Local Instruction Theories as Means of Support for teachers in Reform Mathematics Education

This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to adjust their instruction to the students' thinking. But, the point of departure is that if justice is to be done to the input of the students and their ideas built on, a well-founded plan is needed. Design research on an instructional sequence on addition and subtraction up to 100 is taken as an instance to elucidate how the theory for realistic mathematics education (RME) can be used to develop a local instruction theory that can function as such a plan. Instead of offering an instructional sequence that "works," the objective of design research is to offer teachers an empirically grounded theory on how a certain set of instructional activities can work. The example of addition and subtraction up to 100 is used to clarify how a local instruction theory informs teachers about learning goals, instructional activities, student thinking and learning, and the role of tools and imagery