I can’t help thinking that we are all still being driven by the idea of developing understanding and teaching topics in physics. Although our links are meant to run both ways – from real world ideas through to physics concept and vice versa, our thinking has very much been one way.

There is a (perfectly valid?) sense in which for, say kinematics, v=dx/dt and a=dv/dt with a,v,x vectors **is** the physics of the situation. If we *start* from there we could ask questions such as “What is a reasonable apporximation to this for those currently unaware of calculus?”, “What are some examples to help people ground this in a more concrete reality?” or “If we add further assumptions (e.g. constant a) what simplifications follow?”.

For some people, the ‘final equation’ is the starting point. For others it is the summit we are aiming for and, as a teacher we can look down from there and ask how best to guide students to it. But some teachers will not be at that summit themselves – or not be aware of all the routes – so might prefer a top-down approach.

It may well be possible to incorporate this view into the current map, by emphasising the two-way nature of the process.