Comparing conceptual understanding across institutions with module analysis

The Force Concept Inventory (FCI) is a popular multiple-choice instrument used to measure a student’s conceptual understanding of Newtonian mechanics. Recently, a network analytic technique called module analysis has been used to identify responses to the FCI and other conceptual instruments that are preferentially selected together by students; these groups of responses are called communities. This study uses module analysis to explore the misconception structure of the FCI at five U.S. institutions with varying undergraduate populations (sample sizes of $N=9606$, 4360, 1496, 466, and 213). Students from these universities had a broad range of prior knowledge in physics and of general high school academic preparation, resulting in large differences in FCI normalized gain, pretest, and post-test scores. In the current work, modified module analysis partial was applied and communities of consistently selected responses within the FCI were identified at the five institutions studied. There was substantial similarity between the communities identified postinstruction; somewhat less similarity preinstruction. This suggests that consistently applied Newtonian misconceptions exist both before and after instruction at a wide range of institutions. The most frequently applied misconceptions were “largest force determines motion,” Newton’s third law misconceptions, and “motion implies active forces.” These misconceptions were still consistently applied even after instruction by a substantial number of students at all but the highest performing of the five institutions.

Figure 1

Pretest networks. Communities are shaded consistently with the post-test networks to allow comparison. Shaded communities not found in at least three of the four largest pretest samples are outlined in red. Correct responses are marked with an asterisk. The size of the partial correlation between the responses is proportional to the edge width.

Figure 2

Post-test networks. Communities found in three of the four largest samples are shaded with the same color. Correct responses are marked with an asterisk. The size of the partial correlation between the responses is proportional to the edge width.

Figure 3

The correlation threshold $r$ for the sample 1 post-test network. Each point represents a network calculated at the labeled $r$ value.

Figure 4

Coverage actors, edges, and triangles between samples.