Task design for ways of working: making distinctions in teaching and learning mathematics

A problem identified in the literature around task design is the persistence of a gap between teacher intention and student activity. We show how principles designed around the making of distinctions and having an explicit language of mathematical thinking can eliminate the “gap” by guiding teacher planning, teacher actions in the classroom and student activity in the classroom. We show how our task design principles have developed during the time of our collaboration, over a period of 20 years, across several research projects. We argue for the importance, in task design, of an explicit theory of change and an explicit image of mathematical thinking, where the theory of change is applicable to researchers, teachers and students.