A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their models. We also explore their reflections on modeling as a pedagogical experience. We introduce Modeling Decision Maps as a tool to examine how PSTs construct and refine mathematical models, and we draw on reflective journal entries to capture PSTs' perspectives on the process. Our findings indicate that realistic modeling tasks provide opportunities to foster PSTs' understanding of modeling, grow their mathematical modeling skills, and attune them to important pedagogical practices.