Why two dimensions?



Let's start with perhaps the most controversial suggestion, which is that you begin by reasoning about motions in two dimensions. Note that almost all representational surfaces on which we inscribe records of journeys, or which we use to make plans for journeys, are two-dimensional: from formal paper maps, through GPS trails, to sketch maps of how to get from home to the local shops. This is not accidental. Stories about journeys involve relating ourselves to the local geometry and often involve talking about, for example: 'going left', 'going right', 'going straight on', and 'turning half-left' by some landmark or after travelling for some distance or duration(so with some implied speed). You could co-opt these patterns of thinking and talking in the students' experiences: not something that can so readily be done if we start along the conventional route of teaching about kinematics in one dimension. The phrases that naturally involve two dimensions are a widely-used way to give directions and to talk about paths that are followed. It's possible to see connections here with the revolution in geometrical understanding derived with computational approaches embedded in Logo-like languages. These often appear in many early introductions to computational activity, in languages such as Logo itself or Scratch. The widespread opportunities to 'program' in a set of instructions, much like offering guidance in getting from A to B when 'programming' a human, provides additional support for thinking in two dimensions, often using relative positioning, (implicitly)relative velocities and durations. The availability of more-or-less educational computational toys such as Sphero™ further widens access to this 'two-dimensions first' approach to kinematics.