Aristotle was a student in the Platonic Academy in Athens for over 20 years before moving on to found his own school after Plato's death. Artistotle's teaching career, in fact, started when he began teaching rhetoric in the Platonic academy.
Plato wrote exclusively in dialogue form, never appearing in propria persona in his own writing. In his teaching career, he only lectured once, delivering a single public lecture "On the Good," which has not been preserved, but apparent dealt primarily with the idea-mathematicals. Otherwise, teaching at the Platonic Academy was conducted primarily in dialogue form. It is possible that the Platonic dialogues were used as starting points for discussion at the Academy, but no actual accounts of Plato's teaching have survived, other than Epistle VII, Unfortunately, it is not certain that Epistle VII is authentically Platonic, and thus, while its contribution to assessment of Plato's pedagogy theories is quite important, we cannot state with any certainty whether the theories contained in it are Platonic or neo-platonic.
Aristotle's early works, including the Protrepticus, which has been prefserved in fargments quotes in later authors, and several philosophical dialogues, which have not been preserved (but which are mentioned by Diogenes Laertius, Cicero, and other ancient soucres), appear to have been moderately Platonic in style and pedagogical approach. In his subsequent career, Aristotle seemed to favour lecturing, and a monologucal rather than a dialogical style of presentation.
Plato, one of Socrates's students, taught by writing dialogues in which teachers asked questions. In this so-called dialectic method, a teacher asks questions that help students define terms. By answering the questions, students grapple with the issues in the debate, and then they are cross-examined to come to a deeper understanding of the positions involved in the argument. This type of approach followed from Plato's belief that humans can not grasp truth directly but only see shades of the truth.
Plato also believed that children learned from play and from engaging their enthusiasm, and he also believed that adults benefited from play and from playful engagement with philosophy. The ancient Greeks took play, which they defined as the opposite of work (physical labor) seriously, and Plato was no exception. He wrote:
"No society has ever really noticed how important play is for social stability. My proposal is that one should regulate children’s play. Let them always play the same games, with the same rules and under the same conditions, and have fun playing with the same toys. That way you’ll find that adult behavior and society itself will be stable."
He defined play as so central to children's development into good citizens that play should be strictly regulated.
Aristotle, on the other hand, thought of play as merely the opposite of work, and he defined education as distinct from play. He created a separation between work and play, a distinction that would come to influence the Greek method of education for a long time. In addition, Aristotle often taught through the peripatetic method, which means that he walked around while speaking with his students.
Persuasion: Reception and Responsibility by Charles U. Larson, pages 80-81.
"Plato and Play: Taking Education Seriously in Ancient Greece" by Armand D’Angour.