This study highlights ways in which generative activities may be coupled with network-based technologies in the context of teacher preparation to enhance preservice teachers' cognizance of how their own experience as students provides a blueprint for the learning environments they may need to generate in their future classrooms. In this study, the design of generative learning environments is used as a framework for developing an activity for students to explore modeling by interpolation and function approximation in the classroom. The research question explored whether the implementation of a generative activity on function interpolation can lead to a qualitatively different mathematical space of solutions when used in a calculus class when compared to its use in the context of a class on learning theories in science, technology, engineering, and mathematics (STEM) education. Participating students included preservice STEM teachers and students in a first-year calculus course. In order to determine possible qualitative differences in mathematical activity between the two classroom contexts (calculus class or learning theories in STEM education class), the authors focused on the evidence of student individual and collective thinking from three different groups, as documented in their corresponding generated public spaces and explored and characterized each group by its respective generated mathematical spaces of solutions. (Contains 5 figures.)