Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change.

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students' strategies were classified into four categories.

How to Measure and Explain Achievement Change in Large-Scale Assessments: A Rejoinder.

In this rejoinder, we discuss substantive and methodological validity issues of large-scale assessments of trends in student achievement, commenting on the discussion paper by Van den Heuvel-Panhuizen, Robitzsch, Treffers, and Köller (2009). We focus on methodological challenges in deciding what to measure, how to measure it, and how to foster stability. Next, we discuss what to do with trends that are found.

Testing and modelling non-normality within the one-factor model.

Maximum likelihood estimation in the one-factor model is based on the assumption of multivariate normality for the observed data. This general distributional assumption implies three specific assumptions for the parameters in the one-factor model: the common factor has a normal distribution; the residuals are homoscedastic; and the factor loadings do not vary across the common factor scale. When any of these assumptions is violated, non-normality arises in the observed data.

Loss of Information in Estimating Item Parameters in Incomplete Designs.

In this paper, the efficiency of conditional maximum likelihood (CML) and marginal maximum likelihood (MML) estimation of the item parameters of the Rasch model in incomplete designs is investigated. The use of the concept of F-information (Eggen, 2000) is generalized to incomplete testing designs. The scaled determinant of the F-information matrix is used as a scalar measure of information contained in a set of item parameters.

Estimation of the MIRID: a program and a SAS-based approach.

The MIRID CML program is a program for the estimation of the parameter values of two different componential IRT models: the Rasch-MIRID and the OPLM-MIRID (Butter, 1994; Butter, De Boeck, & Verhelst, 1998). To estimate the parameters of both models, the program uses a CML approach. The model parameters can also be estimated with a MML approach that can be implemented in PROC NLMIXED of SAS Version 8.