In my 9th grade class, I'm expecting students to deal with simple questions and calculations with series and parallel resistors, though not with a single circuit combining both series and parallel resistors. We are teaching series resistors first, for a week; we'll deal with parallel resistors later.
My approach to circuits is not pure modeling, but somewhat close. I don't discuss the subatomic nature of current, or any sort of analogy for current and voltage in a circuit. Rather, I define terms based on what we can see and measure: "Voltage is provided by a battery," for example. My goal is to get, as quickly as possible, to experimental work in which students build circuits and measure voltages.
My colleague Alex Tisch and I made this helpful handout for the first day. You might want to print it out, or load it in an adjacent window, as you read this post.
I write the basic definitions and units on the board, and students copy these in preparation for a quiz the next day. The definitions I use are in this file. We quickly get to two demonstrations.
First, I help the class make a prediction for what a graph of current vs. voltage at constant resistance should look like. Since resistance is constant, V=IR suggests we should get a straight line graph.
Next, we actually do the experiment. I set my "decade box" variable resistor to 50,000 ohms, and vary the voltage from 2-20 V. My ammeter measures the current, usually getting in the hundreds of microamps. Notice that I've already set up reasonable axes in a blank graph on the handout. I have each student in turn come to the front of the room, adjust the voltage, read the voltmeter, and read the ammeter. I write a table of values on the board, and everyone graphs at his seat. Sure enough, 7-8 data form a pretty clear line.
Okay, then... what if we hold the voltage constant and change the resistance? We predict... V=IR says that as resistance increases, current decreases. We decide as a class that a 1/x graph is more likely than a linear upward-sloping graph*. The experiment and the students' graphs verify the prediction, this time setting the voltage at 10 V and changing the resistance between 1 thousand ohms and 100 thousand ohms.
Though I don't use those terms... I sketch a 1/x graph and a y=x graph, and without naming them just ask: which sketch is more likely?
On day two, I actually hand out my definitions for series resistors. We read them and practice using them with an actual circuit with series resistors. By day three, I'm ready to give them each a breadboard and have them predict and measure voltages across series resistors.
Using this approach, my students will be slower than most in figuring out how circuits work. A more traditionally taught class* will build some competence more quickly. But I'm convinced that after a few days of predicting, connecting, and measuring their own circuits, my class will catch up with and perhaps pass by traditionally-taught classes. And they'll pick up parallel resistors more easily. Why? Because they're not calculating dispassionately. They're making predictions for their personal circuit, predictions that they personally will test! It's amazing how much more they care when mother nature is sitting there, ready to prove them right or wrong.
* i.e. one in which you do practice calculations repeatedly in class and for homework
GCJ
[P.S. If I get to it, I'll make a future post explaining how I have everyone calculate the voltage across each resistor without calculating. Yes, I know, it's Zen.]
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