Large-scale assessments provide comprehensive data on the effectiveness of educational policies, allowing countries to evaluate the current state of their education systems. Fundamental elements such as the impact of instructional methods on students, learning barriers, and the contribution of curricula to student achievement are systematically examined through these measurement tools (Erkuş, 2012). In this context, the Programme for International Student Assessment (PISA) conducted by the Organisation for Economic Co-operation and Development (OECD), serves as a critical international comparison tool that enables countries to review their policies and create strategic roadmaps (Ministry of National Education [MoNE], 2019).PISA assesses not only whether 15-year-old students can reproduce knowledge but also how they extrapolate from what they have learned and apply their knowledge in unfamiliar settings, both in and out of school (OECD, 2023). Beyond describing achievement patterns, large-scale assessments such as PISA play a central role in monitoring educational quality and informing system-level improvement strategies, particularly in periods of systemic disruption such as the post-pandemic era. In the PISA 2022 cycle, mathematics literacy was the major domain. Mathematics literacy is defined as the capacity to formulate, employ, and interpret mathematics in a variety of contexts to describe, explain, and predict phenomena (MoNE, 2023). According to PISA 2022 results, Türkiye ranked 39th among 81 countries with a score of 453; while this indicates an improvement compared to 2018, it remains significantly below the OECD average of 472 (Aksakal, 2024).

Social science research often involves investigating relationships between individuals and the environments in which they learn, live, and work (Hox et al., 2018). PISA data is inherently nested, with students clustered within schools. Consequently, traditional single-level analyses that ignore this hierarchical structure often disaggregate group-level variables to the individual level or aggregate individual-level variables to the group level (Hofmann, 1997). Such approaches violate independence assumptions and can lead to biased estimates (Julian, 2001; Muthén & Satorra, 1995). To address these methodological challenges, multilevel models provide a robust framework for simultaneously examining relationships at each level of the data hierarchy, thereby yielding more comprehensive and realistic results (Heck, 2001).

This study aims to examine the structural relationships between students' mathematics literacy and student- and school-level factors in order to provide evidence relevant to educational improvement and quality assurance processes in the Turkish education system. Furthermore, given that PISA 2022 was administered in the aftermath of the COVID-19 pandemic, this research seeks to uncover the variables influencing the education system during this extraordinary period. Specifically, the study addresses the following research questions:

1. Is there a significant difference in mathematics literacy among schools in the PISA 2022 Türkiye sample?
2. What are the student-level determinants of mathematics literacy?
3. What are the school-level determinants of mathematics literacy?
4. To what extent does the proposed multilevel model explain the variance in mathematics literacy, and what are the implications of these findings for system-level quality improvement?

The conceptual framework of the study is informed by ecological and multilevel perspectives on learning. From an ecological standpoint, student achievement is shaped by multiple, nested environments, including classroom and school contexts. Methodologically, the study is grounded in multilevel modelling theory, which explicitly accounts for the nested structure of educational data (Hox et al., 2018). Multilevel SEM extends traditional hierarchical linear modelling by allowing the estimation of latent variables, measurement error, and complex structural relations across levels simultaneously (Heck, 2001; Heck & Thomas, 2020). These features are particularly important when analysing PISA data, which rely on plausible values derived from item response theory and require the appropriate application of sampling weights to ensure valid population-level inferences.

This study adopts a quantitative research design grounded in a relational survey model to examine the factors shaping mathematics literacy during crises. The analysis draws on secondary data from the PISA Türkiye dataset, which provides nationally representative information on students’ academic performance and contextual characteristics. Given the hierarchical structure of the PISA data—students nested within schools—and the presence of latent constructs measured with error, Multilevel Structural Equation Modeling (MSEM) is employed as the primary analytical approach. MSEM enables the simultaneous examination of relationships at both the student and school levels while explicitly accounting for measurement error in latent variables. Compared to conventional multilevel regression techniques, MSEM allows for the estimation of complex pathways, including direct and indirect effects among multiple variables, and offers greater flexibility in handling non-normal distributions and categorical indicators (Heck & Thomas, 2020). This makes MSEM particularly suitable for large-scale assessment data such as PISA. By linking multilevel modeling with latent variable analysis, the study provides an evidence-based framework that can support educational quality assurance and data-informed improvement strategies in post-crisis contexts. Sampling and Weighting Procedures PISA uses a two-stage stratified sampling design, in which schools are sampled first and students are selected within schools in the second stage. To ensure unbiased population estimates and to adjust for unequal probabilities of selection, both student-level and school-level sampling weights are incorporated into all analyses. This weighting procedure enhances the generalizability of the findings to the national student population. Measures Dependent Variable. Mathematics literacy serves as the primary outcome variable. In line with PISA technical guidelines, achievement is represented using ten plausible values rather than a single point estimate. This approach, grounded in Item Response Theory, captures measurement uncertainty and yields more reliable population-level inferences. Independent Variables. The explanatory variables are derived from student and school questionnaires and reflect key contextual dimensions relevant to educational outcomes in crisis contexts. These include indicators of socio-economic background, school climate, and instructional quality. Together, these variables enable an examination of how individual and institutional factors jointly contribute to mathematics literacy in the post-pandemic period. By integrating multilevel modeling with latent variable analysis, this methodological framework provides a robust basis for understanding the multiscalar determinants of mathematics literacy within the Turkish education system.

This research is anticipated to be one of the pioneering studies employing Multilevel Structural Equation Modeling (MSEM) on the PISA 2022 Türkiye dataset. Existing literature on PISA data analysis in Türkiye has often neglected critical methodological components such as sampling weights and plausible values. By rigorously applying these elements within an MSEM framework, this study aims to set a methodological standard for future large-scale assessment research, ensuring high validity and reliability of the findings. Substantively, the study expects to reveal the multi-faceted impact of the COVID-19 pandemic on mathematics achievement. By modeling the relationships between student background, school climate, teacher support, and literacy scores, the findings will identify which factors acted as buffers or barriers during the pandemic. The decomposition of variance into student and school levels will provide policymakers with evidence-based insights on whether interventions should target school-wide systemic changes or individual student support mechanisms. Ultimately, the results will contribute to the development of resilient education policies capable of mitigating the effects of future crises.

Aksakal, D. (2024). PISA 2022 sonuçlarına göre Türkiye başarısının değerlendirilmesi [Evaluation of Türkiye's success according to PISA 2022 results] [Unpublished master's thesis]. Çanakkale Onsekiz Mart University. Erkuş, A. (2012). Psikolojide ölçme ve ölçek geliştirme [Measurement and scale development in psychology]. Pegem Akademi. Heck, R. H. (2001). Multilevel modeling with SEM. In New developments and techniques in structural equation modeling(pp. 109-148). Psychology Press. Heck, R., & Thomas, S. L. (2020). An introduction to multilevel modeling techniques: MLM and SEM approaches. Routledge. Hofmann, D. A. (1997). An overview of the logic and rationale of hierarchical linear models. Journal of management, 23(6), 723-744. Hox, J.J., Moerbeek, M & Van de Schoot, R. (2018). Multilevel analysis: Techniques and applications. Routledge. Julian, M. W. (2001). The consequences of ignoring multilevel data structures in nonhierarchical covariance modeling. Structural equation modeling, 8(3), 325-352. Ministry of National Education. (2023). PISA 2022 Türkiye report. Ministry of National Education. Ministry of National Education. (2019). PISA 2018 Türkiye ön raporu [PISA 2018 Türkiye preliminary report]. Ministry of National Education. Muthén, B. O., & Satorra, A. (1995). Complex sample data in structural equation modeling. Sociological methodology, 267-316.