Questionnaires were sent to 97 computer coordinators in school districts in Texas and 59 program directors in colleges of education throughout the United States to determine: (1) the computer knowledge and skills that school district computer coordinators perceive to be needed by classroom teachers; (2) the computer knowledge and skills that college program directors perceive to be needed by classroom teachers; and (3) whether school district computer coordinators and college program directors have different perceptions of the essential computer competencies needed by classroom teachers. Questionnaires were returned by 88 computer coordinators and 51 program directors. Analyses of their responses indicate that both school district coordinators and college program directors perceive that the competency to evaluate and choose quality software is very important for teachers; the ability to use the computer as an instructional tool in such modes as drill and practice, tutorials, simulations, and problem solving is considered very important by computer coordinators and important by program directors; and the competencies associated with programming and the history of computers are considered moderately important by both groups. The remaining competencies associated with computers and society are considered important by both groups: ethical concerns, record keeping, care of hardware, care of software, word processing, and data processing. The report concludes with a list of 12 competencies to be included in computer education coursework for preservice and inservice teachers, a 13-item list of objectives and supporting text references and lab activities for a suggested computer literacy course for teachers, 4 tables of survey data, a bibliography for the course, and a list of references. (JB)