Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century

This study examines how 21st-century quantitative research addresses the relationship between synthetic and analytic geometry in secondary education using Dynamic Geometry Systems, particularly GeoGebra. Following PRISMA guidelines, a meta-analysis of 38 experimental and quasi-experimental studies was conducted. The random-effects model yielded a large aggregated effect size (Hedges’ g = 1.24), indicating strong associations between GeoGebra-supported instruction and learning outcomes, albeit with substantial heterogeneity. The analysis also explores temporal effect size patterns and identifies geometric topics most frequently associated with coordinating visual-synthetic and algebraic-analytic perspectives. The findings show that most interventions emphasise representational coordination, although only a limited number of studies explicitly foster bidirectional translation between geometric constructions and algebraic reasoning. Ultimately, this review structures how the integration of synthetic and analytic geometry has been operationalised, providing a solid foundation for more fine-grained future investigations.