Development of a two-tier instrument on simple electric circuits

This article reports the development of a two-tier simple electric circuits test (2T-SEC Test). Simple electric circuits are introduced to students early in their school years and are an important part of the physics curriculum all the way to the university level. However, many students do not develop an adequate conceptual understanding of simple electric circuits and especially of electrical voltage. For this reason, six physics education research groups from Germany and Austria started a large study to evaluate and improve middle-school students’ conceptual understanding of simple electric circuits. As a first step, we developed the test instrument presented in this article. First, nine semistructured interviews were conducted with middle-school students in Austria. The interviews were transcribed, analyzed and (common) student difficulties with simple electric circuits were identified. Second, based on the results from the interviews and previous research on this topic, an instrument consisting of 25 two-tier multiple-choice items was developed and administered to $N=1568$ middle-school students in Austria and Germany. Third, the data were evaluated using Rasch analysis. The item reliability of the test was 0.99, while the person reliability of paired scoring was 0.62 and the reliability of separate scoring was 0.75. The average difficulties of the main concepts regarding simple electric circuits (open and closed circuits, electric current, resistance, series and parallel circuits, and electrical voltage) were calculated and compared. The analysis suggests that the concept of voltage is most difficult for students while distinguishing between open and closed circuits is the easiest.

Figure 1

Example of an item on electric voltage.

Figure 2

Question 4.

Figure 3

Question 3A.

Figure 4

Question 1C.

Figure 5

Question 11A.

Figure 6

Question 2A.

Figure 7

Representation of Item 1 in test booklets.

Figure 8

(a) Bubble-chart for MNSQ Infit values for paired scoring. (b) Bubble-chart for MNSQ Infit values for separate scoring.

Figure 9

Wright map for paired (left) and separate scoring (right). $M$ denotes the mean of each distribution.

Figure 10

Cross-plot of persons measures when the test was scored with a separate and paired model. The black lines in the plot represent 95% confidence intervals.

Figure 11

Average difficulties of different key concepts of electric circuits based on the calculation of the average item difficulty of the items corresponding to each concept. The error bars indicate the combined uncertainties of each average value computed as $\mathrm{CE}=\frac{1}{4}\sqrt{{\mathrm{SEM}}^2+{\mathrm{SE}}^2}$, where SEM is the standard error of the mean and SE is the average Rasch standard error.

Figure 12

Wright map for basic items.