With circuits this year, I’ve been teaching a “solve for everything” approach that balances circuit reduction with reasoning about Kirchoff’s rules. First students reduce the circuit and then work to determine the current, potential differences, and power outputs of each device.
For example, on the student whiteboard below, they were supposed to find the power output at Resistor Three. I’ve been pushing for solving for the power input/output of everything, so they can check energy conservation.
I worried about teaching them to use the table, that maybe it would turn it into a mindless numbers game, but the organization actually allows students to spend energy on reasoning for how currents / potential differences should relate. It also just helps with the book-keeping so keeping track of what they know and don’t know easy. It also makes checking work easy. The first two columns should multiply to the third column by Ohm’s Law. And the 2nd and 3rd columns should multiply to the 4th column by the power relationship. A colleague of mine extended my table method to include all the equivalent resistors along the way as well.
Overall, I’m pretty happy with this approach. One tweak I would make would require them to write/diagram their reasoning about how the Kirchoff’s reasoning–either in algebra or using the diagrams.