Although data modeling, the employment of statistical reasoning for the purpose of investigating questions about the world, is central to both mathematics and science, it is rarely emphasized in K-16 instruction. The current work focuses on developing thinking about data modeling with undergraduates in general and preservice teachers in particular. Subjects were 125 undergraduate preservice teachers (118 females) from a highly selective, nationally recognized teacher education program. A design-based research methodology was used, and data analysis took the form of retrospective, cross-iteration comparisons where themes of the design of inquiry, measurement, deficit model of experimentation, and epistemology and nature of science emerged. Our findings are relevant to those who seek ways to support undergraduate understanding of statistical reasoning as well as making a contribution to the challenging problem of how to support and integrate preservice teachers' coordination of data modeling and inquiry into their pedagogical practice.