students to develop a conceptual model for a simple dc (direct current) circuit. Mathematics is not necessary; qualitative reasoning is sufficient.
The students begin the process of model-building by trying to light a small bulb with a battery and a single wire. They develop an operational definition for the concept of a complete circuit. Exploring the effect of adding additional bulbs and wires to the circuit, they find that their observations are consistent with the following assumptions: a current exists in a complete circuit and the relative brightness of identical bulbs indicates the magnitude of the current. As the students conduct further experiments (some suggested, some of their own devising), they find that the brightness of individual bulbs depends both on how many are in the circuit and on how they are connected to the battery and to one another. The students are led to construct the concept of electrical resistance and find that they can predict the behavior of many, but not all, simple circuits of identical bulbs. They recognize the need to extend their model beyond the concepts of current and resistance to include the concept of voltage (which will later be refined to potential difference). As bulbs of different resistance and additional batteries are added, the students find that they need additional concepts to account for the behavior of more complicated circuits. They are guided in developing more complex concepts, such as electrical power and energy. Proceeding step-by-step through deductive and inductive reasoning, the students construct a conceptual model that they can apply to predict relative brightness in any circuit consisting of batteries and bulbs.
We have used this guided-inquiry approach with teachers at all educational levels, from elementary through high school. Having become aware of the intellectual demands through their own experience, the teachers recognize that developmental level will determine the amount of model-building that is appropriate for their students. For the teachers, however, the sense of empowerment that results from in-depth understanding generates confidence that they can deal with unexpected classroom situations.