Principles for the design of teaching

In this introductory article, after some initial discussion of an appropriate approach to mathematics as a curriculum subject, we sketch a theory for designing teaching, based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. We next review the main psychological principles underlying this theory, then consider some examples of teaching designs in the light of the theory. Thus we open the discussion of the theme of this issue, which continues with the fuller discussion of other examples in the remaining articles.