... as a rate of flow of charge.
One of my first lessons with younger students on electricity will be a rope model. I need to define a current as a rate of flow of charge. Some components speed up the flow of charge and some slow it down, but the charge travels around the circuit at one constant rate, and this is all due to the distances between charged particles being maintained, because they are all exerting forces on one another.
I have a knot in the loop of rope and I give someone the job of ammeter, I explain that ammeters measure the rate of flow of charge, i.e. the current. The student counts the number of times per second that the rope passes them as the students move the loop of rope around in their hands. And then we mock up using the equation for current, which is really the best way of defining a current.
charge flow (C) = current (A) × time (s)
It's hard to talk about current without talking about resistance, so I'll introduce the idea of some components slowing the rate of flow of the charge just by having them grip the rope, rather than allow it to slip through their hands, and the students can see this idea of the the flow being the same at all points in the circuit, not the charge speeding up and slowing down, or queuing at certain points in the circuit.
Current gets tricky when you are looking at circuits with multiple branches, so we'll introduce a second loop of rope, going through the same cell, but being passed by another group of students, this rope can move at the same rate as the first, but because the charge flowing through the cell is now doubled, that means that there is more charge per second flowing through the cell than the two branches of the circuit. That's a higher rate of flow of charge and therefore a higher current through the cell.
This idea of currents taking different paths and then joining again is summed up in Kirchhoff's first law, or his current law, the sum of the currents into a point is equal to the sum of the currents out of that point.
The last thing that I think is really important to define is the units that we use of current, it's not like electron per second, as that would be an absolutely huge number, but we use the unit Coulomb of charge, so one Ampere is one Coulomb per second. When you consider that an electron has the charge 1x10-19C you begin to appreciate how many electrons there are in a circuit!