•Do the school-factors teaching quality, climate, and SES influence the within-school slope of achievement on student SES?•Data from TIMSS 2011 Grade 8 for 50 educational systems was analysed with two-level random slopes models.•School SES was the strongest determinant of within-school slope differences for many educational systems.•When school SES relates negatively to within-school slope the system is compensatory with respect to student SES. The main aim of the study was to identify school characteristics that can reduce the relation between socio-economic status (SES) and achievement, so that equity of educational outcomes can be improved. Data from 50 countries participating in the Trends in International Mathematics and Science Study (TIMSS) conducted in 2011, focusing on Grade 8 mathematics, was analysed. Two-level random slopes models fitted at school- and student-levels were used to investigate the influence of quality and quantity of instruction, school climate, and school SES on the within-school regression slope for achievement on SES. The results showed school SES to be the strongest determinant of slope differences across schools and educational systems. Whether school SES relates negatively or positively to the within-school regression of achievement on student SES is an indicator of whether the educational system is compensatory or anti-compensatory with respect to student SES.