Originally, Roman education took place in the home and emphasized behavior in accordance with ancestral practice. Education became more intellectual as it became more important and fashionable to read Greek. (Romans learned and showed off with Greek as we do with French.) The ideal goal of education was a combination of abstract learning and sound character, without too much specialization. (Does this sound like the philosophy of anyplace you know?) Schools were bilingual, and Greek took precedence as a language. Everyone wanted to learn it. The state took more and more of an interest in education, and the emperors virtually controlled the schools. Private libraries were very fashionable and afforded a good opportunity to show off.
There were three different types of teachers: the litterator, or elementary school teacher, who taught reading, writing, and especially arithmetic; the grammaticus, who taught secondary school students to memorize and recite texts aloud, with careful attention to pronunciation and enunciation, and who afterwards added a commentary on literary or philosophical points of the text; and the rhetor, who taught students to make speeches on a given theme, advocating a course of action (this was called declamatio), or to engage in debates. Two types of themes were possible: quaestiones, or abstract general themes; and causae, or themes related to particular people and situations. Students might, for example, be asked to imagine themselves giving advice to Hannibal before he crossed the Alps with all those elephants.
Because rhetoric began to specialize in form and style, rather than content (epigrams were popular), artificiality became a problem. Besides, rhetoric itself (like so many other aspects of Roman civilization) was imported from Greece, and therefore both highly regarded and yet suspicious. Note that Agamemnon has a Greek name.
The rhetorical specialty of declamatio dominated the schools, fascinated adults, and gave style to both oratory and literature. It later became a genre in its own right. The controversia was a more advanced form of declamatio. It was an invented legal case argued before an imaginary jury. It had three parts: the sententiae, or arguments for and against; the divisio, or a skeleton statement of the legal points involved; and the colores, which were conjectures about motive or explanations for what happened (often very far-fetched explanations).
The themes of controversia came from an unreal, romantic world peopled by tyrants and their assassins, wicked stepmothers, erring Vestal Virgins who wrote love poetry, pirate chiefs and their captive daughters, mutilators of exposed children, poisoners, fathers who disinherited sons, and identical stepbrothers. There were stock characters, like Agamemnon's poor man.
The controversia was performed in public and was a fashionable entertainment. Rhetoricians and students gave exhibitions attended by parents, Roman literary society, and even sometimes the emperor Augustus.
You can imagine the influence the controversia had on literature and other storytelling forms (such as film and TV, through the influence of the written word, at first). Think about it: what sort of people populate Shakespeare's comedies? Who stars in fairy tales? What kinds of tragedies fill the lives of soap opera characters?
For a contemporary example of a controversia, click here.