Teaching electric circuits with a focus on potential differences

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Developing a solid understanding of simple electric circuits represents a major challenge to most students in middle school. In particular, students tend to reason exclusively with current and resistance when analyzing electric circuits as they view voltage as a property of the electric current and not an independent physical quantity. As a result, they often struggle to understand the important relationship between voltage and current in electric circuits. Following diSessa’s interpretation of learning as the construction and reorganization of previously loosely connected elements of knowledge (“p-prims”) into a coherent mental structure (“coordination class”), a new curriculum was developed that systematically builds on students’ everyday experiences with air pressure (e.g., with air mattresses and bicycle tires). In order to make voltage rather than current the students’ primary concept when analyzing electric circuits, voltage is introduced as an “electric pressure difference” across a resistor that is as much the cause for an electric current as air pressure differences are the cause for air flow. The objective of the curriculum is to provide a structure for students to develop a qualitative understanding of simple dc circuits that allows them to make intuitive inferences about the electric current based on voltage and resistance. With an effect size of $d=0.94$ the new curriculum has proven to be more effective than traditional approaches for teaching electric circuits in a quasi-experimental field study with 790 students from Frankfurt am Main, Germany.

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Figure 1

The example of an inflated bicycle tire is used to illustrate that a pressure difference leads to an air flow using a particle model.

Figure 2

A simple diagram visualizes the qualitative relationship between air pressure difference, resistance, and air flow.

Figure 3

A sample task to help students distinguish between air pressure and air pressure difference.

Figure 4

The initial juxtaposition of the familiar particle model with color coding in an open circuit is intended to facilitate the students’ transition from the idea of air pressure in pipes to electric pressure in wires.

Figure 5

Measuring of electric pressure differences with three-dimensional voltmeters.

Figure 6

Sample task designed to help students identify electric pressure differences in open circuits by using color coding.

Figure 7

A simple diagram visualizes the qualitative relationship between voltage ($V$), resistance ($R$), and current ($I$).

Figure 8

A microscopic model of conductors (top) and resistors (bottom) based on the Drude model.

Figure 9

Sample task to help students develop a qualitative understanding of how the electric current is dependent on electric pressure difference and resistance. The light bulb in circuit C has a higher resistance (illustrated by thicker lines). In this task, students are expected to identify that the flow of current is highest in circuit B, but might be the same in circuits A and C. The arrows only refer to the direction and not the magnitude of the electron flow.

Figure 10

In the case of an ideal battery, the electric pressure difference remains the same when a second light bulb is connected in parallel. Since the second bulb is identical to the first, the current leaving the battery doubles. The arrows refer to the direction of electron flow.

Figure 11

A sample task to help students determine the electric current in a parallel circuit of three light bulbs based on an analysis of electric pressure differences. The objective of the task is to engage agency in students’ thinking while decreasing the activation priority of the guiding p-prim. The arrows refer to the direction of electron flow.

Figure 12

Analysis of a series circuit using a dynamic mental model. Red stands for high electric pressure, blue for low electric pressure and yellow for normal electric pressure. Light blue stands for an electric pressure slightly lower than normal electric pressure. The upper light bulb with thicker lines has twice the resistance compared to the lower one. The arrows refer to the direction of electron flow.

Figure 13

Sample task in which the students use their dynamic model to qualitatively predict the voltage across two unequal light bulbs connected in series based on the change in electric pressure in the various parts of the circuit.

Figure 14

Juxtaposition of the qualitative and quantitative relationship of voltage ($V$), resistance ($R$), and current ($I$).

Figure 15

A sample item from the test instrument illustrating the two-tier structure. The correct answer (a2) and explanation (b2) are printed in bold.

Figure 16

Post-test results of the control group (CG) and experimental group (EG) with 95% confidence intervals. The pretest results were controlled for using hierarchical linear modeling. The statistically highly significant net effect of the treatment (3.88 points) is printed in bold. The highest achievable score in the test is 26 points.

Figure 17

An illustration to help students reflect on their own thinking when analyzing circuits. The incorrect way to analyze circuits is to think of the battery as a device that supplies a constant current and not a constant voltage (top). Instead, students must realize that the battery maintains an electric pressure difference, e.g., across a light bulb, that in turn leads to a current (bottom).