This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in modelling when such approaches involve students encountering and resolving experimental error. We use a "tensions" framework to explore the capability of learners to make necessary connections between abstract mathematical models and physical phenomena. (Contains 5 tables and 8 figures.)