The stated goal of Individual Computer-Assisted Instruction (ICAI) research is the development of computer software that combines much of the subject matter being studied, any particular student's learning schema, and the pedagogical knowledge of human tutors into a powerful one-to-one learning environment. This report describes the initial steps in the research to design an intelligent tutor for basic algebra. Early observations indicated that one specific tutor version would be too limited, hence emphasis was focused on development of a generic tutor from which many tutor versions could be forged. This report documents the rationale for redirecting the overall research effort, the development of the generic tutor, the development of tutor versions from that generic model, and the efforts to evaluate those various tutor versions. The following are included: (1) an introduction with research goals and report organization; (2) a rationale for development of a core tutor and an outline of its components; (3) the physical specifications of the core tutor and design specifications of three tutor versions--the passive tutor, the multiple-representations tutor, and the goal-commands tutor; (4) an empirical evaluation and subsequent analysis of the passive tutor and its uses; (5) the conclusions drawn from this stage of ICAI research with prospects for future directions; (6) the student attitude/background survey and the mathematics achievement test used in the assessment procedure; and (7) 37 references. (JJK)