Relativity concept inventory: Development, analysis, and results

We report on a concept inventory for special relativity: the development process, data analysis methods, and results from an introductory relativity class. The Relativity Concept Inventory tests understanding of relativistic concepts. An unusual feature is confidence testing for each question. This can provide additional information; for example, high confidence correlated with incorrect answers suggests a misconception. A novel aspect of our data analysis is the use of Monte Carlo simulations to determine the significance of correlations. This approach is particularly useful for small sample sizes, such as ours. Our results show a gender bias that was not present in course assessment, similar to that reported for the Force Concept Inventory.

Figure 1

RCI results by question for the Physics 2 class: the post-test item difficulties (blue $+$), pre-test item difficulties (black $\times$), and the normalized gain (red ○). The question number ordering is by postinstruction item difficulty. The sample sizes were 63 for the post-test and 70 for the pre-test, with 53 individuals doing both tests. Questions 18, 19, and 21 have no pre-test item difficulties or normalized gains as they were changed between the pre- and post-tests. The normalized gain is calculated for the students who took both the pre-test and the post-test. Hence, the normalized gain cannot be calculated using the plotted pre-test and post-test item difficulties, as they include additional students.

Figure 2

Histogram of the Pearson’s $r$ correlations between all 276 question pairs from the post-test data. The correlations are calculated using Eq. (6), with the $p_{XY}$ derived from the data.