Design and research for developing local instruction theories

Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the development of the basic principles of the mathematics of change. The study combines design and research in three successive phases. In the first phase a hypothetical learning trajectory and instructional activities are designed, in the teaching experiment phase the trajectory is acted out, and in the phase of the retrospective analysis the articulated hypotheses are reflected upon. In this way, a cyclic process of (re)design and development of innovative teaching is structured. The resulting local instruction theory is expected to create opportunities for teachers, textbook authors and researchers to consider contextual factors and to adapt results for their research or teaching.