Using Empirical Modelling to Demonstrate Linear Kinematics

Engineering mathematics can be difficult to understand. Often a student’s first step in solving a problem will be to visualise it by drawing a diagram with pen and paper. As described by M Klawe (1995), this paper introduces how interactive electronic tools can be advantageous for learning. An Empirical Model created with Eden scripts is described, and its implementation explained. The software demonstrates the mathematical topic of linear kinematics by visualising the scenario on which an exam-style question is based. The trajectory of an object is randomly chosen, and the user is asked to calculate parameters of its flight. The software allows visualisation of each scenario and some experimental interaction by controlling the simulated motion of a particle. The program shows output in both graphical and numerical forms, to illustrate how they are linked. For example, how the flight path of a projectile changes under varying forces of acceleration due to gravity. The model will primarily be of benefit as an educational tool, to help learn linear kinematics. This particular branch of mathematics is part of the A-level mathematics syllabus, and could prove to be a valuable learning tool for this. Secondly, the study will highlight how the use of Empirical Modelling techniques can aid in the construction of such computer programs as described in our study; how they are ‘oriented towards aspects of computing practice for which formal methods offer limited support’. The example we use is particularly suited to EM since the central concept of dependency is tightly linked with that of mathematical equations. When the user modifies one parameter of a kinematic equation, others must be altered accordingly.