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
- 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.