Reasoning Dynamically About the Area of a Rectangle: The Case of Lora and Isaac

This article reports on an exploratory study that engaged students in dynamic experiences of generating the area of a rectangle as a sweep of a line segment over a distance. A case study from a design experiment with one pair of third-grade students is presented to initiate a discussion around the forms of reasoning that students may exhibit as a result of their engagement with these dynamic motion tasks and the characteristics of the design that supported these particular forms of reasoning. The findings of this study show that engaging students in dynamic experiences of area may help them develop a conceptual understanding of the area of a rectangle as a continuous structure that can dynamically change based on the two linear measures that generate it: the length of the line segment swept and the distance of the sweep. These experiences can also help students from an early age develop a flexible understanding of a unit and reason covariationally about the continuous change of the quantities in measurement.