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

Aitor Alfonso-Castelló; Ismael Cabero-Fayos

doi:10.29333/iejme/18778

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Aitor Alfonso-Castelló ¹ , Ismael Cabero-Fayos ² ^*

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¹ Universitat Politècnica de València, SPAIN² Jaume I university, SPAIN^* Corresponding Author

Abstract

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.

Keywords

analytical geometry
dynamic geometry systems
GeoGebra
meta-analysis
secondary education
synthetic geometry

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Review Article

INT ELECT J MATH ED, Volume 21, Issue 3, August 2026, Article No: em0885

https://doi.org/10.29333/iejme/18778

Publication date: 01 Jul 2026

Online publication date: 18 Jun 2026

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Article Downloads: 5

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How to cite this article

APA

Alfonso-Castelló, A., & Cabero-Fayos, I. (2026). Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century. International Electronic Journal of Mathematics Education, 21(3), em0885. https://doi.org/10.29333/iejme/18778

Vancouver

Alfonso-Castelló A, Cabero-Fayos I. Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century. INT ELECT J MATH ED. 2026;21(3):em0885. https://doi.org/10.29333/iejme/18778

AMA

Alfonso-Castelló A, Cabero-Fayos I. Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century. INT ELECT J MATH ED. 2026;21(3), em0885. https://doi.org/10.29333/iejme/18778

Chicago

Alfonso-Castelló, Aitor, and Ismael Cabero-Fayos. "Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century". International Electronic Journal of Mathematics Education 2026 21 no. 3 (2026): em0885. https://doi.org/10.29333/iejme/18778

Harvard

Alfonso-Castelló, A., and Cabero-Fayos, I. (2026). Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century. International Electronic Journal of Mathematics Education, 21(3), em0885. https://doi.org/10.29333/iejme/18778

MLA

Alfonso-Castelló, Aitor et al. "Synthetic and analytic geometry: A meta-analysis of their didactic relationship in the 21st century". International Electronic Journal of Mathematics Education, vol. 21, no. 3, 2026, em0885. https://doi.org/10.29333/iejme/18778