Focusing on determinants of mathematics and science achievement in primary education in Europe, many factors are considered to foster or hinder achievement. For example there is almost consent among educational researchers that living in a supportive and culturally (cf. Bourdieu, 1986) or socially privileged environment (Coleman, 1988) is a contributing factor for mathematics and science achievement in primary education (Mullis, Martin, Foy, & Arora, 2012). In the light of the history of those consistent and stable findings of school effectiveness research (SER) in Europe, models conceptualizing knowledge growth and factors on multiple layers of the educational system have been developed and centrally focus individual characteristics of primary school students (Creemers, Kyriakides, & Sammons, 2010): for example the comprehensive or the dynamic model of educational effectiveness (cf. Creemers & Kyriakides, 2008). The latter comprises individual characteristics as well as factors on 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 psychomotoric skills and abilities. Therefore the so called dynamic model is regarded as a generic model of school effectiveness and is therefore used as the conceptual framework in this paper.

Many scholars investigating the impact of individual factors on educational achievement use longitudinal measurements and conclude 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 of mathematical and scientific knowledge growth in primary education. Regarding the gender of students, recent publications indicate that the growth of mathematical competencies does not differ between girls and boys and that gender-related differences in mathematics achievement decreased in the past decades (Hanna, 2000).

Although there are many longitudinal European and international investigations in the field, in Germany, however, longitudinal studies investigating the effect of individual and family background characteristics are scarce. This is because the general strategy of educational policy is to conduct cross-sectional studies to assess school effectiveness, quality and change in the German school system at a specific period of time. Furthermore, due to the federalist organization of education in Germany and its federal countries, existing longitudinal studies refer to limited regional areas and  subpopulations.

In the light of this, more comprehensive understandings of the longitudinal growth of mathematic and scientific competencies in the German educational system are needed in order to provide educational stakeholders with information that can be utilized for both quality improvement and assurance. Therefore the present paper focusses on the relevance of individual and family-related characteristics and knowledge growth in mathematics and science in primary education. In detail the following research questions are addressed with this paper:

1. How can the growth in mathematical and scientific competencies be described along central individual background characteristics (gender, migratory status, cultural capital and practice, SES) and previous mathematical and scientific competencies?
2. Which determinants at the individual level contribute to the mathematical and scientific competencies at the end of primary education and how can they be evaluated according to their relative relevance?

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