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Improving the Conceptual Understanding of Kinematics through Graphical Analysis

Glenn W. Ellis, Warren A. Turner

Smith College / Massachusetts Academy of Mathematics and Science at WPI

Abstract

In this study, we use graphical analysis to develop a learner-centered approach to understanding kinematics. The learner-centered approach offers three advantages: it is consistent with pedagogy that has been shown to be effective for learning, it can be naturally integrated with real-time data collection using motion detectors or video analysis, and it provides a mechanism for developing insight into both physics and calculus. Students discover fundamental principles through a series of laboratory modules. The learning process is integrated into a conceptual framework through a variety of activities and application projects.

Introduction

Graphical analysis is an approach to learning kinematics that uses slope and area relationships among motion graphs to solve for unknown variables. Because this is essentially a graphical approach to finding derivatives and integrals, an understanding of graphical analysis is both useful to students learning calculus and broadly applicable to many other subjects. Although mentioned in many textbooks, graphical analysis is typically presented as an optional alternative to the use of constant acceleration equations for solving kinematics problems. While students may learn to solve problems more quickly through the application of constant acceleration equations, we feel that their understanding of motion—particularly the general case in which acceleration may vary with time—does not match the richer learning experience offered by graphical analysis. A graphical analysis approach allows students to visualize motion while working more directly with fundamental principles. Graphical analysis also takes greater advantage of advances in laboratory technology, including real-time data collection using motion detectors (an ideal tool for measuring, viewing and manipulating motion graphs for motion with constant or time-varying acceleration) and video analysis.

To produce the most effective learning, we have developed our kinematics curriculum based upon learner-centered principles. In this paper we will present our approach using the framework of the National Research Council (NRC) findings on effective learning. In a study with strong implications for teaching, the NRC has recently reported the following points as key to successful learning. 1

1. Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they won't change or they may learn for the test and revert to preconceptions.

Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright ã 2002, American Society for Engineering Education

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Turner, W., & Ellis, G. (2002, June), Using Graphical Analysis To Improve The Conceptual Understanding Of Kinematics Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10584