Tasks regularly completed by elementary teachers reveal the mathematical nature of their work. However, preservice teachers demonstrate a lack of depth of mathematical thought. This study investigated the criteria preservice teachers intuitively used to evaluate algorithms. The intent was to use that knowledge as a foundation for modeling mathematical habits of mind for similar tasks. Journal writings and notes from in-class discussions were collected over three semesters of an introductory course for future teachers. Data were analyzed to discover dominant criteria used by preservice teachers to evaluate student algorithms. Four criteria, namely efficiency, generalizability, mathematical validity, and permissibility, were routinely used by preservice teachers.