Learning to use Cartesian coordinate systems to solve physics problems: the case of ‘movability’

Trevor S Volkwyn,Bor Gregorcic,John Airey,Cedric Linder

doi:10.1088/1361-6404/ab8b54

Abstract

In this paper, we show that introductory physics students may initially conceptualise Cartesian coordinate systems as being fixed in a standard orientation. Giving consideration to the role that experiences of variation play in learning, we also present an example of how this learning challenge can be effectively addressed. Using a fine-grained analytical description, we show how students can quickly come to appreciate coordinate system movability. This was done by engaging students in a conceptual learning task that involved them working with a movable magnetometer with a printed-on set of coordinate axes to determine the direction of a constant field (Earth’s magnetic field).

Highlights

Learning how to appropriately select and use coordinate systems is central to physics modelling and problem solving
In this paper, we show that introductory physics students may initially conceptualise Cartesian coordinate systems as being fixed in a standard orientation
As an example of this practice, we present a quotation from an American Association of Physics Teachers (AAPT) reference textbook for college students applying mathematics as a tool for science work: With Cartesian coordinates in two dimensions, you locate points by constructing a horizontal reference direction, called the x axis, and a vertical reference direction, called the y axis [. . . ]

Summary

Introduction

Learning how to appropriately select and use coordinate systems is central to physics modelling and problem solving. The setting up of a coordinate system is essentially an arbitrary process, in textbooks Cartesian coordinate systems are typically presented to students in one particular orientation—x increasing to the right, with y usually pointing ‘up the page’ (or z for 3D systems)—see figure 1, and the discussion . Such standardised presentation may initially lead to students conceptualising that coordinate systems are always fixed in this particular orientation (Volkwyn et al (2018)). In this paper we suggest that one of the reasons for initial student difficulties with using Cartesian coordinate systems to solve physics problems may, in part, stem from a failure to fully appreciate a coordinate system’s movability

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Discussion

Conclusion