The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a powerful method for learning about students' underlying cognitive competence. Cognitive developmental theory is essential because assessment is only as "valid" as the ideas on which it is based. Yet current theories of developmental trajectories need to be supplemented by consideration of obstacles that the student must overcome. These involve the mathematics, instructional materials and the teacher.