Oleanna opens with John on the phone, and Carol is seated across the desk. He's discussing real estate matters with what we presume is his wife Grace (he ends the conversation with "I love you, too"), indignant because there seems to be some problem with a deal. He pledges to meet her in ten to fifteen minutes. He hangs up, and Carol asks him about a term he used on the phone; he attempts to define it, offering a complicated explanation but ultimately does not know what it means himself.
John expresses his frustration at Carol's class performance, although not in so many words, just as she deduces that he is buying a house. He feels she is in reality bright but troubled, and she agrees, citing her social and economic background as impediments to her class performance. To illustrate frustration, he reads a passage from a paper of hers, which says absolutely nothing of any substance. She complains that she read his book and did everything she was told. He protests, "Look. Look. I'm not your father." The telephone rings, it is someone named Jerry calling about the house. John brushes him off, carried by his concern for the situation with Carol.
John wants to level with Carol and asks her to tell him what she wants him to do. She is concerned about her grades and asks him to teach her; she doesn't understand his book or his lectures. After consulting her notes, she brings up one of his phrases, "virtual warehousing of the young." He offers vague platitudes at her lack of understanding, and in reaction she launches into a monologue: people come to college to be helped and to prepare for a full life. Carol feels that because she doesn't understand, she will fail to live that life. She reveals that she believes she is stupid.
John tells her she is not stupid, but angry, and he reminds her that he has pressing appointments and that this meeting was not scheduled. She accuses him of thinking her stupid, citing a comment he made in reference to her paper: "What can that mean?" Carol becomes very frustrated, saying she doesn't understand anything anyone is talking about and is failing the class; she becomes self-hating, calling her work "garbage" and herself "pathetic."
The play opens with a telephone call, evidence of communication's role in Oleanna. John's phone call, as well as the ensuing conversation with Carol, is a great example of Mamet's notorious dialogue style—few sentences are completed, and the characters are constantly overlapping each other for an effect that's more talking at than communicating with. They trail off before any meaning is actually conveyed, ironic because John repeatedly says he wishes to level with Carol and really communicate. The form their dialogue takes also expresses a power dynamic here—it is John that does most of the interrupting, exerting his dominance over Carol in conversation.
Near the beginning of this section, John tries to define "term of art" for Carol, but does not actually know the phrase's meaning. This is indicative of John's character: he's overbearing, relentlessly interrupts her and often does not respond to what she actually says, talking instead on a topic important to him. John is almost entirely output, with very little input. Until Carol is forceful, she can get at most a few words out before he assumes her meaning.
Carol alternates between concern for passing the class and desire to understand the subject material. She begins by expressing an urgent need to pass the class, but once John asks her to tell him what she wants him to do, she explains that she wishes for him to teach her. This muddling of motives will later contrast her concern for John's teachings; initially, she very adamantly wishes only to pass the class. The only topic from the class that comes up in this section—"virtual warehousing of the young"—degenerates into her feelings on the purposes of higher education without any explanation or definition of the term from John.
Carol grows very negative near the end of the section—upset and filled with self-doubt. It is appropriate to note gender roles in this sort of behavior: it is the woman who becomes possessed with her own failures. This will contrast with the next section, where the man admits to previously having experienced such self-doubt but has overcome it. Mamet's female character is weak because of this self-doubt and negativity, while the male character is strong by contrast, having reversed this situation without any outside assistance. Rather than writing the female character as essentially male, Mamet uses the first two sections to set up Carol as different because of her weakness.