The paper focuses on the relationship between cognitive abilities and students’ achievement in reading, mathematics and science at the end of primary school. The joint assessment of the Progress in International Reading Literacy Study (PIRLS) and the Trends in International Mathematics and Science Study (TIMSS) in a common representative sample in 2011 provides a unique dataset which allows discovering common patterns across the achievement domains reading literacy, mathematics and science (Martin & Mullis, 2013). The study at hand presents analyses of the German PIRLS/TIMSS 2011 sample. 3,928 learners from 197 schools participated in all three assessment domains (Bos, Tarelli, et al., 2012; Bos, Wendt, et al., 2012).  In Germany, a national extension of the instruments allows to analyze data of two subscales (figural and verbal) of a cognitive ability test (KFT: Heller & Perleth, 2000).

The distinguished concepts that build the theoretical basis of this work are cognitive abilities and subject specific competencies: especially, the definition of competencies by Weinert (1999, 2001), which can be considered an overarching framework for research on competency concepts in international comparisons of student achievement, and a comparison of the characteristics of the concepts of competence and intelligence (Hartig & Klieme, 2006). The core of the presented work discusses the confounding of the concepts of competence and intelligence in educational measurement. Referring to Rindermann and other researchers, who doubt that large-scale student assessment studies measure nothing else but intelligence, Baumert et al. (2007, 2009) analysed to what extent student assessment studies measure more than a single general cognitive ability. The authors report a comparison of g-factor and nested factor models by Brunner (2005, 2008) using data of 9^th grade students in the German national extension of PISA. The authors’ interpretation of these model comparisons is that intelligence (g) influences the performance on all tasks; moreover, there are domain-specific abilities with an impact on the achievement test results.

For students at the end of primary school only research on the relationships between the achievement in reading, mathematics and science exists (Martin & Mullis, 2013; Bos, Tarelli, et al., 2012; Bos, Wendt, et al., 2012). However, research on the relationship of subject specific test results of large-scale assessments and cognitive ability tests at the end of primary school in Germany is not yet provided.

The work focuses on the following research questions:

1)      How can the relationship between the results of the administered figural and verbal cognitive ability tests and achievement in reading, mathematics and science at the end of primary school be described using latent correlations?

2)      Does a one-dimensional (single general ability), a four-dimensional (reading literacy, mathematics, science, cognitive abilities) or a ten-dimensional (reading: literacy, informational; mathematics: number, geometric shapes and measures, data display; cognitive abilities: figural, verbal) model fit the data best?

3)      To what extent can the variance of achievement in the different competence domains be explained by the measured cognitive abilities? How high is the residual variance?

Is it possible to identify and categorize items that both fit well in a general one-dimensional model and do not fit well in a subject-specific multidimensional model and vice versa?

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