Since educational studies such as TIMSS (Mullis et al., 2020) or PISA (OECD, 2019) have gained public and scientific attention, one stable finding of those studies is that certain groups of students systematically score lower on the underlying mathematics achievement test. Depending on the cultural context, these so-called social disparities affect students with immigrant status, from less privileged socio-economic backgrounds or – depending on the domain focused – male or female students (ibid.).

 However, in recent years research in the field of education has also focused on social disparities that arise from an unfavorable school composition with aforementioned students. While social disparities in mathematics on the individual level are often explained taking advantage of theoretical models such as the notion of economic, social and cultural capital (Bourdieu, 1983; Coleman, 1988), the effects that are related to a less-privileged or unfavorable student body composition need more complex theoretical models since the school learning environment (including instructional quality) can be regarded as a central mediator for students’ mathematics achievement. Here, the contextual model of Baumert et al. (2006) differentiates five factors that can lead to institutionalized social disparities: Among them is the proportion of students with a low socio-economic status (SES). This factor is considered as indirectly affecting student achievement by institutional characteristics and other school-related process factors (e.g. didactics or instructional organization). In this context the school principal can be regarded as keystone agent for the development and adaption of school process characteristics that support disadvantaged students (Moral et al., 2018).

Additionally, research in education has shown that instructional decisions of teachers are not based on the actual e.g. SES composition but to the extent to which teachers are able to make accurate ratings about the actual SES composition in class. In this context it is not the actual social composition that affects instructional processes but how teachers perceive this characteristic. This competence of teachers is often called diagnostic competence (Leuders, et al., 2018). For the purpose of research towards diagnostic competence in educational environments several dimensions to assess diagnostic competence have been developed (Cronbach, 1955): The rank-component is defined as the ability of teachers to accurately reproduce the social position of individuals in class (in terms of raking them in an accurate manner), the level-component which is defined as the teachers’ ability to estimate the social composition of a class in terms of an average SES level and the differentiation component which is the ability of teachers to accurately perceive the SES dispersion in their class.

While for the teacher level it has been shown that there is a considerable amount of variation in teachers accuracy of classroom characteristics (such as the socio-economic composition), the extent to which principals are able to accurately assess the social student body composition has not yet been focused on by empirical educational research – even though in terms of school leadership principals are theoretically and empirically regarded as a keystone agent for implementing supporting measures for disadvantaged students and therefore for their progress (in the mathematics domain). For this reason, this contribution will answer the following research questions:

1.  To which extent are principals of schools able to accurately rate student composition with regard to the percentage of low-SES students as one exemplary measure of social composition? In which countries is this estimation accurate? In which countries can an over- or underestimation be observed?

2. Is there a relation between principal’s estimation accuracy towards social student body composition and average mathematics achievement of a school?

The most persistent problem while identifying a database that could be used to answer the previous mentioned research questions is that this database – besides an achievement test in mathematics – must contain information about the actual student composition of a school and furthermore an estimate of the principal towards this composition-related characteristic of her or his school. In most international studies in the field of education these information are gathered by a school questionnaire that is answered by principals. In this context the database from PISA 2018 (OECD, 2019) provides a principals estimation of the percentage of students from low-SES backgrounds at the school and – through the assessment of students – a reliable measure of the actual student composition. In order to assess principal’s accuracy ordinal measures cannot be used for the analysis in this paper since they would only allow principals only to check prescribed answer categories such as “0 to15 percent”. In this context the subsequent displayed approach to operationalize principals rating would be affected by uncertainties that arise from a prescribed value range of the single ordinal categories. To assess the accuracy of principals towards the student body composition with students from low-SES backgrounds an approach was incorporated that was used in different studies in the field but was not yet used to evaluate the accuracy of principal’s ratings: the level-component (cf. previous section). Here the difference between the actual percentage of students from the focused student population and the principal’s report on this percentage was generated: The main advantage of this procedure is that an overestimation of the focused student population would yield negative scores for ACCU whilst an underestimation of the focused percentage would yield positive scores. Perfectly accurate estimations are characterized by the score zero in this context. For quantifying the socio-economic status (SES) of the students in this context the highest International Socio-Economic Index of Occupational Status (HISEI; Ganzeboom, De Graaf & Treiman, 1992) is used. Further, in order to evaluate the relation between on the one hand principal’s accuracy towards the proportion of low-SES students at their schools and on the other hand mathematics achievement of their students, linear regression analyses were used that acknowledged for the so called plausible values for mathematics achievement and the complex sampling design of PISA 2018 (cf. OECD, 2017 for further technical details).

Analyses towards research question 1 show that across all participating countries of PISA 2018 principals overestimate the proportion of low-SES students by 13.6 percent. The accuracy of this estimation is subject to variation. While for example in Jordan (M=0.0), Montenegro (M=-0.9), and China (M=-1.6) estimations can be regarded as accurate in only few countries principals underestimate the proportion of low-SES students: Belarus (M=6.8), Bosnia and Herzegovina (M=6.4), Turkey (M=5.8), and Georgia (M=5.2). However, focusing on the participating countries of the EU it can be observed that these belong to the group of countries where principals on average overestimate the proportion of students from low-SES backgrounds. Among these are for example Greece (M=-6.5), Italy (M=-7.0), Slovenia (M=-18.0), Germany (M=-22.7) and France (M=-26.8). In order to evaluate the significance of principals judgment accuracy towards the proportion of students from low-SES background for mathematics achievement (research question 2) in a first step scatterplots were derived from the data to confirm the appropriateness of linear regression that were afterwards empirically confirmed. Surprisingly, principal’s accuracy explains tremendous proportions of variation of mathematics achievement between schools in EU countries: Without controlling for any covariates for example in Germany (R2=.325), Ireland (R2=.323), Luxembourg (R2=.296), Denmark (R2=.283), Belgium (R2=.243), and the United Kingdom (R2=.236) the amount of explained variation exceeds 20 percent. However, the highest proportion of explained variance in mathematics could be observed in the non-EU country USA (R2=.477). From the authors’ perspective the results provide indications that it’s not the actual school composition that affects mathematics learning but the accurate perception of the principal as one keystone agent for implementing process characteristics that are considered to mediate the effect of school composition. Therefore, further discussions about expectations towards schools, to compensate educational inequity by enhancing educational measures, may also need to reflect this psychological component.

Baumert, J., Stanat, P. & Watermann, R. (2006). Schulstruktur und die Entstehung differentieller Lern- und Entwicklungsmilieus. In P. Stanat, R. Watermann & J. Baumert (Eds.), Herkunftsbedingte Disparitäten im Bildungswesen: Differenzielle Bildungsprozesse und Probleme der Verteilungsgerechtigkeit (S. 95–188). Wiesbaden: VS Verlag. Bourdieu, P. (1983). Ökonomisches Kapital, kulturelles Kapital, soziales Kapital. In R. Kreckel (Hrsg.), Soziale Ungleichheiten (S. 183–198). Göttingen: Schwartz. Coleman, J. S. (1988). Social capital in the creation of human capital. American Journal of Sociology, 94, 95–120. Cronbach, L. J. (1955). Processes affecting scores on “understanding of others” and “assumed similarity.” Psychological Bulletin, 52, 177–193. Ganzeboom, H. B. G., De Graaf, P. M. & Treiman, D. J. (1992). A standard international socio-economic index of occupational status. Social Science Research, 21(1), 1–56. Leuders, T., Dörfler, T., Leuders, J., & Phillip, K., (2018). Diagnostic Competence of Mathematics Teachers: Unpacking a Complex Construct. In T. Leuders, K. Phillip & J. Leuders (Eds.), Diagnostic Competence of Mathematics Teachers (S. 3-31). Cham: Springer. Moral, C., Martin-Romera, A., Matrinez-Valdivia & Olma-Extremera (2018). Successful secondary school principalship in disadvantaged contexts from a leadership for learning perspective. School Leadership & Management, 38(1), 32–52. Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. Chestnut Hill, MA: TIMSS & PIRLS International Study Center. OECD (2017). PISA 2015 Technical Report. Paris: OECD Publishing. OECD (2019). PISA 2018 Results (Volume I): What Students Know and Can Do. Paris: OECD Publishing.