Learning the Basics with Calculus
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Stroup, W. (2005). Learning the Basics with Calculus. Journal of Computers in Mathematics and Science Teaching, 24(2), 179-196. Norfolk, VA: AACE.
Retrieved from http://www.editlib.org/p/5651.
Journal of Computers in Mathematics and Science Teaching
Volume 24, Issue 2, April 2005
Association for the Advancement of Computing in Education (AACE) Norfolk, VA
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A critical issue related to the use of simulation environments in school-based learning is the relation between the use of these environments and the structure of traditional curricula. Teachers are often caught in the bind of attempting to address significantly 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. Particularly challenging for practitioners and school-based researchers alike is the expectation that students should first master "the basics" before engaging innovation related to learning advanced content like calculus. This paper summarizes years of work related to the early learning the mathematics of change. The goal is to resolve this tension by suggesting that advanced mathematics, embodied in an accessible simulation environment, help situate and deepen students' understanding of the basics as they typically are encountered 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 relations between basics and advanced topics. The delta-blocks approach to the mathematics of change, making use of widely available forms of technology and the MathWorlds simulation software, is introduced and illustrated.
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