Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students' intuition and mathematical rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom…

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…