A choice in how you approach modelling

A traditional modelling approach

• imagine some variables
• write down some algebra
• set some initial values for the variables
• run the system of equations
• inspect the output (usually as a scatter graph), sometimes just as a table
• translate this into an imaginable and intelligible form, to compare with the phenomena

This approach imposes a high imaginative load. You are expecting children to link the abstract algebra with the phenomena, often mediated by another abstract representation: the scatter graph.

A more gradual approach to build up a model, by constructing interactive diagrams, physics interactive diagrams(PID). This approach may, by virtue of presenting a more gradual path to abstraction, and staying close to the physical situation for longer, provide a more fruitful route.

The PID approach

• create representations of the phenomenon, setting values where appropriate
• place those representations on a canvas, to re-describe what you notice and record
• Focus on the physical relationships, expressed through the evolving behaviour of the representations
• write rules about connections between the representations and how they evolve over time

Comparing approaches

• one of these approaches gives you objects to think with that are closely connected to physical descriptions to think about early only
• one of these gives feedback which is connected to things you might notice

For here on in, we're going to suggest a gradualist approach, based on generating interactive diagrams.