Hockaday offers an introductory forensics course as well as a more advanced competitive forensics course in the Upper School. Students interested in participating in debate tournaments must take the introductory course. Below are descriptions of the two courses.

Debate: Debate introduces the student to the art and skills of persuasion as conducted in the Lincoln-Douglas debate format. Each student learns the principles and techniques of debate and applies them in supervised practice during class periods. A major component of the course deals with the tools of research, techniques of critical analysis, and the methodology of preparing oral arguments. The student participates in three debate tournaments and joins in planning and directing an invitational tournament at Hockaday. A student may continue in this course in subsequent years if she does not want to advance to Competitive Forensics.

Competitive Forensics: In Competitive Forensics the student has the opportunity to refine her skills in argumentation and debate. Additional time is spent on research, topic analysis, preparation of briefs, and evaluating and critiquing. Emphasis is placed on Lincoln-Douglas debating and on individual events with responsibility extended to the student to prepare and practice outside the classroom. The student represents Hockaday in forensic tournaments throughout Texas. Certain students are selected for competition in national high school debate tournaments such as those held at Harvard, Northwestern, and Princeton universities. Taking United States Government in Form II is recommended.

In 1937, Miss Hockaday began The Music Institute with its own building and faculty on the Greenville Avenue campus. Her friend, Josef Levine of Julliard, was head of the conservatory. Both women and men were enrolled for study.