A study of preservice student teachers involved 19 undergraduates certified to teach mathematics by the Washburn University (Kansas) teacher preparation program from fall 1984 to fall 1989. The study examined their ability to transmit knowledge of the subject to students through methodologies designed to translate theory into practice. The respective cooperating teachers (n=18) provided data regarding each student teacher's abilities, and the student teachers provided data by using the same evaluative device for assessing their own abilities in secondary school mathematics. Evaluations were made relative to their knowledge of the subject areas of trigonometry, business applications, analytic geometry, modern math, algebra, geometry, and arithmetic. The evaluations also looked at their ability to transmit subject matter to students using lectures, demonstrations, models, data analysis, and simulations. A third part of the evaluation measured their ability to translate theory into practice by providing projects, simulations, clear procedures, fully-explained results, and well-explained applications. Each evaluative instrument was based on a rating scale of 1-5. Data analysis indicated that the student teachers tended to rate themselves slightly higher than did the cooperating teachers. The cooperating teachers had a smaller standard deviation than did the student teachers. The 20 tables and the evaluative instruments are appended. (SM)