Comprehension of calculus concepts based on motion sensor data
AbstractResults from physics education research indicate that laboratory activities using a motion sensor can supply a powerful setting for addressing students' difficulties in interpreting graphs of kinematics variables. Furthermore, graphs are also fundamental mathematics tools, whose application requires various types of mathematical competencies. The focus of the paper is on activities to develop conceptual understanding of fundamental calculus con-cepts, specifically instantaneous rate of change and accumulation of area under a curve by introducing motion sensor devices to the mathematics classroom. Beyond enhancing the teaching of mathematics by making it more realistic, alive and accessible, the motion sensor device enables users to get real time x(t) and v(t) graphs of a moving object or person. Con-secutively, these graphs can be productively used to introduce differentiation and integration on visual levels. In this context, the author presents examples based on real experiments where functions can be viewed from their characteristic behaviour-over-time/rate-of-change patterns, explaining and discussing the steps of such an approach in further detail. In conclu-sion, the technology use in the classroom challenges teachers to re-examine teaching ap-proaches in order to fully exploit the potential of the resources. Calculus, as the mathematics of change and accumulation of quantity, is conceived as a context in which the use of data from real experiments can significantly contribute to conceptual understanding of mathemat-ics concepts.
Copyright (c) 2014 Hildegard Urban-Woldron
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