The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical principle revealed how she came to see problems initially thought to be different as alike, as she slowly came to identify different problems as instances of a single principle. Microgenetic analysis of the data supports diSessa's (1993) knowledge-in-pieces epistemology, which suggests that complex conceptual understanding is supported by the systematization of many different types of knowledge resources, often highly sensitive to context. A "transfer-in-pieces" approach demonstrates how means of attending to (reading out) and coordinating information available in particular instances may vary as a single mathematical principle is perceived as relevant in different contextual circumstances. Transfer is revealed not as rooted in the acquisition of increasingly abstract mental representations, but through the incremental refinement of knowledge resources that account for--rather than overlook--contextual variation.