Recent research literature on educational achievement in primary schools indicates that many factors can be regarded as a fostering or hindering for achievement growth. For example scholars tend to agree that living in a home that is culturally (cf. Bourdieu, 1986) or socially privileged (Coleman, 1988) can be regarded as fostering factor and students with a privileged cultural or social background are more likely to show high achievement in many domains compared to their peers from less privileged families (Mullis, Martin, Foy, & Arora, 2012). In this context individual characteristics of students have proven to have significant if not substantial effects on student’s achievement growth. Hence, many researchers were able to show that migratory status (Georges & Pallas, 2010), cultural capital (Petty, Harbaugh, & Wang, 2013), socio-economic status (SES; Luyten, Schildkamp, & Folmer, 2009) and aptitude (Sasanguie, Van den Busche, & Reynvoet, 2012) are relevant predictors for achievement growth in primary education.

In light of the history of such-like consistent and stable findings of research on mathematics education, theoretical improvements were established: For example, models conceptualizing knowledge growth and their underlying factors on multiple layers of the educational system have been refined and centrally focus on individual characteristics of primary school students. For example the dynamic model of educational effectiveness (cf. Creemers & Kyriakides, 2008) comprises individual characteristics as well as factors on the teacher, school and context level assuming that all of the determinants have a relevant if not substantial effect on various outcomes of school education such as cognitive, affective and psychomotor skills and abilities. Additionally, literature indicates that there are also compositional effects of classes and schools to take into account when mathematics education is under research (Schofield, 2010). Although there are many cross-sectional investigations of compositional effects in the field, longitudinal studies investigating the effect of individual, family-related background characteristics and compositional variables are scarce, especially in the European context. Therefore, acknowledging the concept of the aforementioned theoretical model, individual and compositional effects are focused in this contribution using the data set of the study ADDITION-study (Creemers et al., 2013) which has been conducted in six European countries.

The present paper focuses on the relevance of individual and compositional characteristics and knowledge growth in mathematics in primary education. In detail, the following research questions are addressed in this paper considering the German subsample of primary school students:

1. How can the growth in mathematical competencies be explained by central individual background characteristics (gender, migratory status, cultural capital and practice, SES) and previous mathematical competencies?
2. Taking into account school-related measures of the student body composition, how can the relative relevance of those factors be determined?

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