Choosing and using representations

Some examples

Here is one simple situation where you move from a physical situation through to representations which are quantitative and yet still connected clearly to measurements that might be made. The current arrow is clearly connected to flow and the magnitude of the arrow increases as the flow increased. The potential difference representation is clearly connected to the act of placing a voltmeter across an object and yet can show the magnitude of the potential difference. This presents a representation which is much closer to the physical than writing down a number and a unit or else a single symbol (V or I).

Here is another situation where you move from a depiction of everyday objects the lived-in world through to an austere imagined physics world by using standardised representations.

Deploying representations in a modelling tool

These kinds of first steps towards generating a computational model can now be made using a modelling tool. The physics diagram language, which enables physics interactive diagrams, has building blocks (primitives) which produce all of the standardised representations used in Supporting Physics Teaching. So it's possible to build up a model using a sequence of steps.

Here's the standard example of modelling free fall: a skydiver.

You might start by discussing the forces on the skydiver, and how these combine to produce a resultant force. However, rather than starting with an algebraic statement you might start with the manipulable arrows:

This is no more than an interactive diagram — there are no rules about connecting the forces or relating the forces to the duration of the fall. Instead, it's a place where you can begin to discuss what children's expectations are.

A fairly traditional approach to developing a model of this situation is to create a series of snapshots in which you look at the forces acting on the skydiver, the resultant force, and the acceleration that results. Again this is possible that the same tool. You could use the tool to create a partial model of the situation that calculates the resultant force from the forces acting. doing so would be to where the first rule at your imagined world. You might then look at the relationship between acceleration and velocity, as one of simple accumulation. Finally, and perhaps several steps in the future, you might show a fully developed model.

A choice to make

Developing a full-blown model, such as the skydiver, is quite an undertaking and involves many steps. Making the steps visual and explicit can help children to follow the steps and to see what those steps are — that is to open the steps up for reflection: to reflect on their own theorising. In this way, children can come to see what the process of modelling is, and to apprehend some of the procedural moves that are useful. This can be combined with the graphical language for displaying the moves provide a complete package for representing modelling.