On the use of a standard spreadsheet to model physical systems in school teaching*

Abstract

In the teaching of physics at upper secondary school level (K10–K12), the students aregenerally taught to solve problems analytically, i.e. using the dynamics describing a system(typically in the form of differential equations) to compute its evolution in time, e.g. themotion of a body along a straight line or in a plane. This reduces the scope of problems,i.e. the kind of problems that are within students’ capabilities. To make the tasksmathematically solvable, one is restricted to very idealized situations; more realisticproblems are too difficult (or even impossible) to handle analytically with the mathematicalabilities that may be expected from students at this level. For instance, ordinary ballistictrajectories under the action of gravity, when air resistance is included, have been ‘out ofreach’; in school textbooks such trajectories are generally assumed to take placein a vacuum. Another example is that according to Newton’s law of universalgravitation satellites will in general move around a large central body in ellipticalorbits, but the students can only deal with the special case where the orbit iscircular, thus precluding (for example) a verification and discussion of Kepler’slaws. It is shown that standard spreadsheet software offers a tool that can handlemany such realistic situations in a uniform way, and display the results bothnumerically and graphically on a computer screen, quite independently of whether theformal description of the physical system itself is ‘mathematically tractable’.The method employed, which is readily accessible to high school students, isto perform a numerical integration of the equations of motion, exploiting thespreadsheet’s capability of successive iterations. The software is used to model and studymotion of bodies in external force fields; specifically, ballistic trajectories in ahomogeneous gravity field with air resistance and satellite motion in a centrallysymmetric gravitational field. The article reports briefly on a study of the use ofcomputers in the teaching of physics at K12 level in Norway, as part of an EUresearch project (for details, see the end of the article). It is demonstrated how thesimulation software (the spreadsheet) is implemented in practice, for the systems thathave been studied, and various responses of the students and teachers to thisnew and unfamiliar method for solving problems in physics are discussed. Someperspectives on the future of physics teaching at secondary school level are discussed.