The aim of the study is to investigate the measurement invariance of mathematics self-concept and self-efficacy across 40 countries that participated in the Programme for International Student Assessment (PISA) 2003 and 2012 cycles. The sample of the study consists of 271,760 students in PISA 2003 and 333,804 students in PISA 2012. Firstly, the traditional measurement invariance testing was applied in the multiple-group confirmatory factor analysis (MGCFA). Then, the alignment analyses were performed, allowing non-invariance to a minimum to estimate all of the parameters. Results from MGCFA indicate that mathematics self-concept and self-efficacy hold metric invariance across the 80 groups (cycle by country). The alignment method results suggest that a large proportion of non-invariance exists in both mathematics self-concept and self-efficacy factors, and the factor means cannot be compared across all participating countries. Results of the Monte Carlo simulation show that the alignment results are trustworthy. Implications and limitations are discussed, and some recommendations for future research are proposed.

Background The current study investigates school contextual effects on students’ academic self-concept and achievement, that is, peer socioeconomic effect and big-fish-little-pond effect (BFLPE), in four Nordic education systems (i.e., Denmark, Finland, Norway and Sweden) and selected Chinese education systems (Hong Kong and Beijing-Shanghai-Jiangsu-Zhejiang). The two school contextual effects are studied simultaneously to negate the confounding effects of student and school socioeconomic status (SES), academic self-concept and academic achievement. The study focuses on the following research questions: Are there differences in the between-school variation in school SES composition, academic self-concept and reading literacy across the Nordic and selected Chinese education systems? What are the sizes of peer SES and BFLPE in the Nordic and Chinese education systems? Are there any differences that can be observed between the 2000 and 2018 data for the Programme for International Student Assessment (PISA) in the first two questions for Denmark, Finland, Norway and Sweden and Hong Kong? Methods Using PISA 2000 and 2018 data from Denmark, Finland, Norway, Sweden, Hong Kong and Beijing-Shanghai-Jiangsu-Zhejiang (in 2018 only), a multiple-group two-level structural equation modelling was applied to estimate the school contextual effect. Results The current study indicated that school academic and socioeconomic segregation intensified over the two decades in most of the studied countries. This finding lays the groundwork for understanding the two schools’ contextual effects. School SES compositions positively affected students’ academic achievement, while average school achievement negatively affected students’ academic self-concept. Given that students’ academic and socioeconomic composition has become more homogeneous within schools, the contextual effects were more pronounced. However, variations across diverse education systems were also notable. Conclusions The current study adds evidence of the school contextual effects regarding the peer SES effects and robustness of the BFLPE, considering the nested structure of the data and diverse cultural milieu. We argue that these diversities reflect the varying extent to which educational reforms were introduced in different countries, here as oriented to marketisation, privatisation and choice. These reform actions have changed the composition of students at schools and school culture, which moulds individual students’ cognitive and noncognitive development.