Some views of elementary teacher preparation may include the idea that undergraduate mathematics courses are useful or even crucial for prospective teachers to have. This study sought to identify teacher candidates with mathematics degrees, in order to study their mathematical preparation. The identified prospective teachers were studied to investigate initial understanding of the conceptual underpinnings of elementary mathematics, as well as their beliefs about the importance of conceptual learning. Participants were given a written instrument related to elementary school-level conceptual mathematics knowledge, administered at the beginning and end of an elementary (up to grade 8) mathematics curriculum and instruction ("methods") course. Prospective teachers with university mathematics backgrounds did not appear generally well-prepared in terms of their ability to model or explain the conceptual basis of common elementary school concepts, although they generally claimed to feel such understanding was important. After taking part in the methods course, which focused strongly on experiences learning the mathematical ideas conceptually, they were able to demonstrate increased understanding of the necessary concepts, models, and reasoning related to elementary mathematics teaching.