Assessing Knowledge Structures in a Constructive Statistical Learning Environment

In this report, the method of free recall is put forward as a tool to evaluate a prototypical statistical learning environment. A number of students from the faculty of Health Sciences, Maastricht University, the Netherlands, were required to write down whatever they could remember of a statistics course in which they had participated. By means of examining the free recall protocols of the participants, insight can be obtained into the mental representations they had formed with respect to three statistical concepts. Quantitative as well as qualitative analyses of the free recall protocols showed that the effect of the constructive learning environment was not in line with the expectations. Despite small-group discussions on the statistical concepts, students appeared to have disappointingly low levels of conceptual understanding

Approximations of Normal IRT Models for Change

Keywords: closed form estimators, IRT, longitudinal In this paper, the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an accaptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased

A stochastic growth model applied to repeated tests of academic knowledge

Rasch model, growth curves, regression, itembanking,