Three mixed-e(cid:11)ects regressions models using an extended Weibull with applications on games in di(cid:11)erential and integral calculus

Three new mixed-e(cid:11)ects regressions models using an extended Weibull distribution are de-(cid:12)ned 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 di(cid:11)erential and integral class from the Exact Sciences Department at the University of S~ao 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 identi(cid:12)cation of possible di(cid:14)cult points in a class and provides the teacher with the opportunity of search for di(cid:11)erent strategies to reduce these di(cid:14)culties faced by di(cid:11)erential and integral calculus students when entering higher education, which often result from basic education. We present data analysis for four mixed-e(cid:11)ects regressions models. We compare the performance of the mixed-e(cid:11)ects NWW, BW, KW, Weibull and Normal regressions models to analyze the response time (in seconds) for solving problems in di(cid:11)erential and integral calculus utilizing the Kahoot platform (Kahoot! ) available at the link: https://kahoot.it/ . Kahoot! enables the creation of various types of games, so it can be used as a methodological tool. We devise a mathematical game using Kahoot! in the form of a quiz as part of the calculus curriculum in the (cid:12)rst semester of 2021 for students majoring in Agronomic Engineering and Forest Engineering at the University of S~ao Paulo (campus located in Piracicaba city). The sample consists of 32 students of both major programs, who are assigned to answer six questions related to the subjects: functions, limits and derivatives. The maximum time to solve each problem is 90 seconds. The questions have multiple-choice answers and are focused on exploring the concepts, algebraic techniques and multiple representations (diagrams or graphics) of the di(cid:11)erential and integral calculus, which are combined according to the contents covered. This ludic activity is applied at two moments during the semester, the (cid:12)rst on May 10, 2021, containing questions only on types of functions, and the second on July 20, 2021, on limits and derivatives of functions. At the end of each of these two quizzes, it is possible to create a report of the ingenuity of each student regarding each question. And knowing the gender of each student, it is identi(cid:12)ed the in(cid:13)uence of the covariables, type of question, and right/wrong answers to the questions and the time spent by each student to answer the questions. are: