Final answer:
Joan was likely experiencing client-centered therapy, a non-directive therapeutic approach developed by Carl Rogers that emphasizes an accepting and nonjudgmental environment to promote personal growth.
Step-by-step explanation:
Joan's therapy experience, where her therapist provided a nonjudgmental and accepting environment while Joan talked freely, likely describes client-centered therapy.
This therapeutic approach was developed by Carl Rogers and is characterized by the therapist's display of unconditional positive regard, genuineness, and empathy.
Unlike more directive forms of therapy, such as Freudian psychoanalysis, client-centered therapy allows the client to take the lead in the therapeutic process. Rogers believed that providing these conditions would enable individuals to explore their feelings and develop towards their potential for personal growth.