This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and connect mathematics to real-world and applied situations. A four-step cycle of the modeling process is presented, involving: a real problem situation, the formulated problem, the mathematical model, and conclusions and answers to questions generated through analyzing the model. Three concepts were incorporated into the teacher education course: (1) the importance of developing and understanding one's conceptual model of the situation; (2) emphasis on reflective knowledge; and (3) the participants' evaluation of the entire activity identifying their goals and biases and evaluating their own thought processes. In the course, the teachers found examples of relationships in everyday language that can be described mathematically, drew graphs, and compared the relationships to familiar functions as possible models. They then classified functional relationships to build families of functions through sorting activities. For example, teachers analyzed U.S. census data, investigated problems involving compounded interest, and discussed possible connections between a new business's advertising expenditures and their sales, thereby using linear, quadratic, exponential, logarithmic, periodic, rational, and algebraic functions. Problems encountered in teaching the modeling process are discussed. (Contains 15 references.) (JDD)