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.

Research related to the “teacher characteristics” dimension of teacher quality has proven inconclusive and weakly related to student success, and addressing the teaching contexts may be crucial for furthering this line of inquiry. International large-scale assessments are well positioned to undertake such questions due to their systematic sampling of students, schools, and education systems. However, researchers are frequently prohibited from answering such questions due to measurement invariance related issues. This study uses the traditional multiple group confirmatory factor analysis (MGCFA) and an alignment optimization method to examine measurement invariance in several constructs from the teacher questionnaires in the Trends in International Mathematics and Science Study (TIMSS) 2015 across 46 education systems. Constructs included mathematics teacher’s Job satisfaction, School emphasis on academic success, School condition and resources, Safe and orderly school, and teacher’s Self-efficacy. The MGCFA results show that just three constructs achieve invariance at the metric level. However, an alignment optimization method is applied, and results show that all five constructs fall within the threshold of acceptable measurement non-invariance. This study therefore presents an argument that they can be validly compared across education systems, and a subsequent comparison of latent factor means compares differences across the groups. Future research may utilize the estimated factor means from the aligned models in order to further investigate the role of teacher characteristics and contexts in student outcomes.