This paper examines how middle school students developed understanding of transformational geometry through design activities in Escher's World, a computationally rich design experiment explicitly modeled on an architectural design studio. Escher's World was based on the theory of pedagogical praxis (Shaffer, 2004a), which suggests that preserving linkages between epistemology and pedagogy is a critical step in developing computational learning environments based on professional practices such as architectural design. Here, I examine this theory by analyzing the pedagogical processes at work in Escher's World, focusing on three precursors to the development of mathematical understanding: (a) enactment of participant frameworks from the design studio, (b) the autoexpressive properties of the computational tool being used, and (c) the expression of students' interests through design activities. I take a mesogenetic approach to this analysis of learning, using accounts of students' design work based on extensive field notes to examine how these precursors to mathematical understanding interacted over extended design activities. I present a case study of the work of one student in Escher's World and use quantitative analysis to help demonstrate theoretical saturation for the grounded theory I develop. I conclude by discussing implications of and for the theory of pedagogical praxis: that developers of learning environments based on design activities may need to pay careful attention to linkages between the epistemology and practices of design in creating innovative learning environments, and that adapting existing practices from the design studio may be one particularly effective approach to that challenge. Geometry questions are appended. (Contains 15 figures, 4 tables, and 8 footnotes.) [The research reported in this paper was also supported by the LEGO Corporation, the MIT Media Laboratory Things That Think Consortium, and a Spencer Foundation/National Academy of Education Postdoctoral Fellowship.]