Correlation between student collaboration network centrality and academic performance

We compute nodal centrality measures on the collaboration networks of students enrolled in three upper-division physics courses, usually taken sequentially, at the Colorado School of Mines. These are complex networks in which links between students indicate assistance with homework. The courses included in the study are intermediate classical mechanics, introductory quantum mechanics, and intermediate electromagnetism. By correlating these nodal centrality measures with students’ scores on homework and exams, we find four centrality measures that correlate significantly with students’ homework scores in all three courses: in-strength, out-strength, closeness centrality, and harmonic centrality. These correlations suggest that students who not only collaborate often, but also collaborate significantly with many different people tend to achieve higher grades. Centrality measures between simultaneous collaboration networks (analytical versus numerical homework collaboration) composed of the same students also correlate with each other, suggesting that students’ collaboration strategies remain relatively stable when presented with homework assignments targeting different skills. Additionally, we correlate centrality measures between collaboration networks from different courses and find that the four centrality measures with the strongest relationship to students’ homework scores are also the most stable measures across networks involving different courses. Correlations of centrality measures with exam scores were generally smaller than the correlations with homework scores, though this finding varied across courses.

Figure 1

Course information for classical mechanics, quantum mechanics, and electromagnetism. Lines connecting two courses indicate the number of students common to both courses. There were 67 students enrolled in all three courses.

Figure 2

Student collaboration networks for three upper level physics courses. Weighted student collaboration networks constructed from surveys given to students in three upper-division courses: Classical mechanics, quantum mechanics, and electromagnetism. Note that while these networks were generated from the weighted adjacency matrices, for ease of representation, only the direction of links is represented here. Nodes correspond to students and the direction of each arrow indicates the direction of assistance on homework assignments. The color of a node indicates the grade of a student on homework assignments. Although we do not normalize grades in our analysis we present grades as a percentage here to illustrate multiple courses simultaneously.

Figure 3

Correlation of nodal centrality measures with student grades in three upper level physics courses. Correlation of complex network measures with student grades for three courses: classical mechanics, quantum mechanics, and electromagnetism. Filled markers indicate correlation coefficients that are statistically significantly different from a correlation coefficient of 0 (Holm-Bonferroni corrected $p<0.05$). Statistical significance was determined using a bootstrap resampling with 10 000 resamplings of each correlation coefficient.

Figure 4

Correlation of nodal centrality measures from the classical mechanics analytical network with (a) the corresponding nodal centrality measure from the classical mechanics numerical network, and (b) the corresponding nodal centrality measure from the other two courses: quantum mechanics, and electromagnetism. Filled markers indicate correlation coefficients that are statistically significantly different from a correlation coefficient of 0 (Holm-Bonferroni corrected $p<0.05$). Statistical significance was determined using bootstrap resampling with 10 000 resamplings of each correlation coefficient.