| Abstract [eng] |
Improving educational research and evidence-based education policymaking requires mathematical tools that can take into account the complex interactions between social systems and educational process variables. However, there is a lack of rigorous, theoretically and mathematically sound analysis of educational process outcomes – student achievement. Therefore, the aim of this research is to create a mathematical model capable of quantitatively explaining the influence of educational processes on students' mathematics achievement. The research objectives are: to analyze scientific literature exploring factors influencing high mathematics achievement; to systematize mathematical methods used in educational research for achievement modeling, highlighting their advantages and disadvantages; to quantitatively evaluate missing data imputation methods based on their influence on the reliability and validity of statistical inferences when modeling mathematics achievement; to create a mathematical model revealing the relationship between educational processes and mathematics achievement; to interpret the model parameters and possibilities for methodological expansion. The research employs methods of scientific literature analysis and secondary analysis of the PISA 2022 Lithuanian student achievement data. Due to the design features of the PISA study, a crucial part of the data analysis is missing data imputation. Among the missing data imputation methods, multiple imputation by chained equations (MICE) best reflected the original data distributions. Following mathematical modeling, a model was created describing the relationship between mathematics achievement and statistically significant influencing factors. The model uses variables selected according to Gagné's Differentiated Model of Giftedness and Talent. According to the developed explanatory mathematical model, it was determined that student-level factors, primarily economic, social, and cultural status, and mathematics self-efficacy, are the main factors influencing mathematics achievement, while school-level effects also proved to be significant, especially for the aforementioned factors. The main limitation of the empirical research model is the context of data collection during the COVID-19 pandemic; therefore, further research could test the model by applying it, for example, to PISA 2025 data or by improving its methodology using different mathematical methods in its development process. |
