The theory of didactical situations (TDS) proposed by Brousseau is an influential framework for engineering learning environments in mathematics classrooms. However, this theory does not fully account for the learner’s internal cognitive processes when facing a crisis in an adidactical situation. In this conceptual paper, we introduce the theory of Mathematical Knowledge Architecture (MKA) as a complementary cognitive framework to TDS for addressing the learner’s internal cognitive processes. We argue that the dialectic of generalization and abstraction is the driving engine of this architecture; this dialectic, in response to cognitive crises, activates the fundamental mechanisms of MKA (such as translation, compression and reconfiguration). To demonstrate the analytical power of this framework, two instructional vignettes in analysis (complex numbers) and linear algebra (eigenvectors) are examined. The analyses show how the TDS environment stimulates the dialectic of generalization and abstraction, which in turn requires the activation of MKA mechanisms. This approach provides a deeper understanding of the teacher’s role as an architect of productive cognitive crises and offers important implications for instructional design in advanced mathematics.