Systematic use of teaching models

Ensure that the models you choose can be reasoned with

The rope loop teaching analogy was introduced in the SPT: Electric circuits topic (in the episode Developing an electric circuit model). We're clear that there is much to be gained from the systematic and consistent use of analogies, so we advise that if the rope loop has been used lower down the school, then you and your students should return to it now: rather like renewing acquaintance with an old and trusted friend.

An essential competence in the use of analogies is to be able to move fluently between the target (in this case the electric circuit) and the analogy (in this case the rope loop). If you and your students are revisiting the rope loop model after a break of some time, it's worth carefully talking through the mapping between the target and the analogy:

Teacher Tip: Target: electrical circuit  →  Analogy: rope loop. The cell  →  The person providing pull on rope. The potential difference  →  The size of the pull. The resistor  →  The person gripping the rope. The resistance  →  The slipping force applied by the person. The electric current  →  The rate at which the rope moves

This episode expects that children will come to understand the idea of potential difference rather well, and the mapping above shows that there is a reasonable chance of using this to develop the idea of potential difference (in fact the mathematics of the rope loop and of an electrical loop have identical patterns, which is one reason to believe that such a route is fruitful. ( Here a good place to start is P = F × v and P = V × I).

Here is a simple model of a loop in which you can vary the forces:

And here is a similar electrical loop, with similarly variable quantites. We hope you can see how well the source and target domains are matched, and so how well reasoning about the (tangible) rope can support predictions about the (somewhat less tangible) electrical loop.

(The choice of resistor is not implemented in these models, but it should not be too hard to see how to do so.)

Approaches which might not be so fuitful

We'd suggest that approaches based on hills are not so fuitful and might tilt the children's thinking back towards the idea that charges in circuits in some sense carry energy.

Similarly teaching ideas such as colouring circuits to identify potential differences may be heuristically helpful, but emphasising analogies between being uphill (gravitational potential) and electrical potential are not so fruitful until a rather richer understanding of potential is available, usually attepoted in post-16 studies).

Reasoning and representing

A fuitful question is to ask what you expect childeren to be able to do with the models or analogies that you develop. How far can they be developed?

Here is one (a rather exhaustive account) way in which you might develop the idea of potential difference through the rope loop and then apply it to reasoning about series circuits.