*Lillian.C. McDermott**Department of Physics, University of Washington, Seattle,
Washington, U.S.A.*

This chapter by Reinders Duit and Christoph von Rhöneck provides an overview of much of the research that has been conducted on student understanding of electricity. The emphasis is on simple DC circuits that consist of batteries and bulbs. The authors describe some common conceptual difficulties that have been identified among pre-university students, citing several studies. There is also ample evidence that university students who have studied introductory physics have similar conceptual difficulties (McDermott and Shaffer, 1992). Included in this group are elementary, middle and high school teachers, both those teaching now and those who plan to teach. Since electric circuits are part of the pre-university curriculum, it is important that teachers overcome their difficulties with this material and also become familiar with effective instructional strategies that they can use to help their students.

The authors of this chapter comment briefly on how to help students improve their understanding. Below, we extend this discussion by giving a specific example of an instructional sequence designed on the basis of research. The laboratory-based approach that is used has been shown to be effective in addressing many of the difficulties mentioned in the chapter (Shaffer and McDermott, 1992). The curriculum in which this example is embedded is readily available (McDermott, L.C. & the Physics Education Group, 1996).

**Example of Application of Research to Instruction**

The students are guided through the process of constructing a conceptual model for electric current from direct experience with simple circuits consisting of batteries and bulbs. They perform experiments, make observations and draw inferences through which they formulate the basic concepts of current and resistance. They use both inductive and deductive reasoning to synthesize these concepts into a qualitative model for electric current. As they apply the model to circuits of increasing complexity, the need for other concepts becomes apparent. Below we outline the logical progression through which students develop a conceptual model that they can use to predict and explain the behavior of simple resistive circuits.

The students begin the process of model-building by trying to light a battery with a bulb and a single wire in as many ways as possible. They find that there are four possible arrangements in which the bulb will light. They are asked to compare these with arrangements in which the bulb will not light. They note that for the bulb to light, each of its terminals must be connected to a different terminal of the battery through a continuous conducting path. The students formulate the concept of a complete circuit and realize that all four arrangements can be represented by a single diagram. They investigate the brightness of different configurations of bulbs connected to a single battery. Their observations make plausible the following two assumptions that provide the basis for initial development of the model: (1) a flow (identified as electric current) exists in a complete circuit and (2) bulb brightness indicates the amount of current.

The students next investigate the behavior of series and parallel circuits in a systematic manner. The dimming of a light bulb that occurs when a second identical bulb is added in series to it provides a basis for introducing the concept of resistance. The students recognize that the equal brightness of the two bulbs implies that current is not "used up." They determine that neither the direction of the current nor the order of the elements affects bulb brightness. When they observe that individual bulbs connected in parallel directly across an ideal battery are as bright as a single bulb connected in the same way, they realize that their intuition that the battery is a constant current source is not correct. They are forced to conclude that the current through the battery depends on the configuration of the circuit. The concept of equivalent resistance is introduced. The students find that this quantity depends on the configuration and not merely on the number of elements or branches. The students then investigate the behavior of different configurations of bulbs and observe that changes made anywhere in a circuit often result in changes at other points. They find that the model that they have developed enables them to predict the relative brightness of bulbs in a variety of circuits, but not in all situations.

Only qualitative reasoning has been required for construction of the model thus far. The experience is therefore particularly suitable for students in elementary and middle school and for their teachers, whose mathematical skills are often not strong. For high school students and their teachers and for university students, the development of a conceptual model should not stop with the concepts of current and resistance. The need to extend the model becomes clear through a series of experiments in which the students examine the effect of adding batteries in series in a circuit. The students note that bulb brightness increases with each addition. This effect suggests the idea that the battery is the agent that "drives" current through the circuit. The concept of potential difference is introduced. With the aid of an ammeter and voltmeter, the students develop operational definitions through which they quantify the concepts of current, potential, potential difference and resistance. They formulate Kirchhoff's first and second rules and determine the relationship between current and potential difference for ohmic materials (Ohm's law).

The model that the students have developed enables them to predict relative brightness when bulbs in a circuit are identical but not when their resistances are different. The students conclude that neither current, nor resistance, nor potential difference alone is sufficient to determine brightness. When the model is extended to include the concept of power, the students can make predictions for non-identical bulbs. Experiments that demonstrate that batteries have a finite lifetime help the students to identify energy as the quantity that is dissipated. They can now reconcile their formal knowledge that current is conserved with their intuitive belief that something is "used up" in a circuit.

**Generalization**

This chapter serves a useful purpose in calling the attention to findings from research on student understanding of electric circuits. However, the identification of difficulties is only part of the contribution that research can make to the improvement of instruction. Of equal importance is the use of the results to guide the development and assessment of curriculum. The specific example described is an illustration.

**ACKNOWLEDGMENTS**

The research and curriculum development on which the comments in this paper are based are the results of an ongoing, collaborative effort by many members of the Physics Education Group at the University of Washington. Support from the National Science Foundation is also gratefully acknowledged.

**REFERENCES**

McDermott, L.C. & the Physics Education Group at the University
of Washington (1996). __Physics by Inquiry, Vols. I and II.__ New York:
John Wiley & Sons, Inc.

McDermott, L.C. and P.S. Shaffer (1992). Research as a guide for curriculum
development: An example from introductory electricity, Part I: Investigation
of student understanding. __American Journal of Physics__. 60, 994-1003,
and Printer's erratum to Part I, (1993), ibid. 61, 81.

Shaffer, P.S. & L.C. McDermott (1992). Research as a guide for curriculum
development: An example from introductory electricity, Part II: Design
of instructional strategies. __American Journal of Physics__. 60, 1003-1013.

Section C, *Comments on C2*
from: Connecting Research in Physics Education with
Teacher Education
*An I.C.P.E. Book* ©
International Commission on Physics Education 1997,1998

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