Integrating APOS Theory and Scaffolding in Islamic Boarding Schools: The Conceptual Design and Validation of APOSCAF Learning Model

Lisnasari Andi Mattoliang; Baso Intang Sappaile; Asdar Asdar

doi:10.63922/ijevss.v5i02.3024

Lisnasari Andi Mattoliang Universitas Negeri Makassar
Baso Intang Sappaile Universitas Negeri Makassar
Asdar Asdar Universitas Negeri Makassar

DOI: https://doi.org/10.63922/ijevss.v5i02.3024

Keywords: APOS Theory, Scaffolding, APOSCAF Learning Model, Mathematics Education, Islamic Boarding School

Abstract

Mathematics education in Islamic boarding schools often faces unique pedagogical challenges, particularly in bridging traditional learning habits with the abstract cognitive demands of mathematical concepts. This study aims to develop and validate APOSCAF learning model, a conceptual integration of APOS (Action, Process, Object, Schema) theory and Scaffolding techniques, specifically designed for the Islamic boarding schools context. Using a Research and Development, the model was constructed through process of preliminary analysis and expert validation. The resulting APOSCAF learning model consists of five syntaxes. Expert judgment confirmed that the model is valid, indicating strong theoretical consistency and practical feasibility. This research contributes a culturally responsive yet cognitively rigorous framework, offering a strategic alternative for mathematics educators to enhance students' conceptual understanding within a religious-academic environment.

References

Arnawa, I. M., Yerizon, & Nita, S. (2020). Improvement students’ achievement in elementary linear algebra through APOS theory approach. Journal of Physics: Conference Series, 1567(2), 022080. https://doi.org/10.1088/1742-6596/1567/2/022080
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS Theory A Framework for Research and Curriculum Development in Mathematics Education.
Awi, A., Upu, H., Rusli, R., Ahmar, A. S., & Musa, H. (2025). The role of scaffolding in flipped classroom: improving learning outcomes through Weblog-based and Google Drive-based assignments. Cogent Education, 12(1). https://doi.org/10.1080/2331186X.2025.2543115
Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM, 47(7), 1047–1065. https://doi.org/10.1007/s11858-015-0738-8
De Guerrero, M. C. M., & Villamil, O. S. (2000). Activating the ZPD: Mutual Scaffolding in L2 Peer Revision. The Modern Language Journal, 84(1), 51–68. https://doi.org/10.1111/0026-7902.00052
Faheem Khan, Aqsa Ahmad, Memoona Gul, Shakeel Hussain, & Sobia yousaf. (2022). Effect of Scaffolding Teaching Method on Students’ Academic Achievement in Mathematics. Journal of Social Sciences and Management Studies, 1(2), 48–51. https://doi.org/10.56556/jssms.v1i2.81
Mansyur, M. Z., & Nugraha, D. A. (2021). Pembelajaran metacognitive scaffolding sebagai upaya meningkatkan kemampuan berpikir kritis matematis siswa SMP dalam memecahkan masalah. Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika Dan Statistika, 2(2), 214–224. https://doi.org/10.46306/lb.v2i2.81
McNeill, K. L., Lizotte, D. J., Krajcik, J., & Marx, R. W. (2006). Supporting Students’ Construction of Scientific Explanations by Fading Scaffolds in Instructional Materials. Journal of the Learning Sciences, 15(2), 153–191. https://doi.org/10.1207/s15327809jls1502_1
Mulyono, M. (2011). Teori APOS dan implementasinya dalam pembelajaran. Journal of Mathematics and Mathematics Education, 1(1). https://doi.org/10.20961/jmme.v1i1.9924
Nagle, C., Martínez-Planell, R., & Moore-Russo, D. (2019). Using APOS theory as a framework for considering slope understanding. Journal of Mathematical Behavior, 54. https://doi.org/10.1016/j.jmathb.2018.12.003
Oktac, A. (2022). What’s new with APOS theory? A look into levels and Totality. Avances de Investigación En Educación Matemática, (21), 9–21. https://doi.org/10.35763/aiem21.4245
Ramdhani, S., & Suryadi, D. (2018). The analogical reasoning analysis of Pesantren students in geometry. Journal of Physics: Conference Series, 1132, 1–10. https://doi.org/10.1088/1742-6596/1132/1/012044
Saidul, M. D., & Widyasari, N. (2025). Efficiency of scaffolding method in the learning process of mathematics comparative material in grade V elementary school students. Jurnal Pendidikan Matematika (JUPITEK), 7(2), 111–122. https://doi.org/10.30598/jupitekvol7iss2pp111-122
Shooshtari, Z. G., & Mir, F. (2014). ZPD, Tutor; Peer Scaffolding: Sociocultural Theory in Writing Strategies Application. Procedia - Social and Behavioral Sciences, 98, 1771–1776. https://doi.org/10.1016/j.sbspro.2014.03.605
Sun, L., Kangas, M., Ruokamo, H., & Siklander, S. (2023). A systematic literature review of teacher scaffolding in game-based learning in primary education. Educational Research Review, 40, 1–21. https://doi.org/10.1016/j.edurev.2023.100546
Utomo, D. P., Sulfiah, S. K., & Inganah, S. (2022). Algebraic Literacy among Pesantren-based Senior High School Students. JTAM (Jurnal Teori Dan Aplikasi Matematika), 6(2), 247–260. https://doi.org/10.31764/jtam.v6i2.6746
Vallejo, N. V., Vargas, O. L., & Rodríguez, L. S. (2019). Effect of a metacognitive scaffolding on self-efficacy, metacognition, and achievement in e-learning environments. Knowledge Management & E-Learning: An International Journal, 1–19. https://doi.org/10.34105/j.kmel.2019.11.001
van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in Teacher–Student Interaction: A Decade of Research. Educational Psychology Review, 22(3), 271–296. https://doi.org/10.1007/s10648-010-9127-6
Vygotskiĭ, L. S., & Cole, M. (1978). Mind in society: the development of higher psychological processes. Unknown. https://api.semanticscholar.org/CorpusId:204312038
Yusuf, F. A. (2023). An investigation on the learning barriers of boarding school students In terms of different dimensions of the curriculum implementation. Pegem Journal of Education and Instruction, 13(1), 301–308. https://doi.org/10.47750/pegegog.13.01.33