A handbook for graduate teaching assistants (GTAs) in the Department of Mathematics at the University of Southern Mississippi is presented. General information is provided on GTA supervision, instructor absences, GTA obligations, the office and supplies, and the university's sexual harassment policy. A section on the first day of class covers: the syllabus and course policy, office hours, class roll, drop-add deadlines, class attendance, the Mathematics Learning Center, and the first day lesson. Also discussed are: preparing lessons, 21 instructional techniques, 11 essential chalkboard techniques, class discipline, grading, review sessions, 12 suggestions for composing tests, 5 suggestions for administering tests, 11 suggestions for grading tests, the university grading system, steps in the grade appeal process, evaluation of the GTA by students, and classroom observation of the GTA. Included are a sample syllabus, a sample course policy, a sample instruction appraisal form, and a sample classroom observation form. (SW)