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