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The evaluation of learning in mathematics is a worldwide problem, therefore, new methods are required to assess the understanding of mathematical concepts. In this paper, we propose to use the Item Response Theory to analyze the understanding level of undergraduate students about the real function mathematical concept. The Bayesian approach was used to make inferences about the parameters of interest. We designed a test containing twelve items, to which a reliability analysis and validation test were applied. The experiment consisted in administer our test to 48 undergraduate students (18-20 years old) who are in a math career. We concluded that 25% of the students reached a high level of understanding, 39.6% a medium level of understanding and, 35.4% a low level of understanding. Furthermore, that students obtained low levels of understanding for tasks with high cognitive demand, and they obtained high levels of understanding for tasks with low cognitive demand.

We consider a robust Bayesian approach to the analysis of item response models, using the inverse of an asymmetric exponential power cumulative distribution function as a link function. This provides greater flexibility with respect to classic link functions such as the probit and the logit. We conduct a simulation study to evaluate the performance of our model. In order to draw samples from the posterior distribution of the parameters, we implement a Markov chain Monte Carlo scheme by means of the JAGS software. We also implement a posterior predictive model-checking method to assess the fit and relative performance of the various submodels. Finally, we provide a real-data example to illustrate the modeling approach proposed. [ABSTRACT FROM AUTHOR]

In this work, a simulation study is conducted to evaluate the performance of Bayesian estimators for the log–linear exponential regression model under different levels of censoring and degrees of collinearity for two covariates. The diffuse normal, independent Student-t and multivariate Student-t distributions are considered as prior distributions and to draw from the posterior distributions, the Metropolis algorithm is implemented. Also, the results are compared with the maximum likelihood estimators in terms of the mean squared error, coverages and length of the credibility and confidence intervals. [ABSTRACT FROM PUBLISHER]