’s governors and state school chiefs will propose standards Wednesday for what students should learn in English and math, from kindergarten through high school, a crucial step in President Barack Obama’s bid to raise academic standards across the country.

The blueprint aims to replace a hodgepodge of state benchmarks with common standards. The president has aggressively encouraged the states’ action as a key to improving troubled schools and keeping the nation competitive. Instituting new academic standards would reverberate in textbooks, curriculum, teacher training and student learning from coast to coast.

Fourth-graders, for example, would be expected to explain major differences between poetry and prose and to refer to such elements as stanza, verse, rhythm and meter when writing or speaking about a poem. Eighth-graders would be expected to use linear equations to solve for an unknown and explain a proof of the Pythagorean Theorem on properties of a right triangle — cornerstones of algebra and geometry.

“The states recognize they ought to have very consistent expectations for what their students should learn,” said Michael Cohen of the standards advocacy organization Achieve.

There is no required reading list. But the plan lists dozens of classics to illustrate a level of language complexity that students should be expected to handle.