In the ASSISTments' Skill Builder assignment, mastery is defined as accurately answering three consecutive problems.
While ASSISTments recently added the capability for students to earn partial credit while working through these types of problems, mastery can only be achieved by solving the consecutive problems accurately on the first attempt.
These remaining problems were not considered part of the experimental manipulation and followed a traditional Skill Builder format requiring students to accurately answer three consecutive problems to reach mastery.
To predict students' knowledge levels, we generated regression models from subsets of consecutive problems in a training session in order to understand after how many problems the prediction of students' knowledge level is best.
Instead of solving the equation in a single solution step we decompose the problem into two consecutive problems based on an asymptotic analysis of the physical problem where each problem is asymptotically independent of the ratio of coefficients ε="β−/β+.
While this may be a deterrent to hint usage, the idea of penalizing assistance may actually speak to self-regulated learning in a mastery-learning environment, as students requesting and learning from feedback early on may be more likely to accurately solve the next three consecutive problems.
