APOS Theory-based research in Mathematics Education: A systematic literature review
Abstract
The APOS Theory is one of the most widely used theoretical frameworks in mathematics education research, and it has enjoyed significant popularity among mathematics education researchers, especially over the last decade. In this study, we did a systematic literature review of APOS Theory-based studies published in the Scopus database over the last two decades (2005 – 2024). The aim of the study was to highlight the specific gaps in APOS Theory-based research. The results showed that a total of 125 APOS Theory-based studies were published in the Scopus database from 2005 to 2024. The trend analysis also shows that, over the last decade (2016-2024), a significant increase of an average of 12 articles per year was published as compared to an average of 3 articles per year in the previous decade (2005 – 2015). Additionally, a significant proportion of these studies (83%) were done for study groups at the university level as compared to 17% for the secondary and primary levels. The mathematical concepts in advanced undergraduate Calculus and Algebra constituted 79% of the studies. Finally, it was also found that APOS Theory was complemented with eight different theories in all the studies published. In this regard, Tall’s three worlds of mathematics and the Semiotic Representation theories were the most used to complement APOS Theory. These findings bring to light, the specific gaps in APOS Theory based research, which were discussed in detail
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Altieri, M., & Schirmer, E. (2019). Learning the concept of eigenvalues and eigenvectors: A comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds. ZDM - Mathematics Education, 51(7), 1125–1140. Scopus. https://doi.org/10.1007/s11858-019-01074-4
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education. Springer New York. https://doi.org/10.1007/978-1-4614-7966-6
Bayraktar, F., Tutak, T., & İlhan, A. (2019). An Analysis of The Studies on The APOS Theory. Elektronik Eğitim Bilimleri Dergisi, 8(16), 242–251.
Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. Eurasia Journal of Mathematics, Science and Technology Education, 14(6), 2301–2315. Scopus. https://doi.org/10.29333/ejmste/89514
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247–285.
Davies, P. (2000). The Relevance of Systematic Reviews to Educational Policy and Practice. Oxford Review of Education, 26(3–4), 365–378. https://doi.org/10.1080/713688543
Dogan, H. (2023). Coordinated topics as transitional enablers towards higher-level conceptualisations of the range concept. International Journal of Mathematical Education in Science and Technology, 54(9), 1819– 1832. Scopus. https://doi.org/10.1080/0020739X.2023.2260790
Dubinsky, E., Arnon, I., & Weller, K. (2013). Preservice Teachers’ Understanding of the Relation Between a Fraction or Integer and its Decimal Expansion: The Case of 0.9 ̄ and 1. Canadian Journal of Science, Mathematics and Technology Education, 13, 232–258.
Font Moll, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107–122. Scopus. https://doi.org/10.1007/s10649-015-9639-6
Fuentealba, C. E., Cárcamo, A. D., Badillo, E. R., & Sánchez-Matamoros, G. M. (2023). Analysis of errors in tasks related to the derivative concept: A look from the APOS theory (Action, Process, Object, and Schema). Formacion Universitaria, 16(3), 41– 50. Scopus. https://doi.org/10.4067/S0718-50062023000300041
Jara, M. A. R., Lorca, A. M., Lorca, J. J. F. M., Saldias, P. V., & Del Valle Leo, M. (2019). Cognitive construction of the solution set of a system of linear equations with two unknowns. Ensenanza de Las Ciencias, 37(1), 71–92. Scopus. https://doi.org/10.5565/rev/ensciencias.2194
Martínez-Planell, R., Gaisman, M. T., & McGee, D. (2015). On students’ understanding of the differential calculus of functions of two variables. Journal of Mathematical Behavior, 38, 57– 86. Scopus. https://doi.org/10.1016/j.jmathb.2015.03.003
Martínez-Planell, R., & Trigueros, M. (2019). Using cycles of research in APOS: The case of functions of two variables. Journal of Mathematical Behavior, 55. Scopus. https://doi.org/10.1016/j.jmathb.2019.01.003
Moru, E. K. (2020). An APOS Analysis of University Students’ Understanding of Derivatives: A Lesotho Case Study. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 279–292. Scopus. https://doi.org/10.1080/18117295.2020.1821500
Nilsson, P., Schindler, M., & Bakker, A. (2018). The nature and use of theories in statistics education. International Handbook of Research in Statistics Education, 359–386.
Oktaç, A., Trigueros, M., & Romo, A. (2019). APOS Theory: Connecting Research and Teaching. For the Learning of Mathematics, 39(1), 33–37.
Radmehr, F. (2024). Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics. PRIMUS. Scopus. https://doi.org/10.1080/10511970.2024.2327330
Santos, E. M. (2019). A look into students’ conceptual understanding of the definite integral via the APOS model. 2194. Scopus. https://doi.org/10.1063/1.5139842
Şefi̇K, Ö., Erdem Uzun, Ö., & Dost, Ş. (2021). Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 15(2), 404–428. https://doi.org/10.17522/balikesirnef.1020526
Taghizadeh Bilondi, M., & Radmehr, F. (2023). Students’ mathematical thinking of the tree concept: An integration of APOS with Tall’s three worlds of mathematics. Research in Mathematics Education. Scopus. https://doi.org/10.1080/14794802.2023.2292260
Weller, K., Arnon, I., & Dubinsky, E. (2011). Preservice teachers’ understandings of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief. Canadian Journal of Science, Mathematics and Technology Education, 11, 129–159.
Copyright (c) 2025 Francis Atsu Soku, Gabriel Asare Okyere, PhD, Francis Kwadwo Awuah
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