Final answer:
Today's justice systems continue to use rehabilitation methods to transform offenders into responsible individuals, moving away from medieval punishments such as public floggings, banishment, and exile.
Step-by-step explanation:
Of the correctional methods listed from that historical era, the one that is still being utilized today is rehabilitation. Public floggings, banishment, and exile were medieval punishments and are no longer practiced in modern justice systems. Rehabilitation is preferred as it aims to transform offenders into responsible and productive members of society, rather than simply punishing them. This approach aligns with the ideals of an enlightened justice system as intended by the Eighth Amendment, focusing on creating more sophisticated methods to deal with those incarcerated.