In this paper, we describe a model for systematically improving the mathematics preparation of elementary teachers, one lesson at a time. We begin by identifying a serious obstacle for teacher educators: the absence of mechanisms for developing a shareable knowledge base for teacher preparation. We propose our model as a way to address this challenge, elaborating the principles that define the model to show its relevance. We then provide an example of the model in action, detailing how the model was used to gradually but steadily improve a single mathematics lesson for prospective elementary teachers. We conclude by presenting data indicating that the model is effective in generating and vetting knowledge that helps to improve our mathematics program over time. Although our discussion is situated in the mathematical preparation of prospective elementary teachers and draws on examples from mathematics, we argue that the model could be applied to build knowledge and improve teacher preparation in any discipline. (Contains 3 figures, 3 tables and 1 note.)