As universities strive to produce the best mathematics teachers possible through both graduate and undergraduate programs, teacher educators must constantly work towards helping teacher candidates create their own conceptual understanding of mathematics. This pilot study examined the effect teaching in a constructivist manner had on teacher candidates' conceptual understandings of the arithmetic mean and on their ability to transfer this knowledge into their instruction. Results indicated that teaching in a constructivist manner can have a positive impact on teacher candidates' understanding of the arithmetic mean, but their abilities to transfer this new knowledge into their own instructional practices was inconsistent. (Contains 2 tables.)