The teaching of science, especially at pre-college and teacher education levels has undergone tremendous transformation over the years: from teacher-centred transmission to student-centred approaches rooted in constructivism. Whereas constructivism has been charged with all manner of shortfalls, it still can be of benefit to the way physics instructions are organized and implemented. In this paper, the importance of learners' prior knowledge in understanding physics concepts is discussed. This study comprised a case of two cohorts of physics teacher candidates who had strong content knowledge of physics, but lacked pedagogical knowledge as demonstrated by their struggles to implement appropriate grade-level strategies in physics problem solving tasks (which are amenable to a variety of mathematical tool-choices). The case cohorts we used as exemplars to underscore the importance of learners' prior mathematical knowledge. Further, we focus on implications for pre-service teacher preparation, and the effects mathematical tool-choice can bear on students' conceptions. (Contains 1 figure and 2 tables.)