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

The effect of distributed practice on students' conceptual understanding of statistics

In this study the effect of the reduced distribution of study activities on students' conceptual understanding of statistics is investigated in a quasi-experiment. Conceptual understanding depends on coherent and error free knowledge structures. Students need time to construct such knowledge structures. A curriculum reform at our university resulted in statistics courses which were considerably shortened in time, thereby limiting students' possibility to distribute study activities. Independent samples of students from before and after the reform were compared. To gauge conceptual understanding of statistics, students answered open ended questions in which they were asked to explain and relate important statistical concepts. It was shown that the reduction of distributed practice had a negative effect on students' understanding. The finding that condensed courses make it more difficult for students to reach proper understanding of the subject matter is of interest for anyone who is engaged in reforming curricula or designing courses

The effect of guiding questions on students' performance and attitude towards statistics

Background. In this study, the effect of guidance on students performance was investigated. This effect was hypothesized to be manifested through a reduction of cognitive load and enhancement of self-explanations. Aim. The goal of this study was to investigate the effect of guiding questions on students understanding of statistics. Sample and Method. In an experimental setting, two randomly selected groups of students (N= 49) answered achievement and transfer questions on statistics as a measure of performance. Students in the intervention condition were given guiding questions to direct their way of reasoning before they answered the achievement questions. The students in the control condition were asked to write down their way of thinking before they answered the same achievement questions. In this way, both groups were stimulated to self-explain, but only the reasoning processes of the students in the intervention condition were guided. Results and Conclusion. It was found that students in the intervention condition performed significantly better on achievement and transfer questions and that this effect of guidance was mediated by self-explanations. Attitude towards statistics was positively related to performance