DNR-Based Curricula: The Case of Complex Numbers

Abstract

"DNR is a research-based framework which seeks to understand fundamental problems of mathematics learning and teaching. This paper discusses DNR with a particular reference to a curricular unit on complex numbers. Originally designed for college-bound high school students, the unit is structured to progress along a path that roughly parallels the development on complex numbers in the history of mathematics. We have tested the unit in three teaching experiments with in-service and prospective secondary mathematics teachers. The results from these experiments demonstrate the ways of thinking afforded and targeted by the unit. The correspondence between these ways of thinking and the Standards Practices outlined by the Common Core State Standards are also discussed."