Three mixed-effects regression models using an extended Weibull with applications on games in differential and integral calculus

Abstract

Three new mixed-effects regressions models using an extended Weibull distribution are defined for repeated measures, and their parameters are estimated by maximum likelihood. Monte Carlo simulations report the accuracy of the maximum likelihood estimators and the distribution of the quantile residuals in these regressions. The usefulness of the proposed regressions is illustrated in differential and integral class from the Exact Sciences Department at the University of São Paulo (Brazil) with the objective of showing a pedagogical alternative of learning diagnostic methodology as a game approach. The results indicate that the questions correctly answered by the students took less time to be solved than those incorrectly answered. In addition, the algebraic application and multiple representation questions has the lowest percentages of correct answers and, in general, the longest time to be solved. So, it is possible to note that the used game approach enables the identification of possible difficult points in a class and provides the teacher with the opportunity of search for different strategies to reduce these difficulties faced by differential and integral calculus students when entering higher education, which often result from basic education.