Benefits of completing homework for students with different aptitudes in an introductory electricity and magnetism course

We examine how student aptitudes impact how much students learn from doing graded online and written homework in an introductory electricity and magnetism course. Our analysis examines the correlation between successful homework completion rates and exam performance as well as how changes in homework completion correlate with changes in exam scores for students with different physics aptitudes. On average, successfully completing many homework problems correlated to better exam scores only for students with high physics aptitude. On the other hand, all other students showed zero or even a negative correlation between successful homework completion and exam performance. Low- and medium-aptitude students who did more homework did no better and sometimes scored lower on exams than their low- and medium-aptitude peers who did less homework. Our work also shows that long-term changes in homework completion correlated to long-term changes in exam scores only for students with high physics aptitude, but not for students with medium or low aptitude. We offer several explanations for the disparity in homework learning gains, including cognitive load theory, ineffective homework strategies, and various mismatches between homework and exams. Several solutions are proposed to address these possible deficiencies in graded online and written homework.

Figure 1

The weighted-average score on all exams vs homework completion score for students in different aptitude groups who took the USAFA E&M course in fall 2010 (left plots) and spring 2011 (right plots). Line fits are included with the data. The semesters shown here are representative of the correlations of the other 7 semesters studied.

Figure 2

Average of the slopes of the line fits between successful homework completion and exam score for four different aptitude groups. The data are from 7 semesters of E&M when homework was administered online and graded only for correctness. Error bars are the standard deviations of the slopes for the 7 different semesters.

Figure 3

Average of the slopes of written homework scores vs total exam score plots as a function of student aptitude for four semesters when homework problems were administered in a graded, written format. Error bars are the standard deviations of the slopes for the 4 different semesters where written homework was used.

Figure 4

Plots of the change in the total exam score vs the change in homework score for students moving from spring 2009 mechanics to fall 2009 E&M. Each plot shows students in different aptitude groups. Line fits are included with the data. These results shown here are typical of all the semesters we examined.

Figure 5

The average correlation between the change in HW score vs change in total exam score from mechanics to E&M as a function of student aptitude for 5 semesters of E&M being studied. Error bars are the standard deviations of the slopes for the different semesters.

Figure 6

Average slopes of line fit data of change in homework score vs change in exam score (left) from midterm 1 to midterm 2, and (right) from midterms 1 and 2 to midterm 3. Only 6 of the 7 semesters being studied are included in this analysis, with spring 2009 left out because there were only 2 midterms during that semester.