Longitudinal research in educational inequality aims to understand how earlier achievement and social background shape subsequent learning trajectories. While prior achievement is a strong predictor of later performance, theoretical perspectives diverge on whether it leads to cumulative advantage—where high-achieving students experience greater gains—or compensatory patterns, where lower-achieving students show relatively stronger growth. Empirical evidence from large-scale studies has often challenged strong cumulative advantage assumptions, instead pointing to modest or absent Matthew effects in reading and mathematics. These patterns are frequently attributed to regression-to-the-mean dynamics, instructional differentiation, or ceiling effects (Baumert et al., 2012; Nennstiel, 2023). Beyond prior achievement, social background characteristics like socioeconomic status (SES) play a key role in shaping outcomes. SES captures inequalities in access to material resources, cultural capital, and learning support. While SES differences in achievement levels are well-documented, longitudinal research suggests that growth gaps are often stable rather than widening over time once prior achievement is taken into account. Evidence from Germany, for example, indicates persistent SES differences in mathematics and language levels but little support for cumulative SES-related divergence in trajectories (Nennstiel, 2023). Examining SES effects net of prior achievement allows for a precise assessment of whether students with similar starting points diverge. Gender differences in mathematics achievement represent another longstanding topic. Cross-national evidence shows that gender gaps vary considerably across countries and grade levels. Longitudinal analyses suggest these differences tend to remain relatively stable over time, with only modest changes during secondary education. Recent evidence indicates that gender differences in mathematics development are generally small once prior achievement is controlled for, though persistent patterns may still be observed in specific systems or cohorts (Uunk & Blossfeld, 2025). Controlling for prior achievement provides a framework for assessing whether gender is associated with differential achievement outcomes beyond earlier performance. This study addresses these issues by drawing on the complete longitudinal dataset from the TIMSS Longitudinal Study. The analysis encompasses a primary cohort following students from Grade 4 to Grade 5 across nine countries, and a lower secondary cohort following students from Grade 8 to Grade 9 across three countries. Focusing on mathematics, the study employs two-level regression models with students nested within schools to examine achievement at the second measurement occasion while explicitly controlling for prior achievement. By investigating prior achievement, gender, and SES, this study provides a baseline individual-level model of achievement growth.

Baumert, J., Nagy, G., & Lehmann, R. (2012). Cumulative advantages and the emergence of social and ethnic inequality: Matthew effects in reading and mathematics development within elementary schools?. Child development, 83(4), 1347-1367. Nennstiel, R. (2023). No Matthew effects and stable SES gaps in math and language achievement growth throughout schooling: Evidence from Germany. European sociological review, 39(5), 724-740. Uunk, W., & Blossfeld, P. (2025). Gender-specific development of mathematics and language performance in lower secondary education in Germany. Zeitschrift für Bildungsforschung, 15(1), 95-119.