This contribution addresses the developments towards an inclusive education for all from the perspective of School Effectiveness Research (SER) and asks the question of whether or not there are effects of the school body composition towards students with certain characteristics that showed to be confounded with substantial educational disparities (such as gender, migratory background, low cultural capital and low socio-economic status). In doing so, this paper focuses on the mathematics achievement of primary school students from the Trends in International Mathematics and Science Study (TIMSS 2015, cf. Mullis, Martin, Foy, & Hooper, 2016).    

In the discussion about schools' contribution to educational achievement, scholars mainly focus on student characteristics such as students’ individual and/or family characteristics. In this context scholars investigating the impact of individual factors on mathematics proficiency in primary education conclude that migratory status (Petty, Harbaugh, & Wang, 2013), cultural capital, and socio-economic status (Shin et al., 2013) are relevant predictors for progress in mathematics. In contrast, recent approaches to modelling educational effectiveness in mathematics education in primary schools also include compositional characteristics of the school body (cf. Andersson & Malmberg, 2015) which also seem to play a role in the acquisition of mathematics achievement (Schofield, 2010). Having in mind the ongoing developments towards inclusive education in Europe, educational inclusion has the potential of changing the achievement-related and social composition of school classes and/or whole schools. In the light of these results and developments, the research presented examines the effects of school compositional variables in primary mathematics education utilizing the newest database of TIMSS and the multivariate analytical method of Hierarchical Linear Modelling (HLM, cf. Raudenbush & Bryk, 2002).

From a theoretical perspective, the composition of school classes and whole schools is not prominently accounted for in several models of educational effectiveness. For example the Dynamic Model of Educational Effectiveness (DMoEE; cf. Creemers & Kyriakides, 2008) – which can be regarded as a generic model of educational effectiveness that claims to be valid in various cognitive, non-cognitive, and psychomotor domains – does not explicitly take school or class composition into account. Therefore, models acknowledging school or class composition stem from an earlier phase of SER – for example the Integrated Model of Educational Effectiveness by Scheerens (1990). Taking into account ongoing developments towards an inclusive education for all, the question of the existence of school-specific compositional effects with regards to students’ mathematics performance is worth to be addressed.

While there is some evidence that compositional effects can affect school classes, the existence of school-compositional effects in the mathematics domain in primary education is less clear. Therefore the present paper focuses on the relevance of compositional effects on the school level, individual characteristics of students and their families, and achievement in mathematics in primary education. In detail, the following research questions are addressed within this contribution:

1. In the context of the current European inclusion debate: Is the mathematics achievement in primary schools affected by social- and achievement-related compositional effects?
2. If so, which compositional effects (achievement-related vs. social composition) are more relevant to students when individual characteristics are statistically controlled for (gender, migratory background, amount of books, SES, etc.)?
3. Do country-specific differences in the relevance of school compositional variables emerge between the European countries Belgium (Flemish), Denmark, and Germany?

The research presented in this paper is carried out as secondary analysis of data from IEA-TIMSS 2015. The study revealed – among other cycles of the TIMS study – that mathematics achievement in primary education is substantially confounded with students’ background characteristics such as gender, the amount of cultural capital, the family’s socio-economic (SES) or immigrant status (Wendt, Schwippert, & Stubbe, 2016). Using the German, the Danish and the Flemish subsample of the TIMS study, aforementioned research questions are addressed for the European context. Using hierarchical linear modelling (HLM) techniques and the representative multi-stratified cross-sectional sample of the TIMSS-2015-study (Martin, Mullis, Foy, & Hooper, 2016) the relations between student background variables, achievement-related and social-related compositional characteristics of schools and the mathematics proficiency of 4th-graders are explored comprising representative student samples from three European countries (Germany: N = 3.948, Denmark: N = 3.710 and Belgium [Flemish] N = 5.504) and a 3-step analytical approach that will be described in the following paragraphs. In a first step, a so called Nullmodel (One-Way ANOVA with Random Effects) without any predictors was specified in order to determine the proportion of variation that can be attributed to and explained by characteristics on the individual and the school level. In step 2 those social- and achievement-related compositional measures of schools that were generated by aggregating students’ background characteristics and mathematics test scores on school level were included in the model without covariates on the individual level. Here two different overarching categories of measures have to be differentiated: On the one hand achievement-related measures of the student composition refer to the school absolute level of mathematics proficiency (average of student test scores) and the heterogeneity of student test scores (school-specific standard deviation). On the other hand measures of the social student composition were generated by determining the proportion of boys (gender), the proportion of students with a low amount of cultural capital, and the proportion of students with a low SES. In a final third step, those characteristics of school and those of the students are modelled together in order to determine whether compositional measures are able to explain variation in mathematics proficiency beyond individual characteristics. All analyses in this contribution were calculated with the statistical modelling software MPlus 7.0 (Muthén & Muthén, 2012) taking into account weighting, the plausible values approach (type = imputation) and the clustered sampling approach (type = twolevel complex).

Overall, the results indicate that compositional variables are relevant in all countries under research. First analyses regarding the relevance of school characteristics (research question 1) show that in Belgium (Flemish) slightly more variation in mathematics achievement can be explained by school characteristics (ρMaths=.237) compared to the other educational systems (Denmark: ρMaths=.203 vs. Germany: ρMaths=.159). Taking into account measures of the student body composition (research question 1), it can be observed, that the average school mathematics performance shows a strong coherence with mathematics competencies in all countries. The effects of the social student body composition (proportion of boys, of students with a low amount of cultural capital, and of students with a low SES) – in contrast – vary among the countries under research. When compositional variables of schools and individual characteristics of students are modelled together (research question 2) in order to determine whether or not the school body has an additional effect beyond individual characteristics, the result emerges that individual characteristics remain of high relevance but also compositional effects can be observed. However, the latter varies from country to country (research question 3). For instance in Germany the achievement heterogeneity, shows a significant (positive) effect on mathematics test scores while these effects cannot be observed in Belgium (Flemish) or Denmark. On the other hand Belgium (Flemish) is the only country where the proportion of boys is negatively related to mathematics performance – independently of controlling for individual characteristics or not. In total, analyses in this contribution stress the relevance of individual characteristics but also indicate that contextual effects in terms of achievement-related and social student body composition are not negligible and will therefore be discussed with regard to the recent educational inclusion debate in Europe. Additionally methodological limitations and challenges are discussed.

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