DNR-Based Curricula: The Case of Complex Numbers

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 of complex numbers in the history of mathematics. We have tested the unit in three teaching experiments with inservice 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

Intellectual need and problem-free activity in the mathematics classroom

Intellectual need, a key part of the DNR theoretical framework, is posited to be necessary for significant learning to occur. This paper provides a theoretical examination of intellectual need and its absence in mathematics classrooms. Although this is not an empirical study, we use data from observed high school algebra classrooms to illustrate four categories of activity students engage in while feeling little or no intellectual need. We present multiple examples for each category in order to draw out different nuances of the activity, and we contrast the observed situations with ones that would provide various types of intellectual need. Finally, we offer general suggestions for teaching with intellectual need