I am analyzing some data on ALEKS for my home institution (ALEKS, an acronym that stands for "Assessment and Learning in Knowledge Spaces", is an online tutoring and assessment program that includes course material in mathematics and many of the sciences). ALEKS has an adaptive assessment program that is used by many institutions of higher learning for placement purposes. I am currently in the process of analyzing the assessment scores from ALEKS for placement into our Calculus 1 class. The way ALEKS was administered was that the students were allowed to take the placement test multiple times and given the chance to improve their background (i.e. remediate) using ALEKS in between test attempts. My data set consists of the ALEKS placement test scores and the total time spent in remediation with ALEKS (for each student).
I am trying to find a ballpark estimate for the expected rate of improvement (in terms of number of new topics learned or % increase in score) a student should see from remediation. I would like to have some benchmark with which to compare the rate of improvement from my data set. In other words, are my students doing better, worse , or about the same as expected using the remediation available via ALEKS?