What does the poet want for the children of the slum? How can their lives be made to change?
The speaker wants the children to get more than donations from the rich. Instead of bringing things into the classroom that represent what they can never have, he wants the children to have opportunities.
Break O break open 'till they break the town
And show the children green fields and make their world (lines 29-30).
Currently, the poor children in the slum have nothing and no opportunities. The donations of the rich serve only to whet their appetite and lead them to a life of crime.
Surely, Shakespeare is wicked, and the map a bad example
With ships and sun and love tempting them to steal—(lines 17-18)
Instead, the speaker wishes the children could actually get an education that will open the world up to them and provide them with real opportunities.
History is theirs whose language is the sun. (line 33)
Education and opportunity is the only thing that will change their lives.