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After the teachers have developed the concepts and learned to reason with them they are then in a position to give meaning to the mathematical equations that relate the concepts. Why can't we just took this to the amp meter and then hook that the other thing like I think that's a great idea. I think it's much of a difference it's better it's easier. I have taught them both about the right. Right in order to enable students to quantify the concept of resistance. Michael Myers introduced his students compare its behavior to that of buds and then go on to develop rules for how the resistance of the wire depends on its length. Okay so that last is how I got to the file that was just. This length of wire. Which is five centimeters. And the resistance of that circuit. Is equivalent to five centimeters of micro wire single different airline. It's often a circuit diagram is very difficult to associate with a particular circuit that students have put together that represents just a jumble of

wires they need to be able to translate between those two and they need explicit practice doing it. These wires along of the five senators each post be 10 centimeters too long wires. When put together give you less resistance because in parallel right the longer wire alone would be more resistance right. When put in parallel it equals the same as a shorter five centimeter why you came here and why and so we should. Have found because of the results of this student's at this point are able to give meaning to the concept of the quote resistance. They then have the understanding necessary to go on and examine circuits of increasing complexity. You've added three pathways three pathways all of 30 centimeters each right. Right. Now weighs one third it makes total sense. This is offering three times the resistance of 110 centimeters. But there are three pathways of the door through so that brings it back to equally 10:10 71 so adding which this is a series.

Of stuff that I was assistant parallel which allowed a pathway that's actually it's decreasing the resistance not more resistance less current less resistance more current and look at this as your system with a qualitative section three four hours just as a pelican But absolutely the bottom of the brightness of the bulbs right. The balls were as. They were in the Pelly brightly put on parole so now we have a quantitative rule. We're actually putting numbers to last.