Fig 1.
Interface for assignments und their execution in Bettermarks.
(1) Teachers and students can select from a library with over 100 different books. Each book contains an introduction as well as different mathematical problem sets. (2) A problem set contains several individual problems. (3) When students compute a problem and submit an answer, they receive immediate feedback on whether their answer is right or wrong. Students have two attempts on each problem. (4) Students may request up to one hint when computing a problem.
Fig 2.
Hypothetical regression analysis of relative performance.
Students’ relative error rate in 2020 (ordinate) is regressed against their relative error rate in 2019 (abscissa). Three different hypothetical outcomes are illustrated in red, black and green (see legend and text).
Fig 3.
Estimates of absolute error rate, relative error rate and problem set difficulty as a function of time.
Results from the Analyses 1a-c are depicted. Error rates and relative error rates significantly decreases during the shutdown compared to the same time in the previous year. There was no significant difference in problem set difficulty between the two time windows. Points indicate mean estimates, error bars indicate the standard errors of the mean across students. Connected lines denote that both time windows include results from the same students.
Fig 4.
Relative error rate in 2020 as a function of relative error rate in 2019.
Each data point corresponds to a student, showing their average relative error rate in 2019 (abscissa) and 2020 (ordinate). The green line corresponds to a linear regression fitted to the data. Grey shades indicate the standard error of the mean across students. The black line depicts the identify function (intercept of 0 with a slope of 1) for reference. The intercept of the regression (green) is below zero, indicating that the relative error rate of students decreased from 2019 to 2020. The slope of the regression is below 1, indicating that students categorized as low-performing in 2019 showed greater decrements in relative error rate than students categorized as high-performing (cf. Fig 2), suggesting a narrowing performance gap between students.