Learning the Basics with Calculus
Walter M. Stroup · 2005
A critical issue related to the use of simulation environments in school-based learning is the relationship between the use of these environments and the structure of traditional curri-cula. Teachers are often caught in the bind of attempting to address signifi cantly raised standards for what all students should know, yet receiving very little support to innovate in their use of simulations in their approaches to teaching. Par-ticularly challenging for practitioners and school-based re-searchers alike is the expectation that students should fi rst master “the basics ” before engaging innovation related to learning advanced content such as calculus. This paper sum-marizes years of work related to the early learning of the mathematics of change. The goal is to resolve this tension by suggesting that advanced mathematics, embodied in an accessible simulation environment, helps situate and deepen students ’ understanding of the basics as they typically are en-countered in the traditional mathematics curriculum. Selected episodes transcribed from work in economically challenged schools in the United States are used to illustrate the practical potential of this reconsideration of the relationships between basic and advanced topics. The delta-blocks approach to the mathematics of change, making use of widely available forms