In the secondary schools here in the US, this type of performance could be found in forensics, although from the description given here: http://www.seal-pa.org/admin/sasd/forensics/index.html
it appears that the poetry section is simulated reading. At any rate, the Slam poetry competitions probably are most like what you have in mind. Thanks to Stone Circle, a daughter who excelled in forensics, and her friends who are Slam poets, this old(er) lady knows exactly what you have in mind!